A Very Incomplete Survey of Basic Statistical Tests in R
EDP 619 Week 5
Dr. Abhik Roy
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Getting Ready

To follow along, please make sure to do the following

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Getting Ready

To follow along, please make sure to do the following

Run Basic Statistical Tests install.R

3 / 46

Getting Ready

To follow along, please make sure to do the following

Run Basic Statistical Tests install.R
Open up a blank .R script

3 / 46

Getting Ready

To follow along, please make sure to do the following

Run Basic Statistical Tests install.R
Open up a blank .R script

Load up the following packages

library(tidyverse)
library(car)
library(foreign)
library(lme4)
library(MASS)
library(CCA)
library(psych)

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Purpose

This is not a traditional presentation per say, rather it is a collection of common statistical tests used for survey analyses that you may need to use at some point. Review the content simply to see what is included and then come back as needed.

The examples are of course presented with R in mind, but obviously not restricted to the platform.

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Purpose

The examples are of course presented with R in mind, but obviously not restricted to the platform.

The content is intended to cast a wide net so some may look familiar while others will not

4 / 46

Purpose

The examples are of course presented with R in mind, but obviously not restricted to the platform.

The content is intended to cast a wide net so some may look familiar while others will not

You can think of this as a toolkit

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Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths

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Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario
Since this is not a statistics course, only test names and examples are provided

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario
Since this is not a statistics course, only test names and examples are provided
Some of the syntax may be structured in an odd way. This is only done so so that they be fit within the slide. Remember in general spacing doesn't mean much in R

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario
Since this is not a statistics course, only test names and examples are provided
Some of the syntax may be structured in an odd way. This is only done so so that they be fit within the slide. Remember in general spacing doesn't mean much in R
These are presented in alphabetical order according to the standard name of the test

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Decisions Decisions Decisions

When deciding which test is appropriate to use, it is important to consider the type of variables that you have. Please load in the following data sets (and look at them by using View() or head()

some_ed_data <- 
  read_csv("some_ed_data.csv")

some_exercise_data <- 
  read_csv("some_exercise_data.csv")

some_survey_data <- 
  read_csv("some_survey_data.csv")

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The Datas (1/3)

some_ed_data

## # A tibble: 200 × 11
##       id female  race   ses schtyp  prog  read write  math science socst
##    <dbl>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl>
##  1    70      0     4     1      1     1    57    52    41      47    57
##  2   121      1     4     2      1     3    68    59    53      63    61
##  3    86      0     4     3      1     1    44    33    54      58    31
##  4   141      0     4     3      1     3    63    44    47      53    56
##  5   172      0     4     2      1     2    47    52    57      53    61
##  6   113      0     4     2      1     2    44    52    51      63    61
##  7    50      0     3     2      1     1    50    59    42      53    61
##  8    11      0     1     2      1     2    34    46    45      39    36
##  9    84      0     4     2      1     1    63    57    54      58    51
## 10    48      0     3     2      1     2    57    55    52      50    51
## # … with 190 more rows

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The Datas (2/3)

some_exercise_data

## # A tibble: 90 × 6
##       id  diet exertype pulse  time highpulse
##    <dbl> <dbl>    <dbl> <dbl> <dbl>     <dbl>
##  1     1     1        1    85     1         0
##  2     1     1        1    85     2         0
##  3     1     1        1    88     3         0
##  4     2     1        1    90     1         0
##  5     2     1        1    92     2         0
##  6     2     1        1    93     3         0
##  7     3     1        1    97     1         0
##  8     3     1        1    97     2         0
##  9     3     1        1    94     3         0
## 10     4     1        1    80     1         0
## # … with 80 more rows

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The Datas (3/3)

some_survey_data

## # A tibble: 20 × 4
##    respondent gender item_1 item_2
##         <dbl>  <dbl>  <dbl>  <dbl>
##  1          1      1      5      1
##  2          2      2      4      3
##  3          3      1      2      5
##  4          4      2      4      4
##  5          5      2      2      3
##  6          6      1      3      2
##  7          7      1      4      1
##  8          8      2      5      4
##  9          9      2      3      3
## 10         10      2      3      5
## 11         11      1      2      3
## 12         12      2      3      3
## 13         13      2      1      5
## 14         14      1      4      4
## 15         15      2      2      5
## 16         16      1      2      5
## 17         17      1      3      5
## 18         18      1      5      2
## 19         19      1      3      2
## 20         20      2      5      5

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An Incomplete Table of Approaches

Number of Dependent Variables	Number and Type of Independent Variables	Type of Dependent Variables	Test(s)
1	0 IVs (1 population)	interval & normal	one-sample t-test
1	0 IVs (1 population)	ordinal or interval	one-sample median
1	0 IVs (1 population)	categorical (2 categories)	binomial test
1	0 IVs (1 population)	categorical	Chi-square goodness-of-fit
1	1 IV with 2 levels (independent groups)	interval & normal	2 independent sample t-test

Showing 1 to 5 of 32 entries

Previous1 2 3 4 5 6 7Next

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Tests

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ANOVA

summary(aov(some_ed_data$write ~ some_ed_data$prog + some_ed_data$read))

##                    Df Sum Sq Mean Sq F value  Pr(>F)    
## some_ed_data$prog   1    586     586    10.2 0.00164 ** 
## some_ed_data$read   1   5965    5965   103.7 < 2e-16 ***
## Residuals         197  11327      57                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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Binomial Test

prop.test(sum(some_ed_data$female), length(some_ed_data$female), p = 0.5)

## 
##     1-sample proportions test with continuity correction
## 
## data:  sum(some_ed_data$female) out of length(some_ed_data$female), null probability 0.5
## X-squared = 1.445, df = 1, p-value = 0.2293
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.4733037 0.6149394
## sample estimates:
##     p 
## 0.545

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Canonical Correlation

cc(cbind(some_ed_data$read, some_ed_data$write), 
   cbind(some_ed_data$math, some_ed_data$science))

## $cor
## [1] 0.7728409 0.0234784
## 
## $names
## $names$Xnames
## NULL
## 
## $names$Ynames
## NULL
## 
## $names$ind.names
## NULL
## 
## 
## $xcoef
##             [,1]       [,2]
## [1,] -0.06326131 -0.1037908
## [2,] -0.04924918  0.1219084
## 
## $ycoef
##             [,1]       [,2]
## [1,] -0.06698268  0.1201425
## [2,] -0.04824063 -0.1208860
## 
## $scores
## $scores$xscores
##               [,1]         [,2]
##   [1,] -0.26358835 -0.589561062
##   [2,] -1.30420707 -0.877901269
##   [3,]  1.49454321 -1.556539586
##   [4,] -0.24916276 -2.187572699
##   [5,]  0.36902478  0.448346869
##   [6,]  0.55880872  0.759719249
##   [7,] -0.16550344  0.990333008
##   [8,]  1.48691695  1.066177022
##   [9,] -0.88940214 -0.602764022
##  [10,] -0.41133590 -0.223835983
##  [11,] -0.15787718 -1.632383600
##  [12,] -0.90382773  0.995247615
##  [13,] -1.66976282 -1.274946875
##  [14,] -0.61554542  1.062803275
##  [15,]  0.24930149  1.265470254
##  [16,]  0.83307890  0.601575756
##  [17,]  0.36902478  0.448346869
##  [18,] -0.50983426  0.019980737
##  [19,] -1.59970217 -0.146451110
##  [20,]  0.50317366 -1.966788153
##  [21,] -0.49540867 -1.578030900
##  [22,] -1.18489724  0.128686136
##  [23,]  0.77023105 -1.325925827
##  [24,] -0.45337228 -0.900933442
##  [25,]  1.39563138  0.510987923
##  [26,]  1.93015961 -0.030998216
##  [27,] -1.40991823  0.164921269
##  [28,]  0.12277887  1.057888668
##  [29,]  1.24829729 -0.946997788
##  [30,]  0.44671169 -1.045873974
##  [31,]  1.71956420 -1.592774720
##  [32,] -1.46555329 -2.561586132
##  [33,] -1.50841660  0.408737989
##  [34,]  1.22707237 -0.373691122
##  [35,] -0.29202606  0.782751422
##  [36,] -1.09361167  0.683875235
##  [37,] -1.05796116 -1.487443067
##  [38,] -1.26217068 -0.200803810
##  [39,]  1.40325764 -2.111728685
##  [40,]  1.90934814 -1.281402340
##  [41,]  0.61527070 -0.161194929
##  [42,] -0.48181000  0.471379042
##  [43,] -0.04578015  0.173209623
##  [44,]  1.22707237 -0.373691122
##  [45,] -1.40991823  0.164921269
##  [46,] -0.48181000  0.471379042
##  [47,]  0.77023105 -1.325925827
##  [48,] -1.11442313 -0.566528889
##  [49,]  0.02428050  1.301705388
##  [50,] -0.36208671 -0.345744343
##  [51,] -0.45378574  0.922777348
##  [52,]  1.81084977 -1.037585621
##  [53,]  0.95280219 -0.215547629
##  [54,] -0.98790051 -0.358947303
##  [55,] -1.76826119 -1.031130155
##  [56,]  1.51535467 -0.306135462
##  [57,]  1.74037567 -0.342370595
##  [58,]  1.32557073 -0.617507842
##  [59,] -0.88940214 -0.602764022
##  [60,]  0.45351102 -0.021169003
##  [61,]  0.47473595 -0.594475669
##  [62,] -0.12346705  1.667430467
##  [63,]  0.95280219 -0.215547629
##  [64,]  2.12715634 -0.518631655
##  [65,]  0.67173268 -1.082109108
##  [66,]  1.10054974 -0.581272708
##  [67,] -0.55187065 -0.657116722
##  [68,]  1.00926417 -1.136461807
##  [69,] -0.19991357 -2.309481059
##  [70,]  1.11497533 -2.179284345
##  [71,]  0.95280219 -0.215547629
##  [72,] -0.55187065 -0.657116722
##  [73,] -2.01450711 -0.421588356
##  [74,] -1.30420707 -0.877901269
##  [75,]  0.20767856 -1.235337994
##  [76,]  0.96001499 -1.014553448
##  [77,] -0.58030837  0.715195762
##  [78,] -1.30420707 -0.877901269
##  [79,]  2.16919273  0.158465804
##  [80,]  0.91076580 -0.892645088
##  [81,] -0.98790051 -0.358947303
##  [82,]  1.21264678  1.224320515
##  [83,] -1.30420707 -0.877901269
##  [84,] -1.28339561  0.372502856
##  [85,]  0.40467530 -1.722971433
##  [86,] -0.62955755  0.837104122
##  [87,]  0.59445924 -1.411599054
##  [88,]  1.33916940  1.431902101
##  [89,]  1.21347370 -2.423101065
##  [90,]  0.01068183 -0.747704555
##  [91,] -0.43977362  1.148476501
##  [92,] -0.49540867 -1.578030900
##  [93,] -1.45195462 -0.512176189
##  [94,]  1.26910876  0.303406337
##  [95,]  0.95280219 -0.215547629
##  [96,] -0.31325099  1.356058087
##  [97,] -1.78948611 -0.457823489
##  [98,] -1.28339561  0.372502856
##  [99,]  1.58541532  0.822360302
## [100,] -1.18489724  0.128686136
## [101,] -1.35345626 -0.755992909
## [102,]  0.02428050  1.301705388
## [103,]  0.66451988 -0.283103289
## [104,] -0.64315622 -1.212305821
## [105,] -0.29202606  0.782751422
## [106,] -0.23556409 -0.138162756
## [107,] -0.94586412  0.318150156
## [108,]  1.96539666 -0.378605729
## [109,]  0.27052642  0.692163589
## [110,] -1.78948611 -0.457823489
## [111,] -0.26358835 -0.589561062
## [112,]  0.65730709  0.515902529
## [113,] -1.11442313 -0.566528889
## [114,] -1.59970217 -0.146451110
## [115,] -1.71901201 -1.153038515
## [116,]  1.45889269  0.614778716
## [117,]  0.52357167  1.107326761
## [118,] -2.01450711 -0.421588356
## [119,] -0.19352770  0.538934702
## [120,]  0.99483858  0.461549830
## [121,] -0.55187065 -0.657116722
## [122,]  0.17924085  0.136974490
## [123,]  0.17924085  0.136974490
## [124,]  0.66451988 -0.283103289
## [125,] -0.12346705  1.667430467
## [126,] -0.38331164  0.227562323
## [127,]  0.72098186 -1.204017467
## [128,]  0.82586610  1.400581574
## [129,]  0.32698840 -0.228750589
## [130,]  2.02865797 -0.274814935
## [131,] -0.60833263  0.263797456
## [132,] -0.90382773  0.995247615
## [133,] -1.45195462 -0.512176189
## [134,]  0.58683298  1.211117555
## [135,] -0.86137788 -0.151365716
## [136,] -2.00729431 -1.220594175
## [137,]  0.02428050  1.301705388
## [138,]  0.43228610  0.552137663
## [139,]  1.41685631 -0.062318743
## [140,]  0.20046577 -0.436332176
## [141,]  1.86648483  1.688921781
## [142,]  0.58683298  1.211117555
## [143,]  0.86151662 -0.770736728
## [144,]  0.12277887  1.057888668
## [145,] -0.29202606  0.782751422
## [146,]  0.36902478  0.448346869
## [147,] -0.31325099  1.356058087
## [148,]  0.55880872  0.759719249
## [149,]  0.91076580 -0.892645088
## [150,]  0.34779986  1.021653535
## [151,]  1.10776254 -1.380278527
## [152,] -0.86817722 -1.176070688
## [153,]  0.37582412  1.473051841
## [154,]  0.27052642  0.692163589
## [155,] -0.75608018  0.629522535
## [156,] -1.30420707 -0.877901269
## [157,] -0.09502933  0.295117983
## [158,]  0.43908543  1.576842634
## [159,]  1.32557073 -0.617507842
## [160,] -1.57167791  0.304947196
## [161,] -0.12346705  1.667430467
## [162,] -0.16508998 -0.833377782
## [163,] -0.07421787  1.545522107
## [164,] -0.75608018  0.629522535
## [165,] -0.29202606  0.782751422
## [166,]  0.95280219 -0.215547629
## [167,] -0.16550344  0.990333008
## [168,]  0.77661692  1.522489934
## [169,] -0.75608018  0.629522535
## [170,] -0.65758181  0.385705816
## [171,]  0.43908543  1.576842634
## [172,]  0.66451988 -0.283103289
## [173,]  1.47331828 -0.983232921
## [174,] -0.79811657 -0.047574923
## [175,]  0.70655627  0.393994170
## [176,] -1.03714969 -0.237038943
## [177,] -1.50841660  0.408737989
## [178,]  0.77661692  1.522489934
## [179,]  0.17924085  0.136974490
## [180,] -0.58752117  1.514201580
## [181,] -0.94586412  0.318150156
## [182,]  0.70655627  0.393994170
## [183,] -0.68601953  1.758018300
## [184,] -0.77730510  1.202829201
## [185,] -0.55949691  1.965599886
## [186,] -1.40991823  0.164921269
## [187,] -0.04578015  0.173209623
## [188,]  0.76301825 -0.526920009
## [189,] -1.13564806  0.006777776
## [190,]  0.47473595 -0.594475669
## [191,]  0.58683298  1.211117555
## [192,]  0.81865331  2.199587393
## [193,]  0.17924085  0.136974490
## [194,]  0.40384838  1.924450147
## [195,] -0.27121460  2.033155546
## [196,] -0.48181000  0.471379042
## [197,]  0.98082645  0.235850677
## [198,]  0.27815267 -1.930553019
## [199,] -0.62955755  0.837104122
## [200,] -1.28339561  0.372502856
## 
## $scores$yscores
##                [,1]        [,2]
##   [1,]  1.013980334 -0.81276184
##   [2,] -0.561661891 -1.30522812
##   [3,] -0.387441410 -0.58065576
##   [4,]  0.322640484 -0.81722302
##   [5,] -0.347186284  0.38420150
##   [6,] -0.427696537 -1.54551302
##   [7,]  0.657553868 -1.41793527
##   [8,]  1.131974678  0.63489582
##   [9,] -0.387441410 -0.58065576
##  [10,]  0.132448995  0.14614718
##  [11,]  0.054709777 -0.33665321
##  [12,] -0.427696537 -1.54551302
##  [13,] -1.670868810  1.09910797
##  [14,] -0.443667546  0.14242953
##  [15,]  1.182986345  2.20269592
##  [16,]  0.735293086 -0.93513488
##  [17,]  0.199431671  0.02600473
##  [18,] -0.789337471  0.14019895
##  [19,] -0.778580931  0.74314179
##  [20,] -0.347186284  0.38420150
##  [21,]  0.499304397 -3.83045019
##  [22,] -2.469446463  0.24993198
##  [23,]  0.360124575 -1.29927988
##  [24,] -0.733111335 -0.58288635
##  [25,]  1.131974678  0.63489582
##  [26,]  1.064992001  0.75503827
##  [27,] -1.335955426  0.49839571
##  [28,] -0.588389441 -0.22022841
##  [29,]  0.864043971  1.11546562
##  [30,]  0.092193868 -0.81871008
##  [31,] -0.057742495  1.10951738
##  [32,] -1.346711967 -0.10454714
##  [33,] -1.376210553 -0.46646155
##  [34,] -1.263758281 -1.91263214
##  [35,] -0.264232597 -1.42388351
##  [36,] -0.800094012 -0.46274390
##  [37,] -2.180002675  0.97524787
##  [38,] -1.711123937  0.13425071
##  [39,]  1.343679249  0.87741131
##  [40,]  1.466888062  0.03418356
##  [41,]  1.255183491 -0.20833193
##  [42,] -0.923302825  0.38048385
##  [43,] -0.443667546  0.14242953
##  [44,]  0.735293086 -0.93513488
##  [45,] -0.226748507 -1.90594038
##  [46,] -1.520932447 -0.82911949
##  [47,]  1.051464425 -1.29481870
##  [48,] -1.700367396  0.73719355
##  [49,] -0.749082344  1.10505620
##  [50,] -0.191707849  1.34980229
##  [51,] -0.808079517  0.38122738
##  [52,]  1.214928364 -1.17318919
##  [53,] -0.470395097  1.22742925
##  [54,]  0.092193868 -0.81871008
##  [55,] -2.190759215  0.37230502
##  [56,]  1.826085563  2.08627112
##  [57,]  1.622366497  0.99978435
##  [58,]  0.713780005 -2.14102057
##  [59,] -0.454424087 -0.46051331
##  [60,]  0.421892783  0.87146307
##  [61,]  0.215402681 -1.66193782
##  [62,] -1.386967094 -1.06940440
##  [63,]  1.775073896  0.51847102
##  [64,]  1.544627280  0.51698396
##  [65,]  0.941783188  1.59826602
##  [66,]  0.936241116 -1.29556223
##  [67,] -0.644615577  0.50285689
##  [68,]  0.853287430  0.51252278
##  [69,] -1.060039214 -0.82614537
##  [70,]  0.622840814  0.51103572
##  [71,]  1.064992001  0.75503827
##  [72,] -0.655372118 -0.10008596
##  [73,] -1.767350073  0.85733600
##  [74,] -1.427222220 -2.03426166
##  [75,]  0.148420004 -1.54179537
##  [76,]  0.976496243 -0.33070497
##  [77,]  0.046724273  0.50731807
##  [78,] -0.762609921 -0.94480077
##  [79,]  1.064992001  0.75503827
##  [80,]  0.384408693  1.35351994
##  [81,] -0.443667546  0.14242953
##  [82,] -0.532163305 -0.94331371
##  [83,] -1.912071967  0.49467806
##  [84,] -0.226748507 -1.90594038
##  [85,]  1.225684905 -0.57024634
##  [86,] -1.298471336  0.01633884
##  [87,]  0.054709777 -0.33665321
##  [88,]  1.389148845 -0.44861683
##  [89,]  1.708091219  0.63861347
##  [90,] -1.001042042 -0.10231655
##  [91,] -0.660586586  2.19079945
##  [92,] -0.438453078 -2.14845587
##  [93,] -1.654897801 -0.58883459
##  [94,]  0.421892783  0.87146307
##  [95,]  0.679066950 -0.21204958
##  [96,] -1.097523305 -0.34408851
##  [97,] -1.979054644  0.61482051
##  [98,] -2.056793862  0.13202012
##  [99,]  1.466888062  0.03418356
## [100,] -1.536903457  0.85882306
## [101,] -1.587915124 -0.70897704
## [102,] -0.907331815 -1.30745871
## [103,]  1.153487759  1.84078151
## [104,] -0.001516359  0.38643209
## [105,] -0.465180628 -1.06345616
## [106,] -0.419383429  2.79522935
## [107,] -0.872291157  1.94828395
## [108,]  0.888000485 -1.41644821
## [109,]  0.534345056 -0.57470752
## [110,] -1.392181562  1.22148101
## [111,]  0.405594171 -2.62530802
## [112,]  1.399905385  0.15432601
## [113,] -0.009501864  1.23040337
## [114,] -0.703612749 -0.22097194
## [115,] -0.443667546  0.14242953
## [116,]  1.523114198 -0.68890174
## [117,] -0.309702193 -0.09785537
## [118,] -0.923302825  0.38048385
## [119,] -1.057268178  0.62076875
## [120,]  1.466888062  0.03418356
## [121,]  0.266414348 -0.09413772
## [122,]  0.534345056 -0.57470752
## [123,]  0.596113264  1.59603543
## [124,]  0.228930258  0.38791915
## [125,]  1.373177835  1.23932572
## [126,] -0.521406764 -0.34037086
## [127,]  0.890771521  0.03046591
## [128,] -0.001516359  0.38643209
## [129,]  0.009240182  0.98937493
## [130,]  1.882311700  1.36318582
## [131,] -0.001516359  0.38643209
## [132,] -1.400167067  2.06545229
## [133,] -0.135481713  0.62671699
## [134,]  0.612084273 -0.09190713
## [135,]  0.622840814  0.51103572
## [136,] -1.223503154 -0.94777488
## [137,] -0.387441410 -0.58065576
## [138,]  0.220944753  1.23189042
## [139,]  1.791044905 -1.16947154
## [140,]  0.622840814  0.51103572
## [141,]  1.024736875 -0.20981899
## [142,]  0.266414348 -0.09413772
## [143,]  0.663095940  1.47589298
## [144,]  0.689823490  0.39089327
## [145,] -0.414168960  0.50434395
## [146,]  0.831774349 -0.69336292
## [147,]  0.628055282 -1.77984969
## [148,]  1.024736875 -0.20981899
## [149,]  1.016751370  0.63415229
## [150,]  1.440160512  1.11918327
## [151,]  1.121218137  0.03195297
## [152,] -0.856320148  0.26034140
## [153,]  0.936241116 -1.29556223
## [154,]  0.188675131 -0.57693811
## [155,] -0.521406764 -0.34037086
## [156,] -0.711598254  0.62299934
## [157,]  0.073451823 -0.57768164
## [158,]  0.344153566  0.38866268
## [159,]  1.188200814 -0.08818948
## [160,] -1.402938103  0.61853816
## [161,] -0.079255576 -0.09636831
## [162,]  0.218173717 -0.21502370
## [163,] -0.427696537 -1.54551302
## [164,] -1.737851487  1.21925042
## [165,]  0.159176545 -0.93885253
## [166,]  1.418647431 -0.08670242
## [167,] -0.465180628 -1.06345616
## [168,]  1.147945687 -1.05304674
## [169,] -0.845563607  0.86328424
## [170,]  0.054709777 -0.33665321
## [171,]  0.601327732 -0.69484998
## [172,]  1.147945687 -1.05304674
## [173,]  1.718847760  1.24155631
## [174,] -1.068024719  0.01782590
## [175,]  1.391919881  0.99829729
## [176,] -0.931288329  1.22445513
## [177,] -0.845563607  0.86328424
## [178,] -0.146238253  0.02377414
## [179,]  0.215402681 -1.66193782
## [180,] -0.692856208  0.38197091
## [181,]  0.333397025 -0.21428017
## [182,]  0.931026648  0.99532317
## [183,] -0.829592598 -0.82465831
## [184,] -0.068499036  0.50657454
## [185,] -1.577158583 -0.10603420
## [186,] -1.057268178  0.62076875
## [187,] -0.213220930  0.14391659
## [188,]  1.188200814 -0.08818948
## [189,] -0.376684870  0.02228708
## [190,] -0.079255576 -0.09636831
## [191,]  1.255183491 -0.20833193
## [192,]  0.802275763 -1.05527733
## [193,] -0.175736839 -0.33814027
## [194,]  1.574125866  0.87889837
## [195,] -0.403412420  1.10728679
## [196,]  0.518374046  1.11323503
## [197,]  1.745575310  0.15655660
## [198,] -0.443667546  0.14242953
## [199,] -0.655372118 -0.10008596
## [200,] -0.883047698  1.34534111
## 
## $scores$corr.X.xscores
##            [,1]      [,2]
## [1,] -0.9271970 -0.374574
## [2,] -0.8538903  0.520453
## 
## $scores$corr.Y.xscores
##            [,1]         [,2]
## [1,] -0.7177974  0.008701966
## [2,] -0.6750187 -0.011433002
## 
## $scores$corr.X.yscores
##            [,1]         [,2]
## [1,] -0.7165758 -0.008794398
## [2,] -0.6599214  0.012219404
## 
## $scores$corr.Y.yscores
##            [,1]       [,2]
## [1,] -0.9287778  0.3706371
## [2,] -0.8734252 -0.4869583

14 / 46

Chi-square Test

chisq.test(table(some_ed_data$female, some_ed_data$schtyp))

## 
##     Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(some_ed_data$female, some_ed_data$schtyp)
## X-squared = 0.00054009, df = 1, p-value = 0.9815

15 / 46

Chi-square Goodness of Fit

chisq.test(table(some_ed_data$race), p = c(10, 10, 10, 70)/100)

## 
##     Chi-squared test for given probabilities
## 
## data:  table(some_ed_data$race)
## X-squared = 5.0286, df = 3, p-value = 0.1697

16 / 46

Correlation

cor(some_ed_data$read, some_ed_data$write)

## [1] 0.5967765

cor.test(some_ed_data$read, some_ed_data$write)

## 
##     Pearson's product-moment correlation
## 
## data:  some_ed_data$read and some_ed_data$write
## t = 10.465, df = 198, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4993831 0.6792753
## sample estimates:
##       cor 
## 0.5967765

17 / 46

Discriminant Analysis

lda(factor(some_ed_data$prog) ~ some_ed_data$read + some_ed_data$write + some_ed_data$math, data = some_ed_data)

## Call:
## lda(factor(some_ed_data$prog) ~ some_ed_data$read + some_ed_data$write + 
##     some_ed_data$math, data = some_ed_data)
## 
## Prior probabilities of groups:
##     1     2     3 
## 0.225 0.525 0.250 
## 
## Group means:
##   some_ed_data$read some_ed_data$write some_ed_data$math
## 1          49.75556           51.33333          50.02222
## 2          56.16190           56.25714          56.73333
## 3          46.20000           46.76000          46.42000
## 
## Coefficients of linear discriminants:
##                           LD1         LD2
## some_ed_data$read  0.02919876  0.04385321
## some_ed_data$write 0.03832289 -0.13698224
## some_ed_data$math  0.07034625  0.07931008
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9874 0.0126

18 / 46

Factor Analysis

fa(r = cor(model.matrix(~read + write + math + science + socst - 1, data = some_ed_data)), rotate = "none", fm = "pa", 2)

## maximum iteration exceeded

## Factor Analysis using method =  pa
## Call: fa(r = cor(model.matrix(~read + write + math + science + socst - 
##     1, data = some_ed_data)), nfactors = 2, rotate = "none", 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##          PA1   PA2   h2   u2 com
## read    0.81  0.06 0.66 0.34 1.0
## write   0.76  0.00 0.58 0.42 1.0
## math    0.80  0.17 0.67 0.33 1.1
## science 0.75  0.26 0.62 0.38 1.2
## socst   0.79 -0.48 0.85 0.15 1.6
## 
##                        PA1  PA2
## SS loadings           3.06 0.33
## Proportion Var        0.61 0.07
## Cumulative Var        0.61 0.68
## Proportion Explained  0.90 0.10
## Cumulative Proportion 0.90 1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  10  and the objective function was  2.51
## The degrees of freedom for the model are 1  and the objective function was  0.01 
## 
## The root mean square of the residuals (RMSR) is  0.01 
## The df corrected root mean square of the residuals is  0.03 
## 
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    PA1  PA2
## Correlation of (regression) scores with factors   0.95 0.79
## Multiple R square of scores with factors          0.91 0.62
## Minimum correlation of possible factor scores     0.82 0.23

19 / 46

Factorial ANOVA (Analysis of Variance)

anova(lm(write ~ female * ses, data = some_ed_data))

## Analysis of Variance Table
## 
## Response: write
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## female       1  1176.2 1176.21 14.7212 0.0001680 ***
## ses          1  1042.3 1042.32 13.0454 0.0003862 ***
## female:ses   1     0.0    0.04  0.0005 0.9827570    
## Residuals  196 15660.3   79.90                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

20 / 46

Factorial Logistic Regression

summary(glm(female ~ prog * schtyp, data = some_ed_data, family = binomial))

## 
## Call:
## glm(formula = female ~ prog * schtyp, family = binomial, data = some_ed_data)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -1.698  -1.247   1.069   1.109   1.572  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  -2.2765     1.8857  -1.207    0.227
## prog          1.2303     0.9398   1.309    0.191
## schtyp        2.2405     1.7017   1.317    0.188
## prog:schtyp  -1.1313     0.8622  -1.312    0.189
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 275.64  on 199  degrees of freedom
## Residual deviance: 273.65  on 196  degrees of freedom
## AIC: 281.65
## 
## Number of Fisher Scoring iterations: 4

21 / 46

Friedman Test

friedman.test(cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math))

## 
##     Friedman rank sum test
## 
## data:  cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math)
## Friedman chi-squared = 0.64491, df = 2, p-value = 0.7244

22 / 46

Kruskal Wallis Test

kruskal.test(some_ed_data$write, some_ed_data$prog)

## 
##     Kruskal-Wallis rank sum test
## 
## data:  some_ed_data$write and some_ed_data$prog
## Kruskal-Wallis chi-squared = 34.045, df = 2, p-value = 4.047e-08

23 / 46

McNemar Test

# Some made up data in matrix form
made_up_matrixdata <- matrix(c(150, 22, 21, 12), 2, 2)
mcnemar.test(made_up_matrixdata)

## 
##     McNemar's Chi-squared test with continuity correction
## 
## data:  made_up_matrixdata
## McNemar's chi-squared = 0, df = 1, p-value = 1

24 / 46

Multiple Regression

lm(some_ed_data$write ~ 
     some_ed_data$female + some_ed_data$read + some_ed_data$math + some_ed_data$science + some_ed_data$socst)

## 
## Call:
## lm(formula = some_ed_data$write ~ some_ed_data$female + some_ed_data$read + 
##     some_ed_data$math + some_ed_data$science + some_ed_data$socst)
## 
## Coefficients:
##          (Intercept)   some_ed_data$female     some_ed_data$read  
##               6.1388                5.4925                0.1254  
##    some_ed_data$math  some_ed_data$science    some_ed_data$socst  
##               0.2381                0.2419                0.2293

25 / 46

Multivariate Multiple Regression

mmrlm <- lm(cbind(write, read) ~ female + math + science + socst, data = some_ed_data)
summary(Anova(mmrlm))

## 
## Type II MANOVA Tests:
## 
## Sum of squares and products for error:
##          write     read
## write 7258.783 1091.057
## read  1091.057 8699.762
## 
## ------------------------------------------
##  
## Term: female 
## 
## Sum of squares and products for the hypothesis:
##           write       read
## write 1413.5284 -133.48461
## read  -133.4846   12.60544
## 
## Multivariate Tests: female
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1698853 19.85132      2    194 1.4335e-08 ***
## Wilks             1 0.8301147 19.85132      2    194 1.4335e-08 ***
## Hotelling-Lawley  1 0.2046528 19.85132      2    194 1.4335e-08 ***
## Roy               1 0.2046528 19.85132      2    194 1.4335e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: math 
## 
## Sum of squares and products for the hypothesis:
##          write      read
## write 714.8665  856.2825
## read  856.2825 1025.6735
## 
## Multivariate Tests: math
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1599321 18.46685      2    194 4.5551e-08 ***
## Wilks             1 0.8400679 18.46685      2    194 4.5551e-08 ***
## Hotelling-Lawley  1 0.1903800 18.46685      2    194 4.5551e-08 ***
## Roy               1 0.1903800 18.46685      2    194 4.5551e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: science 
## 
## Sum of squares and products for the hypothesis:
##          write     read
## write 857.8824 901.3191
## read  901.3191 946.9551
## 
## Multivariate Tests: science
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1664254 19.36631      2    194 2.1459e-08 ***
## Wilks             1 0.8335746 19.36631      2    194 2.1459e-08 ***
## Hotelling-Lawley  1 0.1996526 19.36631      2    194 2.1459e-08 ***
## Roy               1 0.1996526 19.36631      2    194 2.1459e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: socst 
## 
## Sum of squares and products for the hypothesis:
##          write     read
## write 1105.653 1277.393
## read  1277.393 1475.810
## 
## Multivariate Tests: socst
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.2206710 27.46604      2    194 3.1399e-11 ***
## Wilks             1 0.7793290 27.46604      2    194 3.1399e-11 ***
## Hotelling-Lawley  1 0.2831551 27.46604      2    194 3.1399e-11 ***
## Roy               1 0.2831551 27.46604      2    194 3.1399e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

26 / 46

Non-parametric Correlation

cor.test(some_ed_data$read, some_ed_data$write, method = "spearman")

## Warning in cor.test.default(some_ed_data$read, some_ed_data$write, method =
## "spearman"): Cannot compute exact p-value with ties

## 
##     Spearman's rank correlation rho
## 
## data:  some_ed_data$read and some_ed_data$write
## S = 510993, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.6167455

27 / 46

One Sample t-test

t.test(some_ed_data$read, mu = 50)

## 
##     One Sample t-test
## 
## data:  some_ed_data$read
## t = 3.0759, df = 199, p-value = 0.002394
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  50.80035 53.65965
## sample estimates:
## mean of x 
##     52.23

28 / 46

One-way Analysis of Variance (ANOVA)

summary(aov(some_ed_data$read ~ some_ed_data$prog))

##                    Df Sum Sq Mean Sq F value Pr(>F)  
## some_ed_data$prog   1    381   381.1   3.674 0.0567 .
## Residuals         198  20538   103.7                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

29 / 46

One-way Multivariate Analysis of Variance (MANOVA)

summary(
  manova(
    cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math) ~ some_ed_data$prog
    )
  )

##                    Df   Pillai approx F num Df den Df  Pr(>F)  
## some_ed_data$prog   1 0.035319    2.392      3    196 0.06984 .
## Residuals         198                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

30 / 46

One-way Repeated Measures Analysis of Variance (ANOVA)

model <-  lm(gender ~ item_1 + item_2, data = some_survey_data)
analysis <- Anova(model, idata = factor_surveydata, idesign = ~s) 
print(analysis)

## Anova Table (Type II tests)
## 
## Response: gender
##           Sum Sq Df F value Pr(>F)
## item_1    0.0601  1  0.2396 0.6307
## item_2    0.7268  1  2.8974 0.1069
## Residuals 4.2642 17

31 / 46

Ordered Logistic Regression# Create ordered variable write3 as 
# a factor with levels 1, 2, and 3
some_ed_data$write3 <- 
  cut(some_ed_data$write, c(0, 48, 57, 70), 
      right = TRUE, 
      labels = c(1,2,3))
table(some_ed_data$write3)

## 
##  1  2  3 
## 61 61 78
# fit ordered logit model and store results 'some_write_data'
some_write_data <- 
  polr(write3 ~ 
         female + read + socst, data = some_ed_data, 
       Hess=TRUE)
summary(some_write_data)

## Call:
## polr(formula = write3 ~ female + read + socst, data = some_ed_data, 
##     Hess = TRUE)
## 
## Coefficients:
##          Value Std. Error t value
## female 1.28543    0.32445   3.962
## read   0.11772    0.02136   5.512
## socst  0.08019    0.01944   4.124
## 
## Intercepts:
##     Value   Std. Error t value
## 1|2  9.7037  1.1968     8.1080
## 2|3 11.8001  1.3041     9.0486
## 
## Residual Deviance: 312.5526 
## AIC: 322.5526
32 / 46

Principal Components Analysis (PCA)

princomp(formula = ~read + write + math + science + socst, data = some_ed_data)

## Call:
## princomp(formula = ~read + write + math + science + socst, data = some_ed_data)
## 
## Standard deviations:
##    Comp.1    Comp.2    Comp.3    Comp.4    Comp.5 
## 18.252929  7.677044  6.213371  5.774331  5.429881 
## 
##  5  variables and  200 observations.

33 / 46

Repeated Measures Logistic Regression

glmer(highpulse ~ diet + (1 | id), data = some_exercise_data, family = binomial)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: highpulse ~ diet + (1 | id)
##    Data: some_exercise_data
##      AIC      BIC   logLik deviance df.resid 
## 105.4679 112.9674 -49.7340  99.4679       87 
## Random effects:
##  Groups Name        Std.Dev.
##  id     (Intercept) 1.821   
## Number of obs: 90, groups:  id, 30
## Fixed Effects:
## (Intercept)         diet  
##      -3.148        1.145

34 / 46

Simple Linear Regression

lm(some_ed_data$write ~ some_ed_data$read)

## 
## Call:
## lm(formula = some_ed_data$write ~ some_ed_data$read)
## 
## Coefficients:
##       (Intercept)  some_ed_data$read  
##           23.9594             0.5517

35 / 46

Simple Logistic Regression

glm(some_ed_data$female ~ some_ed_data$read, family = binomial)

## 
## Call:  glm(formula = some_ed_data$female ~ some_ed_data$read, family = binomial)
## 
## Coefficients:
##       (Intercept)  some_ed_data$read  
##           0.72609           -0.01044  
## 
## Degrees of Freedom: 199 Total (i.e. Null);  198 Residual
## Null Deviance:        275.6 
## Residual Deviance: 275.1     AIC: 279.1

36 / 46

Two Independent Samples t-test

t.test(some_ed_data$read ~ some_ed_data$female)

## 
##     Welch Two Sample t-test
## 
## data:  some_ed_data$read by some_ed_data$female
## t = 0.74506, df = 188.46, p-value = 0.4572
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.796263  3.976725
## sample estimates:
## mean in group 0 mean in group 1 
##        52.82418        51.73394

37 / 46

Wilcoxon-Mann-Whitney Test

wilcox.test(some_ed_data$read ~ some_ed_data$female)

## 
##     Wilcoxon rank sum test with continuity correction
## 
## data:  some_ed_data$read by some_ed_data$female
## W = 5300, p-value = 0.4029
## alternative hypothesis: true location shift is not equal to 0

38 / 46

Wilcoxon Signed Rank Sum Test

wilcox.test(some_ed_data$write, some_ed_data$read, paired = TRUE)

## 
##     Wilcoxon signed rank test with continuity correction
## 
## data:  some_ed_data$write and some_ed_data$read
## V = 9261, p-value = 0.3666
## alternative hypothesis: true location shift is not equal to 0

39 / 46

Other Approaches

There are so many other approaches that are for specific cases or use statistical approaches, but aren't themselves statistics. With that said, the approaches given in this overview cover the gambit of what you will likely need

40 / 46

Some Extra Things

41 / 46

Reporting

After running a statistical test successfully, it can be difficult to know how to report the results. The report package automatically produces reports of models and dataframes according to best practices guidelines. Click here for more information.

42 / 46

Visualizations

Interested in making incredible visuals? Check out #tidytuesday on Twitter. You do not need an account for access.

43 / 46

Something useless

If you are a fan of the show Rick & Morty, consider downloading the most pointless package mortyr to do pointless statistics on pointless data. More about the package here.

44 / 46

Source

A majority of the information included in this survey of approached was scraped from the web using R via the UCLA Institute for Digital Research & Education site using the xml2 package. They also fully support SAS, SPSS (for some reason), Stata, and Mplus.

45 / 46

Thats it!

If you have any questions, please reach out

46 / 46

Thats it!

If you have any questions, please reach out

This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

46 / 46

A Very Incomplete Survey of Basic Statistical Tests in R
EDP 619 Week 5
Dr. Abhik Roy
1 / 46

2 / 46

Getting Ready

To follow along, please make sure to do the following

3 / 46

Getting Ready

To follow along, please make sure to do the following

Run Basic Statistical Tests install.R

3 / 46

Getting Ready

To follow along, please make sure to do the following

Run Basic Statistical Tests install.R
Open up a blank .R script

3 / 46

Getting Ready

To follow along, please make sure to do the following

Run Basic Statistical Tests install.R
Open up a blank .R script

Load up the following packages

library(tidyverse)
library(car)
library(foreign)
library(lme4)
library(MASS)
library(CCA)
library(psych)

3 / 46

Purpose

The examples are of course presented with R in mind, but obviously not restricted to the platform.

4 / 46

Purpose

The examples are of course presented with R in mind, but obviously not restricted to the platform.

The content is intended to cast a wide net so some may look familiar while others will not

4 / 46

Purpose

The examples are of course presented with R in mind, but obviously not restricted to the platform.

The content is intended to cast a wide net so some may look familiar while others will not

You can think of this as a toolkit

4 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario
Since this is not a statistics course, only test names and examples are provided

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario
Since this is not a statistics course, only test names and examples are provided
Some of the syntax may be structured in an odd way. This is only done so so that they be fit within the slide. Remember in general spacing doesn't mean much in R

5 / 46

Note

Here are some things to consider as you go through this

Items in here will apply depending on your focus and strengths
Never memorize formulas - that's what the Internet is for. Rather it is important to know what test applies to which scenario
Since this is not a statistics course, only test names and examples are provided
Some of the syntax may be structured in an odd way. This is only done so so that they be fit within the slide. Remember in general spacing doesn't mean much in R
These are presented in alphabetical order according to the standard name of the test

5 / 46

Decisions Decisions Decisions

When deciding which test is appropriate to use, it is important to consider the type of variables that you have. Please load in the following data sets (and look at them by using View() or head()

some_ed_data <- 
  read_csv("some_ed_data.csv")

some_exercise_data <- 
  read_csv("some_exercise_data.csv")

some_survey_data <- 
  read_csv("some_survey_data.csv")

6 / 46

The Datas (1/3)

some_ed_data

## # A tibble: 200 × 11
##       id female  race   ses schtyp  prog  read write  math science socst
##    <dbl>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl>
##  1    70      0     4     1      1     1    57    52    41      47    57
##  2   121      1     4     2      1     3    68    59    53      63    61
##  3    86      0     4     3      1     1    44    33    54      58    31
##  4   141      0     4     3      1     3    63    44    47      53    56
##  5   172      0     4     2      1     2    47    52    57      53    61
##  6   113      0     4     2      1     2    44    52    51      63    61
##  7    50      0     3     2      1     1    50    59    42      53    61
##  8    11      0     1     2      1     2    34    46    45      39    36
##  9    84      0     4     2      1     1    63    57    54      58    51
## 10    48      0     3     2      1     2    57    55    52      50    51
## # … with 190 more rows

7 / 46

The Datas (2/3)

some_exercise_data

## # A tibble: 90 × 6
##       id  diet exertype pulse  time highpulse
##    <dbl> <dbl>    <dbl> <dbl> <dbl>     <dbl>
##  1     1     1        1    85     1         0
##  2     1     1        1    85     2         0
##  3     1     1        1    88     3         0
##  4     2     1        1    90     1         0
##  5     2     1        1    92     2         0
##  6     2     1        1    93     3         0
##  7     3     1        1    97     1         0
##  8     3     1        1    97     2         0
##  9     3     1        1    94     3         0
## 10     4     1        1    80     1         0
## # … with 80 more rows

8 / 46

The Datas (3/3)

some_survey_data

## # A tibble: 20 × 4
##    respondent gender item_1 item_2
##         <dbl>  <dbl>  <dbl>  <dbl>
##  1          1      1      5      1
##  2          2      2      4      3
##  3          3      1      2      5
##  4          4      2      4      4
##  5          5      2      2      3
##  6          6      1      3      2
##  7          7      1      4      1
##  8          8      2      5      4
##  9          9      2      3      3
## 10         10      2      3      5
## 11         11      1      2      3
## 12         12      2      3      3
## 13         13      2      1      5
## 14         14      1      4      4
## 15         15      2      2      5
## 16         16      1      2      5
## 17         17      1      3      5
## 18         18      1      5      2
## 19         19      1      3      2
## 20         20      2      5      5

9 / 46

An Incomplete Table of Approaches

10 / 46

Tests

11 / 46

ANOVA

summary(aov(some_ed_data$write ~ some_ed_data$prog + some_ed_data$read))

##                    Df Sum Sq Mean Sq F value  Pr(>F)    
## some_ed_data$prog   1    586     586    10.2 0.00164 ** 
## some_ed_data$read   1   5965    5965   103.7 < 2e-16 ***
## Residuals         197  11327      57                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

12 / 46

Binomial Test

prop.test(sum(some_ed_data$female), length(some_ed_data$female), p = 0.5)

## 
##     1-sample proportions test with continuity correction
## 
## data:  sum(some_ed_data$female) out of length(some_ed_data$female), null probability 0.5
## X-squared = 1.445, df = 1, p-value = 0.2293
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.4733037 0.6149394
## sample estimates:
##     p 
## 0.545

13 / 46

Canonical Correlation

cc(cbind(some_ed_data$read, some_ed_data$write), 
   cbind(some_ed_data$math, some_ed_data$science))

## $cor
## [1] 0.7728409 0.0234784
## 
## $names
## $names$Xnames
## NULL
## 
## $names$Ynames
## NULL
## 
## $names$ind.names
## NULL
## 
## 
## $xcoef
##             [,1]       [,2]
## [1,] -0.06326131 -0.1037908
## [2,] -0.04924918  0.1219084
## 
## $ycoef
##             [,1]       [,2]
## [1,] -0.06698268  0.1201425
## [2,] -0.04824063 -0.1208860
## 
## $scores
## $scores$xscores
##               [,1]         [,2]
##   [1,] -0.26358835 -0.589561062
##   [2,] -1.30420707 -0.877901269
##   [3,]  1.49454321 -1.556539586
##   [4,] -0.24916276 -2.187572699
##   [5,]  0.36902478  0.448346869
##   [6,]  0.55880872  0.759719249
##   [7,] -0.16550344  0.990333008
##   [8,]  1.48691695  1.066177022
##   [9,] -0.88940214 -0.602764022
##  [10,] -0.41133590 -0.223835983
##  [11,] -0.15787718 -1.632383600
##  [12,] -0.90382773  0.995247615
##  [13,] -1.66976282 -1.274946875
##  [14,] -0.61554542  1.062803275
##  [15,]  0.24930149  1.265470254
##  [16,]  0.83307890  0.601575756
##  [17,]  0.36902478  0.448346869
##  [18,] -0.50983426  0.019980737
##  [19,] -1.59970217 -0.146451110
##  [20,]  0.50317366 -1.966788153
##  [21,] -0.49540867 -1.578030900
##  [22,] -1.18489724  0.128686136
##  [23,]  0.77023105 -1.325925827
##  [24,] -0.45337228 -0.900933442
##  [25,]  1.39563138  0.510987923
##  [26,]  1.93015961 -0.030998216
##  [27,] -1.40991823  0.164921269
##  [28,]  0.12277887  1.057888668
##  [29,]  1.24829729 -0.946997788
##  [30,]  0.44671169 -1.045873974
##  [31,]  1.71956420 -1.592774720
##  [32,] -1.46555329 -2.561586132
##  [33,] -1.50841660  0.408737989
##  [34,]  1.22707237 -0.373691122
##  [35,] -0.29202606  0.782751422
##  [36,] -1.09361167  0.683875235
##  [37,] -1.05796116 -1.487443067
##  [38,] -1.26217068 -0.200803810
##  [39,]  1.40325764 -2.111728685
##  [40,]  1.90934814 -1.281402340
##  [41,]  0.61527070 -0.161194929
##  [42,] -0.48181000  0.471379042
##  [43,] -0.04578015  0.173209623
##  [44,]  1.22707237 -0.373691122
##  [45,] -1.40991823  0.164921269
##  [46,] -0.48181000  0.471379042
##  [47,]  0.77023105 -1.325925827
##  [48,] -1.11442313 -0.566528889
##  [49,]  0.02428050  1.301705388
##  [50,] -0.36208671 -0.345744343
##  [51,] -0.45378574  0.922777348
##  [52,]  1.81084977 -1.037585621
##  [53,]  0.95280219 -0.215547629
##  [54,] -0.98790051 -0.358947303
##  [55,] -1.76826119 -1.031130155
##  [56,]  1.51535467 -0.306135462
##  [57,]  1.74037567 -0.342370595
##  [58,]  1.32557073 -0.617507842
##  [59,] -0.88940214 -0.602764022
##  [60,]  0.45351102 -0.021169003
##  [61,]  0.47473595 -0.594475669
##  [62,] -0.12346705  1.667430467
##  [63,]  0.95280219 -0.215547629
##  [64,]  2.12715634 -0.518631655
##  [65,]  0.67173268 -1.082109108
##  [66,]  1.10054974 -0.581272708
##  [67,] -0.55187065 -0.657116722
##  [68,]  1.00926417 -1.136461807
##  [69,] -0.19991357 -2.309481059
##  [70,]  1.11497533 -2.179284345
##  [71,]  0.95280219 -0.215547629
##  [72,] -0.55187065 -0.657116722
##  [73,] -2.01450711 -0.421588356
##  [74,] -1.30420707 -0.877901269
##  [75,]  0.20767856 -1.235337994
##  [76,]  0.96001499 -1.014553448
##  [77,] -0.58030837  0.715195762
##  [78,] -1.30420707 -0.877901269
##  [79,]  2.16919273  0.158465804
##  [80,]  0.91076580 -0.892645088
##  [81,] -0.98790051 -0.358947303
##  [82,]  1.21264678  1.224320515
##  [83,] -1.30420707 -0.877901269
##  [84,] -1.28339561  0.372502856
##  [85,]  0.40467530 -1.722971433
##  [86,] -0.62955755  0.837104122
##  [87,]  0.59445924 -1.411599054
##  [88,]  1.33916940  1.431902101
##  [89,]  1.21347370 -2.423101065
##  [90,]  0.01068183 -0.747704555
##  [91,] -0.43977362  1.148476501
##  [92,] -0.49540867 -1.578030900
##  [93,] -1.45195462 -0.512176189
##  [94,]  1.26910876  0.303406337
##  [95,]  0.95280219 -0.215547629
##  [96,] -0.31325099  1.356058087
##  [97,] -1.78948611 -0.457823489
##  [98,] -1.28339561  0.372502856
##  [99,]  1.58541532  0.822360302
## [100,] -1.18489724  0.128686136
## [101,] -1.35345626 -0.755992909
## [102,]  0.02428050  1.301705388
## [103,]  0.66451988 -0.283103289
## [104,] -0.64315622 -1.212305821
## [105,] -0.29202606  0.782751422
## [106,] -0.23556409 -0.138162756
## [107,] -0.94586412  0.318150156
## [108,]  1.96539666 -0.378605729
## [109,]  0.27052642  0.692163589
## [110,] -1.78948611 -0.457823489
## [111,] -0.26358835 -0.589561062
## [112,]  0.65730709  0.515902529
## [113,] -1.11442313 -0.566528889
## [114,] -1.59970217 -0.146451110
## [115,] -1.71901201 -1.153038515
## [116,]  1.45889269  0.614778716
## [117,]  0.52357167  1.107326761
## [118,] -2.01450711 -0.421588356
## [119,] -0.19352770  0.538934702
## [120,]  0.99483858  0.461549830
## [121,] -0.55187065 -0.657116722
## [122,]  0.17924085  0.136974490
## [123,]  0.17924085  0.136974490
## [124,]  0.66451988 -0.283103289
## [125,] -0.12346705  1.667430467
## [126,] -0.38331164  0.227562323
## [127,]  0.72098186 -1.204017467
## [128,]  0.82586610  1.400581574
## [129,]  0.32698840 -0.228750589
## [130,]  2.02865797 -0.274814935
## [131,] -0.60833263  0.263797456
## [132,] -0.90382773  0.995247615
## [133,] -1.45195462 -0.512176189
## [134,]  0.58683298  1.211117555
## [135,] -0.86137788 -0.151365716
## [136,] -2.00729431 -1.220594175
## [137,]  0.02428050  1.301705388
## [138,]  0.43228610  0.552137663
## [139,]  1.41685631 -0.062318743
## [140,]  0.20046577 -0.436332176
## [141,]  1.86648483  1.688921781
## [142,]  0.58683298  1.211117555
## [143,]  0.86151662 -0.770736728
## [144,]  0.12277887  1.057888668
## [145,] -0.29202606  0.782751422
## [146,]  0.36902478  0.448346869
## [147,] -0.31325099  1.356058087
## [148,]  0.55880872  0.759719249
## [149,]  0.91076580 -0.892645088
## [150,]  0.34779986  1.021653535
## [151,]  1.10776254 -1.380278527
## [152,] -0.86817722 -1.176070688
## [153,]  0.37582412  1.473051841
## [154,]  0.27052642  0.692163589
## [155,] -0.75608018  0.629522535
## [156,] -1.30420707 -0.877901269
## [157,] -0.09502933  0.295117983
## [158,]  0.43908543  1.576842634
## [159,]  1.32557073 -0.617507842
## [160,] -1.57167791  0.304947196
## [161,] -0.12346705  1.667430467
## [162,] -0.16508998 -0.833377782
## [163,] -0.07421787  1.545522107
## [164,] -0.75608018  0.629522535
## [165,] -0.29202606  0.782751422
## [166,]  0.95280219 -0.215547629
## [167,] -0.16550344  0.990333008
## [168,]  0.77661692  1.522489934
## [169,] -0.75608018  0.629522535
## [170,] -0.65758181  0.385705816
## [171,]  0.43908543  1.576842634
## [172,]  0.66451988 -0.283103289
## [173,]  1.47331828 -0.983232921
## [174,] -0.79811657 -0.047574923
## [175,]  0.70655627  0.393994170
## [176,] -1.03714969 -0.237038943
## [177,] -1.50841660  0.408737989
## [178,]  0.77661692  1.522489934
## [179,]  0.17924085  0.136974490
## [180,] -0.58752117  1.514201580
## [181,] -0.94586412  0.318150156
## [182,]  0.70655627  0.393994170
## [183,] -0.68601953  1.758018300
## [184,] -0.77730510  1.202829201
## [185,] -0.55949691  1.965599886
## [186,] -1.40991823  0.164921269
## [187,] -0.04578015  0.173209623
## [188,]  0.76301825 -0.526920009
## [189,] -1.13564806  0.006777776
## [190,]  0.47473595 -0.594475669
## [191,]  0.58683298  1.211117555
## [192,]  0.81865331  2.199587393
## [193,]  0.17924085  0.136974490
## [194,]  0.40384838  1.924450147
## [195,] -0.27121460  2.033155546
## [196,] -0.48181000  0.471379042
## [197,]  0.98082645  0.235850677
## [198,]  0.27815267 -1.930553019
## [199,] -0.62955755  0.837104122
## [200,] -1.28339561  0.372502856
## 
## $scores$yscores
##                [,1]        [,2]
##   [1,]  1.013980334 -0.81276184
##   [2,] -0.561661891 -1.30522812
##   [3,] -0.387441410 -0.58065576
##   [4,]  0.322640484 -0.81722302
##   [5,] -0.347186284  0.38420150
##   [6,] -0.427696537 -1.54551302
##   [7,]  0.657553868 -1.41793527
##   [8,]  1.131974678  0.63489582
##   [9,] -0.387441410 -0.58065576
##  [10,]  0.132448995  0.14614718
##  [11,]  0.054709777 -0.33665321
##  [12,] -0.427696537 -1.54551302
##  [13,] -1.670868810  1.09910797
##  [14,] -0.443667546  0.14242953
##  [15,]  1.182986345  2.20269592
##  [16,]  0.735293086 -0.93513488
##  [17,]  0.199431671  0.02600473
##  [18,] -0.789337471  0.14019895
##  [19,] -0.778580931  0.74314179
##  [20,] -0.347186284  0.38420150
##  [21,]  0.499304397 -3.83045019
##  [22,] -2.469446463  0.24993198
##  [23,]  0.360124575 -1.29927988
##  [24,] -0.733111335 -0.58288635
##  [25,]  1.131974678  0.63489582
##  [26,]  1.064992001  0.75503827
##  [27,] -1.335955426  0.49839571
##  [28,] -0.588389441 -0.22022841
##  [29,]  0.864043971  1.11546562
##  [30,]  0.092193868 -0.81871008
##  [31,] -0.057742495  1.10951738
##  [32,] -1.346711967 -0.10454714
##  [33,] -1.376210553 -0.46646155
##  [34,] -1.263758281 -1.91263214
##  [35,] -0.264232597 -1.42388351
##  [36,] -0.800094012 -0.46274390
##  [37,] -2.180002675  0.97524787
##  [38,] -1.711123937  0.13425071
##  [39,]  1.343679249  0.87741131
##  [40,]  1.466888062  0.03418356
##  [41,]  1.255183491 -0.20833193
##  [42,] -0.923302825  0.38048385
##  [43,] -0.443667546  0.14242953
##  [44,]  0.735293086 -0.93513488
##  [45,] -0.226748507 -1.90594038
##  [46,] -1.520932447 -0.82911949
##  [47,]  1.051464425 -1.29481870
##  [48,] -1.700367396  0.73719355
##  [49,] -0.749082344  1.10505620
##  [50,] -0.191707849  1.34980229
##  [51,] -0.808079517  0.38122738
##  [52,]  1.214928364 -1.17318919
##  [53,] -0.470395097  1.22742925
##  [54,]  0.092193868 -0.81871008
##  [55,] -2.190759215  0.37230502
##  [56,]  1.826085563  2.08627112
##  [57,]  1.622366497  0.99978435
##  [58,]  0.713780005 -2.14102057
##  [59,] -0.454424087 -0.46051331
##  [60,]  0.421892783  0.87146307
##  [61,]  0.215402681 -1.66193782
##  [62,] -1.386967094 -1.06940440
##  [63,]  1.775073896  0.51847102
##  [64,]  1.544627280  0.51698396
##  [65,]  0.941783188  1.59826602
##  [66,]  0.936241116 -1.29556223
##  [67,] -0.644615577  0.50285689
##  [68,]  0.853287430  0.51252278
##  [69,] -1.060039214 -0.82614537
##  [70,]  0.622840814  0.51103572
##  [71,]  1.064992001  0.75503827
##  [72,] -0.655372118 -0.10008596
##  [73,] -1.767350073  0.85733600
##  [74,] -1.427222220 -2.03426166
##  [75,]  0.148420004 -1.54179537
##  [76,]  0.976496243 -0.33070497
##  [77,]  0.046724273  0.50731807
##  [78,] -0.762609921 -0.94480077
##  [79,]  1.064992001  0.75503827
##  [80,]  0.384408693  1.35351994
##  [81,] -0.443667546  0.14242953
##  [82,] -0.532163305 -0.94331371
##  [83,] -1.912071967  0.49467806
##  [84,] -0.226748507 -1.90594038
##  [85,]  1.225684905 -0.57024634
##  [86,] -1.298471336  0.01633884
##  [87,]  0.054709777 -0.33665321
##  [88,]  1.389148845 -0.44861683
##  [89,]  1.708091219  0.63861347
##  [90,] -1.001042042 -0.10231655
##  [91,] -0.660586586  2.19079945
##  [92,] -0.438453078 -2.14845587
##  [93,] -1.654897801 -0.58883459
##  [94,]  0.421892783  0.87146307
##  [95,]  0.679066950 -0.21204958
##  [96,] -1.097523305 -0.34408851
##  [97,] -1.979054644  0.61482051
##  [98,] -2.056793862  0.13202012
##  [99,]  1.466888062  0.03418356
## [100,] -1.536903457  0.85882306
## [101,] -1.587915124 -0.70897704
## [102,] -0.907331815 -1.30745871
## [103,]  1.153487759  1.84078151
## [104,] -0.001516359  0.38643209
## [105,] -0.465180628 -1.06345616
## [106,] -0.419383429  2.79522935
## [107,] -0.872291157  1.94828395
## [108,]  0.888000485 -1.41644821
## [109,]  0.534345056 -0.57470752
## [110,] -1.392181562  1.22148101
## [111,]  0.405594171 -2.62530802
## [112,]  1.399905385  0.15432601
## [113,] -0.009501864  1.23040337
## [114,] -0.703612749 -0.22097194
## [115,] -0.443667546  0.14242953
## [116,]  1.523114198 -0.68890174
## [117,] -0.309702193 -0.09785537
## [118,] -0.923302825  0.38048385
## [119,] -1.057268178  0.62076875
## [120,]  1.466888062  0.03418356
## [121,]  0.266414348 -0.09413772
## [122,]  0.534345056 -0.57470752
## [123,]  0.596113264  1.59603543
## [124,]  0.228930258  0.38791915
## [125,]  1.373177835  1.23932572
## [126,] -0.521406764 -0.34037086
## [127,]  0.890771521  0.03046591
## [128,] -0.001516359  0.38643209
## [129,]  0.009240182  0.98937493
## [130,]  1.882311700  1.36318582
## [131,] -0.001516359  0.38643209
## [132,] -1.400167067  2.06545229
## [133,] -0.135481713  0.62671699
## [134,]  0.612084273 -0.09190713
## [135,]  0.622840814  0.51103572
## [136,] -1.223503154 -0.94777488
## [137,] -0.387441410 -0.58065576
## [138,]  0.220944753  1.23189042
## [139,]  1.791044905 -1.16947154
## [140,]  0.622840814  0.51103572
## [141,]  1.024736875 -0.20981899
## [142,]  0.266414348 -0.09413772
## [143,]  0.663095940  1.47589298
## [144,]  0.689823490  0.39089327
## [145,] -0.414168960  0.50434395
## [146,]  0.831774349 -0.69336292
## [147,]  0.628055282 -1.77984969
## [148,]  1.024736875 -0.20981899
## [149,]  1.016751370  0.63415229
## [150,]  1.440160512  1.11918327
## [151,]  1.121218137  0.03195297
## [152,] -0.856320148  0.26034140
## [153,]  0.936241116 -1.29556223
## [154,]  0.188675131 -0.57693811
## [155,] -0.521406764 -0.34037086
## [156,] -0.711598254  0.62299934
## [157,]  0.073451823 -0.57768164
## [158,]  0.344153566  0.38866268
## [159,]  1.188200814 -0.08818948
## [160,] -1.402938103  0.61853816
## [161,] -0.079255576 -0.09636831
## [162,]  0.218173717 -0.21502370
## [163,] -0.427696537 -1.54551302
## [164,] -1.737851487  1.21925042
## [165,]  0.159176545 -0.93885253
## [166,]  1.418647431 -0.08670242
## [167,] -0.465180628 -1.06345616
## [168,]  1.147945687 -1.05304674
## [169,] -0.845563607  0.86328424
## [170,]  0.054709777 -0.33665321
## [171,]  0.601327732 -0.69484998
## [172,]  1.147945687 -1.05304674
## [173,]  1.718847760  1.24155631
## [174,] -1.068024719  0.01782590
## [175,]  1.391919881  0.99829729
## [176,] -0.931288329  1.22445513
## [177,] -0.845563607  0.86328424
## [178,] -0.146238253  0.02377414
## [179,]  0.215402681 -1.66193782
## [180,] -0.692856208  0.38197091
## [181,]  0.333397025 -0.21428017
## [182,]  0.931026648  0.99532317
## [183,] -0.829592598 -0.82465831
## [184,] -0.068499036  0.50657454
## [185,] -1.577158583 -0.10603420
## [186,] -1.057268178  0.62076875
## [187,] -0.213220930  0.14391659
## [188,]  1.188200814 -0.08818948
## [189,] -0.376684870  0.02228708
## [190,] -0.079255576 -0.09636831
## [191,]  1.255183491 -0.20833193
## [192,]  0.802275763 -1.05527733
## [193,] -0.175736839 -0.33814027
## [194,]  1.574125866  0.87889837
## [195,] -0.403412420  1.10728679
## [196,]  0.518374046  1.11323503
## [197,]  1.745575310  0.15655660
## [198,] -0.443667546  0.14242953
## [199,] -0.655372118 -0.10008596
## [200,] -0.883047698  1.34534111
## 
## $scores$corr.X.xscores
##            [,1]      [,2]
## [1,] -0.9271970 -0.374574
## [2,] -0.8538903  0.520453
## 
## $scores$corr.Y.xscores
##            [,1]         [,2]
## [1,] -0.7177974  0.008701966
## [2,] -0.6750187 -0.011433002
## 
## $scores$corr.X.yscores
##            [,1]         [,2]
## [1,] -0.7165758 -0.008794398
## [2,] -0.6599214  0.012219404
## 
## $scores$corr.Y.yscores
##            [,1]       [,2]
## [1,] -0.9287778  0.3706371
## [2,] -0.8734252 -0.4869583

14 / 46

Chi-square Test

chisq.test(table(some_ed_data$female, some_ed_data$schtyp))

## 
##     Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(some_ed_data$female, some_ed_data$schtyp)
## X-squared = 0.00054009, df = 1, p-value = 0.9815

15 / 46

Chi-square Goodness of Fit

chisq.test(table(some_ed_data$race), p = c(10, 10, 10, 70)/100)

## 
##     Chi-squared test for given probabilities
## 
## data:  table(some_ed_data$race)
## X-squared = 5.0286, df = 3, p-value = 0.1697

16 / 46

Correlation

cor(some_ed_data$read, some_ed_data$write)

## [1] 0.5967765

cor.test(some_ed_data$read, some_ed_data$write)

## 
##     Pearson's product-moment correlation
## 
## data:  some_ed_data$read and some_ed_data$write
## t = 10.465, df = 198, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4993831 0.6792753
## sample estimates:
##       cor 
## 0.5967765

17 / 46

Discriminant Analysis

lda(factor(some_ed_data$prog) ~ some_ed_data$read + some_ed_data$write + some_ed_data$math, data = some_ed_data)

## Call:
## lda(factor(some_ed_data$prog) ~ some_ed_data$read + some_ed_data$write + 
##     some_ed_data$math, data = some_ed_data)
## 
## Prior probabilities of groups:
##     1     2     3 
## 0.225 0.525 0.250 
## 
## Group means:
##   some_ed_data$read some_ed_data$write some_ed_data$math
## 1          49.75556           51.33333          50.02222
## 2          56.16190           56.25714          56.73333
## 3          46.20000           46.76000          46.42000
## 
## Coefficients of linear discriminants:
##                           LD1         LD2
## some_ed_data$read  0.02919876  0.04385321
## some_ed_data$write 0.03832289 -0.13698224
## some_ed_data$math  0.07034625  0.07931008
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9874 0.0126

18 / 46

Factor Analysis

fa(r = cor(model.matrix(~read + write + math + science + socst - 1, data = some_ed_data)), rotate = "none", fm = "pa", 2)

## maximum iteration exceeded

## Factor Analysis using method =  pa
## Call: fa(r = cor(model.matrix(~read + write + math + science + socst - 
##     1, data = some_ed_data)), nfactors = 2, rotate = "none", 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##          PA1   PA2   h2   u2 com
## read    0.81  0.06 0.66 0.34 1.0
## write   0.76  0.00 0.58 0.42 1.0
## math    0.80  0.17 0.67 0.33 1.1
## science 0.75  0.26 0.62 0.38 1.2
## socst   0.79 -0.48 0.85 0.15 1.6
## 
##                        PA1  PA2
## SS loadings           3.06 0.33
## Proportion Var        0.61 0.07
## Cumulative Var        0.61 0.68
## Proportion Explained  0.90 0.10
## Cumulative Proportion 0.90 1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  10  and the objective function was  2.51
## The degrees of freedom for the model are 1  and the objective function was  0.01 
## 
## The root mean square of the residuals (RMSR) is  0.01 
## The df corrected root mean square of the residuals is  0.03 
## 
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    PA1  PA2
## Correlation of (regression) scores with factors   0.95 0.79
## Multiple R square of scores with factors          0.91 0.62
## Minimum correlation of possible factor scores     0.82 0.23

19 / 46

Factorial ANOVA (Analysis of Variance)

anova(lm(write ~ female * ses, data = some_ed_data))

## Analysis of Variance Table
## 
## Response: write
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## female       1  1176.2 1176.21 14.7212 0.0001680 ***
## ses          1  1042.3 1042.32 13.0454 0.0003862 ***
## female:ses   1     0.0    0.04  0.0005 0.9827570    
## Residuals  196 15660.3   79.90                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

20 / 46

Factorial Logistic Regression

summary(glm(female ~ prog * schtyp, data = some_ed_data, family = binomial))

## 
## Call:
## glm(formula = female ~ prog * schtyp, family = binomial, data = some_ed_data)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -1.698  -1.247   1.069   1.109   1.572  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  -2.2765     1.8857  -1.207    0.227
## prog          1.2303     0.9398   1.309    0.191
## schtyp        2.2405     1.7017   1.317    0.188
## prog:schtyp  -1.1313     0.8622  -1.312    0.189
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 275.64  on 199  degrees of freedom
## Residual deviance: 273.65  on 196  degrees of freedom
## AIC: 281.65
## 
## Number of Fisher Scoring iterations: 4

21 / 46

Friedman Test

friedman.test(cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math))

## 
##     Friedman rank sum test
## 
## data:  cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math)
## Friedman chi-squared = 0.64491, df = 2, p-value = 0.7244

22 / 46

Kruskal Wallis Test

kruskal.test(some_ed_data$write, some_ed_data$prog)

## 
##     Kruskal-Wallis rank sum test
## 
## data:  some_ed_data$write and some_ed_data$prog
## Kruskal-Wallis chi-squared = 34.045, df = 2, p-value = 4.047e-08

23 / 46

McNemar Test

# Some made up data in matrix form
made_up_matrixdata <- matrix(c(150, 22, 21, 12), 2, 2)
mcnemar.test(made_up_matrixdata)

## 
##     McNemar's Chi-squared test with continuity correction
## 
## data:  made_up_matrixdata
## McNemar's chi-squared = 0, df = 1, p-value = 1

24 / 46

Multiple Regression

lm(some_ed_data$write ~ 
     some_ed_data$female + some_ed_data$read + some_ed_data$math + some_ed_data$science + some_ed_data$socst)

## 
## Call:
## lm(formula = some_ed_data$write ~ some_ed_data$female + some_ed_data$read + 
##     some_ed_data$math + some_ed_data$science + some_ed_data$socst)
## 
## Coefficients:
##          (Intercept)   some_ed_data$female     some_ed_data$read  
##               6.1388                5.4925                0.1254  
##    some_ed_data$math  some_ed_data$science    some_ed_data$socst  
##               0.2381                0.2419                0.2293

25 / 46

Multivariate Multiple Regression

mmrlm <- lm(cbind(write, read) ~ female + math + science + socst, data = some_ed_data)
summary(Anova(mmrlm))

## 
## Type II MANOVA Tests:
## 
## Sum of squares and products for error:
##          write     read
## write 7258.783 1091.057
## read  1091.057 8699.762
## 
## ------------------------------------------
##  
## Term: female 
## 
## Sum of squares and products for the hypothesis:
##           write       read
## write 1413.5284 -133.48461
## read  -133.4846   12.60544
## 
## Multivariate Tests: female
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1698853 19.85132      2    194 1.4335e-08 ***
## Wilks             1 0.8301147 19.85132      2    194 1.4335e-08 ***
## Hotelling-Lawley  1 0.2046528 19.85132      2    194 1.4335e-08 ***
## Roy               1 0.2046528 19.85132      2    194 1.4335e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: math 
## 
## Sum of squares and products for the hypothesis:
##          write      read
## write 714.8665  856.2825
## read  856.2825 1025.6735
## 
## Multivariate Tests: math
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1599321 18.46685      2    194 4.5551e-08 ***
## Wilks             1 0.8400679 18.46685      2    194 4.5551e-08 ***
## Hotelling-Lawley  1 0.1903800 18.46685      2    194 4.5551e-08 ***
## Roy               1 0.1903800 18.46685      2    194 4.5551e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: science 
## 
## Sum of squares and products for the hypothesis:
##          write     read
## write 857.8824 901.3191
## read  901.3191 946.9551
## 
## Multivariate Tests: science
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1664254 19.36631      2    194 2.1459e-08 ***
## Wilks             1 0.8335746 19.36631      2    194 2.1459e-08 ***
## Hotelling-Lawley  1 0.1996526 19.36631      2    194 2.1459e-08 ***
## Roy               1 0.1996526 19.36631      2    194 2.1459e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: socst 
## 
## Sum of squares and products for the hypothesis:
##          write     read
## write 1105.653 1277.393
## read  1277.393 1475.810
## 
## Multivariate Tests: socst
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.2206710 27.46604      2    194 3.1399e-11 ***
## Wilks             1 0.7793290 27.46604      2    194 3.1399e-11 ***
## Hotelling-Lawley  1 0.2831551 27.46604      2    194 3.1399e-11 ***
## Roy               1 0.2831551 27.46604      2    194 3.1399e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

26 / 46

Non-parametric Correlation

cor.test(some_ed_data$read, some_ed_data$write, method = "spearman")

## Warning in cor.test.default(some_ed_data$read, some_ed_data$write, method =
## "spearman"): Cannot compute exact p-value with ties

## 
##     Spearman's rank correlation rho
## 
## data:  some_ed_data$read and some_ed_data$write
## S = 510993, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.6167455

27 / 46

One Sample t-test

t.test(some_ed_data$read, mu = 50)

## 
##     One Sample t-test
## 
## data:  some_ed_data$read
## t = 3.0759, df = 199, p-value = 0.002394
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  50.80035 53.65965
## sample estimates:
## mean of x 
##     52.23

28 / 46

One-way Analysis of Variance (ANOVA)

summary(aov(some_ed_data$read ~ some_ed_data$prog))

##                    Df Sum Sq Mean Sq F value Pr(>F)  
## some_ed_data$prog   1    381   381.1   3.674 0.0567 .
## Residuals         198  20538   103.7                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

29 / 46

One-way Multivariate Analysis of Variance (MANOVA)

summary(
  manova(
    cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math) ~ some_ed_data$prog
    )
  )

##                    Df   Pillai approx F num Df den Df  Pr(>F)  
## some_ed_data$prog   1 0.035319    2.392      3    196 0.06984 .
## Residuals         198                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

30 / 46

One-way Repeated Measures Analysis of Variance (ANOVA)

model <-  lm(gender ~ item_1 + item_2, data = some_survey_data)
analysis <- Anova(model, idata = factor_surveydata, idesign = ~s) 
print(analysis)

## Anova Table (Type II tests)
## 
## Response: gender
##           Sum Sq Df F value Pr(>F)
## item_1    0.0601  1  0.2396 0.6307
## item_2    0.7268  1  2.8974 0.1069
## Residuals 4.2642 17

31 / 46

Ordered Logistic Regression# Create ordered variable write3 as 
# a factor with levels 1, 2, and 3
some_ed_data$write3 <- 
  cut(some_ed_data$write, c(0, 48, 57, 70), 
      right = TRUE, 
      labels = c(1,2,3))
table(some_ed_data$write3)

## 
##  1  2  3 
## 61 61 78
# fit ordered logit model and store results 'some_write_data'
some_write_data <- 
  polr(write3 ~ 
         female + read + socst, data = some_ed_data, 
       Hess=TRUE)
summary(some_write_data)

## Call:
## polr(formula = write3 ~ female + read + socst, data = some_ed_data, 
##     Hess = TRUE)
## 
## Coefficients:
##          Value Std. Error t value
## female 1.28543    0.32445   3.962
## read   0.11772    0.02136   5.512
## socst  0.08019    0.01944   4.124
## 
## Intercepts:
##     Value   Std. Error t value
## 1|2  9.7037  1.1968     8.1080
## 2|3 11.8001  1.3041     9.0486
## 
## Residual Deviance: 312.5526 
## AIC: 322.5526
32 / 46

Principal Components Analysis (PCA)

princomp(formula = ~read + write + math + science + socst, data = some_ed_data)

## Call:
## princomp(formula = ~read + write + math + science + socst, data = some_ed_data)
## 
## Standard deviations:
##    Comp.1    Comp.2    Comp.3    Comp.4    Comp.5 
## 18.252929  7.677044  6.213371  5.774331  5.429881 
## 
##  5  variables and  200 observations.

33 / 46

Repeated Measures Logistic Regression

glmer(highpulse ~ diet + (1 | id), data = some_exercise_data, family = binomial)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: highpulse ~ diet + (1 | id)
##    Data: some_exercise_data
##      AIC      BIC   logLik deviance df.resid 
## 105.4679 112.9674 -49.7340  99.4679       87 
## Random effects:
##  Groups Name        Std.Dev.
##  id     (Intercept) 1.821   
## Number of obs: 90, groups:  id, 30
## Fixed Effects:
## (Intercept)         diet  
##      -3.148        1.145

34 / 46

Simple Linear Regression

lm(some_ed_data$write ~ some_ed_data$read)

## 
## Call:
## lm(formula = some_ed_data$write ~ some_ed_data$read)
## 
## Coefficients:
##       (Intercept)  some_ed_data$read  
##           23.9594             0.5517

35 / 46

Simple Logistic Regression

glm(some_ed_data$female ~ some_ed_data$read, family = binomial)

## 
## Call:  glm(formula = some_ed_data$female ~ some_ed_data$read, family = binomial)
## 
## Coefficients:
##       (Intercept)  some_ed_data$read  
##           0.72609           -0.01044  
## 
## Degrees of Freedom: 199 Total (i.e. Null);  198 Residual
## Null Deviance:        275.6 
## Residual Deviance: 275.1     AIC: 279.1

36 / 46

Two Independent Samples t-test

t.test(some_ed_data$read ~ some_ed_data$female)

## 
##     Welch Two Sample t-test
## 
## data:  some_ed_data$read by some_ed_data$female
## t = 0.74506, df = 188.46, p-value = 0.4572
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.796263  3.976725
## sample estimates:
## mean in group 0 mean in group 1 
##        52.82418        51.73394

37 / 46

Wilcoxon-Mann-Whitney Test

wilcox.test(some_ed_data$read ~ some_ed_data$female)

## 
##     Wilcoxon rank sum test with continuity correction
## 
## data:  some_ed_data$read by some_ed_data$female
## W = 5300, p-value = 0.4029
## alternative hypothesis: true location shift is not equal to 0

38 / 46

Wilcoxon Signed Rank Sum Test

wilcox.test(some_ed_data$write, some_ed_data$read, paired = TRUE)

## 
##     Wilcoxon signed rank test with continuity correction
## 
## data:  some_ed_data$write and some_ed_data$read
## V = 9261, p-value = 0.3666
## alternative hypothesis: true location shift is not equal to 0

39 / 46

Other Approaches

40 / 46

Some Extra Things

41 / 46

Reporting

42 / 46

Visualizations

Interested in making incredible visuals? Check out #tidytuesday on Twitter. You do not need an account for access.

43 / 46

Something useless

If you are a fan of the show Rick & Morty, consider downloading the most pointless package mortyr to do pointless statistics on pointless data. More about the package here.

44 / 46

Source

45 / 46

Thats it!

If you have any questions, please reach out

46 / 46

Thats it!

If you have any questions, please reach out

This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

46 / 46

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A Very Incomplete Survey of Basic Statistical Tests in R

EDP 619 Week 5

Dr. Abhik Roy

Getting Ready

Getting Ready

Getting Ready

Getting Ready

Purpose

Purpose

Purpose

Note

Note

Note

Note

Note

Decisions Decisions Decisions

The Datas (1/3)

The Datas (2/3)

The Datas (3/3)

An Incomplete Table of Approaches

Tests

ANOVA

Binomial Test

Canonical Correlation

Chi-square Test

Chi-square Goodness of Fit

Correlation

Discriminant Analysis

Factor Analysis

Factorial ANOVA (Analysis of Variance)

Factorial Logistic Regression

Friedman Test

Kruskal Wallis Test

McNemar Test

Multiple Regression

Multivariate Multiple Regression

Non-parametric Correlation

One Sample t-test

One-way Analysis of Variance (ANOVA)

One-way Multivariate Analysis of Variance (MANOVA)

One-way Repeated Measures Analysis of Variance (ANOVA)

Ordered Logistic Regression

Principal Components Analysis (PCA)

Repeated Measures Logistic Regression

Simple Linear Regression

Simple Logistic Regression

Two Independent Samples t-test

Wilcoxon-Mann-Whitney Test

Wilcoxon Signed Rank Sum Test

Other Approaches

Some Extra Things

Reporting

Visualizations

Something useless

Source

Thats it!

Thats it!

Help

A Very Incomplete Survey of Basic Statistical Tests in R

A Very Incomplete Survey of Basic Statistical Tests in R

EDP 619 Week 5

Dr. Abhik Roy

Getting Ready

Getting Ready

Getting Ready

Getting Ready

Purpose

Purpose

Purpose

Note

Note

Note

Note

Note

Decisions Decisions Decisions

The Datas (1/3)

The Datas (2/3)

The Datas (3/3)

An Incomplete Table of Approaches

Tests