What statistical analysis should I use in R?

What statistical analysis should I use in R?

By /

The appropriate method for rewriting a sentence is to carefully analyze the original sentence and determine the main idea or message it is conveying. Then, using proper grammar and sentence structure, rephrase the sentence in a clear and concise manner without changing the intended meaning. It is important to also consider the tone and style of writing when rewriting a sentence. Overall, the proper way to rewrite a sentence is to effectively communicate the same information in a more effective and polished manner.

What statistical analysis should I use? Statistical analyses using R

Version info: Code for this page was tested in R 2.15.2.

Introduction

This page shows how to perform a number of statistical tests using R.
Each section gives a brief description of the aim of the statistical test,
when it is used, an example showing the R commands and R output with
a brief interpretation of the output. You can see the page

Choosing the Correct Statistical Test for a table that shows an overview
of when each test is appropriate to use.  In deciding which test is
appropriate to use, it is important to consider the type of variables that
you have (i.e., whether your variables are categorical, ordinal or interval
and whether they are normally distributed), see

What is the difference between categorical, ordinal and interval variables?
for more information on this.

Setup

hsb2 <- within(read.csv("https://stats.idre.ucla.edu/stat/data/hsb2.csv"), {
    race <- as.factor(race)
    schtyp <- as.factor(schtyp)
    prog <- as.factor(prog)
})

attach(hsb2)

One sample t-test

t.test(write, mu = 50)

## 
## 	One Sample t-test
## 
## data:  write 
## t = 4.14, df = 199, p-value = 5.121e-05
## alternative hypothesis: true mean is not equal to 50 
## 95 percent confidence interval:
##  51.5 54.1 
## sample estimates:
## mean of x 
##      52.8

One sample median test

wilcox.test(write, mu = 50)

## 
## 	Wilcoxon signed rank test with continuity correction
## 
## data:  write 
## V = 13177, p-value = 3.702e-05
## alternative hypothesis: true location is not equal to 50

Binomial test

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

## 
## 	1-sample proportions test with continuity correction
## 
## data:  sum(female) out of length(female), null probability 0.5 
## X-squared = 1.45, df = 1, p-value = 0.2293
## alternative hypothesis: true p is not equal to 0.5 
## 95 percent confidence interval:
##  0.473 0.615 
## sample estimates:
##     p 
## 0.545

Chi-square goodness of fit

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

## 
## 	Chi-squared test for given probabilities
## 
## data:  table(race) 
## X-squared = 5.03, df = 3, p-value = 0.1697

Two independent samples t-test

t.test(write ~ female)

## 
## 	Welch Two Sample t-test
## 
## data:  write by female 
## t = -3.66, df = 170, p-value = 0.0003409
## alternative hypothesis: true difference in means is not equal to 0 
## 95 percent confidence interval:
##  -7.50 -2.24 
## sample estimates:
## mean in group 0 mean in group 1 
##            50.1            55.0

Wilcoxon-Mann-Whitney test

wilcox.test(write ~ female)

## 
## 	Wilcoxon rank sum test with continuity correction
## 
## data:  write by female 
## W = 3606, p-value = 0.0008749
## alternative hypothesis: true location shift is not equal to 0

Chi-square test

chisq.test(table(female, schtyp))

## 
## 	Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(female, schtyp) 
## X-squared = 5e-04, df = 1, p-value = 0.9815

Fisher’s exact test

fisher.test(table(race, schtyp))

## 
## 	Fisher's Exact Test for Count Data
## 
## data:  table(race, schtyp) 
## p-value = 0.5975
## alternative hypothesis: two.sided

One-way ANOVA

summary(aov(write ~ prog))

##              Df Sum Sq Mean Sq F value  Pr(>F)    
## prog          2   3176    1588    21.3 4.3e-09 ***
## Residuals   197  14703      75                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Kruskal Wallis test

kruskal.test(write, prog)

## 
## 	Kruskal-Wallis rank sum test
## 
## data:  write and prog 
## Kruskal-Wallis chi-squared = 34, df = 2, p-value = 4.047e-08

Paired t-test

t.test(write, read, paired = TRUE)

## 
## 	Paired t-test
## 
## data:  write and read 
## t = 0.867, df = 199, p-value = 0.3868
## alternative hypothesis: true difference in means is not equal to 0 
## 95 percent confidence interval:
##  -0.694  1.784 
## sample estimates:
## mean of the differences 
##                   0.545

Wilcoxon signed rank sum test

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

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

McNemar test

X <- matrix(c(172, 7, 6, 15), 2, 2)
mcnemar.test(X)

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

One-way repeated measures ANOVA

require(car)

## Loading required package: car

## Loading required package: MASS

## Loading required package: nnet

## Loading required package: survival

## Loading required package: splines

require(foreign)

## Loading required package: foreign

kirk <- within(read.dta("https://stats.idre.ucla.edu/stat/stata/examples/kirk/rb4.dta"), 
    {
        s <- as.factor(s)
        a <- as.factor(a)
    })

model <- lm(y ~ a + s, data = kirk)
analysis <- Anova(model, idata = kirk, idesign = ~s)
print(analysis)

## Anova Table (Type II tests)
## 
## Response: y
##           Sum Sq Df F value  Pr(>F)    
## a           49.0  3    11.6 0.00011 ***
## s           31.5  7     3.2 0.01802 *  
## Residuals   29.5 21                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Repeated measures logistic regression

require(lme4)

## Loading required package: lme4

## Loading required package: Matrix

## Loading required package: lattice

## Attaching package: 'lme4'

## The following object(s) are masked from 'package:stats':
## 
## AIC, BIC

exercise <- within(read.dta("https://stats.idre.ucla.edu/stat/stata/whatstat/exercise.dta"), 
    {
        id <- as.factor(id)
        diet <- as.factor(diet)
    })
glmer(highpulse ~ diet + (1 | id), data = exercise, family = binomial)

## Generalized linear mixed model fit by the Laplace approximation 
## Formula: highpulse ~ diet + (1 | id) 
##    Data: exercise 
##  AIC BIC logLik deviance
##  105 113  -49.7     99.5
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 3.32     1.82    
## Number of obs: 90, groups: id, 30
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept)   -2.004      0.663   -3.02   0.0025 **
## diet2          1.145      0.898    1.27   0.2022   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Correlation of Fixed Effects:
##       (Intr)
## diet2 -0.738

Factorial ANOVA

anova(lm(write ~ female * ses, data = hsb2))

## Analysis of Variance Table
## 
## Response: write
##             Df Sum Sq Mean Sq F value  Pr(>F)    
## female       1   1176    1176    14.7 0.00017 ***
## ses          1   1042    1042    13.1 0.00039 ***
## female:ses   1      0       0     0.0 0.98276    
## Residuals  196  15660      80                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Friedman test

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

## 
## 	Friedman rank sum test
## 
## data:  cbind(read, write, math) 
## Friedman chi-squared = 0.645, df = 2, p-value = 0.7244

Factorial logistic regression

summary(glm(female ~ prog * schtyp, data = hsb2, family = binomial))

## 
## Call:
## glm(formula = female ~ prog * schtyp, family = binomial, data = hsb2)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
##  -1.89   -1.25    1.06    1.11    1.20  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)
## (Intercept)    -0.0513     0.3204   -0.16     0.87
## prog2           0.3246     0.3911    0.83     0.41
## prog3           0.2183     0.4319    0.51     0.61
## schtyp2         1.6607     1.1413    1.46     0.15
## prog2:schtyp2  -1.9340     1.2327   -1.57     0.12
## prog3:schtyp2  -1.8278     1.8402   -0.99     0.32
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 275.64  on 199  degrees of freedom
## Residual deviance: 272.49  on 194  degrees of freedom
## AIC: 284.5
## 
## Number of Fisher Scoring iterations: 3

Correlation

cor(read, write)

## [1] 0.597

cor.test(read, write)

## 
## 	Pearson's product-moment correlation
## 
## data:  read and write 
## t = 10.5, df = 198, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0 
## 95 percent confidence interval:
##  0.499 0.679 
## sample estimates:
##   cor 
## 0.597

Simple linear regression

lm(write ~ read)

## 
## Call:
## lm(formula = write ~ read)
## 
## Coefficients:
## (Intercept)         read  
##      23.959        0.552

Non-parametric correlation

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

## Warning: Cannot compute exact p-values with ties

## 
## 	Spearman's rank correlation rho
## 
## data:  write and read 
## S = 510993, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0 
## sample estimates:
##   rho 
## 0.617

Simple logistic regression

glm(female ~ read, family = binomial)

## 
## Call:  glm(formula = female ~ read, family = binomial)
## 
## Coefficients:
## (Intercept)         read  
##      0.7261      -0.0104  
## 
## Degrees of Freedom: 199 Total (i.e. Null);  198 Residual
## Null Deviance:	    276 
## Residual Deviance: 275 	AIC: 279

Multiple regression

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

## 
## Call:
## lm(formula = write ~ female + read + math + science + socst)
## 
## Coefficients:
## (Intercept)       female         read         math      science  
##       6.139        5.493        0.125        0.238        0.242  
##       socst  
##       0.229

Analysis of covariance

summary(aov(write ~ prog + read))

##              Df Sum Sq Mean Sq F value  Pr(>F)    
## prog          2   3176    1588    28.6 1.2e-11 ***
## read          1   3842    3842    69.3 1.4e-14 ***
## Residuals   196  10861      55                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Multiple logistic regression

glm(female ~ read + write, family = binomial)

## 
## Call:  glm(formula = female ~ read + write, family = binomial)
## 
## Coefficients:
## (Intercept)         read        write  
##      -1.706       -0.071        0.106  
## 
## Degrees of Freedom: 199 Total (i.e. Null);  197 Residual
## Null Deviance:	    276 
## Residual Deviance: 248 	AIC: 254

Ordered logistic regression

Ordered logistic regression is used when the dependent variable is
ordered, but not continuous. For example, using the hsb2 data file we will
create an ordered variable called write3. This variable will have
the values 1, 2 and 3, indicating a low, medium or high writing score. We
do not generally recommend categorizing a continuous variable in this way;
we are simply creating a variable to use for this example. We will use
gender (female), reading score (read) and social studies score
(socst) as predictor variables in this model.

require(MASS)
## Creat order variable write3 as a factor with levels 1, 2, and 3hsb2$write3<-cut(hsb2$write,c(0,48,57,70),right=TRUE,labels=c(1,2,3))table(hsb2$write3)
## 
##  1  2  3 
## 61 61 78

## fit ordered logit model and store results 'm'm<-polr(write3~female+read+socst,data= hsb2,Hess=TRUE)## view a summary of the modelsummary(m)
## Call:
## polr(formula = write3 ~ female + read + socst, data = hsb2, Hess = TRUE)
## 
## Coefficients:
##         Value Std. Error t value
## female 1.2854     0.3244    3.96
## read   0.1177     0.0214    5.51
## socst  0.0802     0.0194    4.12
## 
## Intercepts:
##     Value  Std. Error t value
## 1|2  9.704  1.197      8.108 
## 2|3 11.800  1.304      9.049 
## 
## Residual Deviance: 312.55 
## AIC: 322.55

Discriminant analysis

Discriminant analysis is used when you have one or more normally
distributed interval independent variables and a categorical dependent
variable. It is a multivariate technique that considers the latent
dimensions in the independent variables for predicting group membership in
the categorical dependent variable. For example, using the hsb2 data say we wish to use
read,
write and
math
scores to predict the type of program a student belongs to (prog).

require(MASS)
fit<-lda(factor(prog)~read+write+math,data= hsb2)fit# show results 
## Call:
## lda(factor(prog) ~ read + write + math, data = hsb2)
## 
## Prior probabilities of groups:
##     1     2     3 
## 0.225 0.525 0.250 
## 
## Group means:
##   read write math
## 1 49.8  51.3 50.0
## 2 56.2  56.3 56.7
## 3 46.2  46.8 46.4
## 
## Coefficients of linear discriminants:
##          LD1     LD2
## read  0.0292  0.0439
## write 0.0383 -0.1370
## math  0.0703  0.0793
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9874 0.0126

One-way MANOVA

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

##            Df Pillai approx F num Df den Df  Pr(>F)    
## prog        2  0.267     10.1      6    392 2.3e-10 ***
## Residuals 197                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Multivariate multiple regression

M1 <- lm(cbind(write, read) ~ female + math + science + socst, data = hsb2)

require(car)
summary(Anova(M1))

## 
## Type II MANOVA Tests:
## 
## Sum of squares and products for error:
##       write read
## write  7259 1091
## read   1091 8700
## 
## ------------------------------------------
##  
## Term: female 
## 
## Sum of squares and products for the hypothesis:
##       write   read
## write  1414 -133.5
## read   -133   12.6
## 
## Multivariate Tests: female
##                  Df test stat approx F num Df den Df  Pr(>F)    
## Pillai            1     0.170     19.9      2    194 1.4e-08 ***
## Wilks             1     0.830     19.9      2    194 1.4e-08 ***
## Hotelling-Lawley  1     0.205     19.9      2    194 1.4e-08 ***
## Roy               1     0.205     19.9      2    194 1.4e-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   715  856
## read    856 1026
## 
## Multivariate Tests: math
##                  Df test stat approx F num Df den Df  Pr(>F)    
## Pillai            1      0.16     18.5      2    194 4.6e-08 ***
## Wilks             1      0.84     18.5      2    194 4.6e-08 ***
## Hotelling-Lawley  1      0.19     18.5      2    194 4.6e-08 ***
## Roy               1      0.19     18.5      2    194 4.6e-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   858  901
## read    901  947
## 
## Multivariate Tests: science
##                  Df test stat approx F num Df den Df  Pr(>F)    
## Pillai            1     0.166     19.4      2    194 2.1e-08 ***
## Wilks             1     0.834     19.4      2    194 2.1e-08 ***
## Hotelling-Lawley  1     0.200     19.4      2    194 2.1e-08 ***
## Roy               1     0.200     19.4      2    194 2.1e-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  1106 1277
## read   1277 1476
## 
## Multivariate Tests: socst
##                  Df test stat approx F num Df den Df  Pr(>F)    
## Pillai            1     0.221     27.5      2    194 3.1e-11 ***
## Wilks             1     0.779     27.5      2    194 3.1e-11 ***
## Hotelling-Lawley  1     0.283     27.5      2    194 3.1e-11 ***
## Roy               1     0.283     27.5      2    194 3.1e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Canonical correlation

require(CCA)

## Loading required package: CCA

## Loading required package: fda

## Loading required package: zoo

## Attaching package: 'zoo'

## The following object(s) are masked from 'package:base':
## 
## as.Date, as.Date.numeric

## Attaching package: 'fda'

## The following object(s) are masked from 'package:graphics':
## 
## matplot

## Loading required package: fields

## Loading required package: spam

## Spam version 0.29-3 (2013-04-23) is loaded. Type 'help( Spam)' or 'demo(
## spam)' for a short introduction and overview of this package. Help for
## individual functions is also obtained by adding the suffix '.spam' to the
## function name, e.g. 'help( chol.spam)'.

## Attaching package: 'spam'

## The following object(s) are masked from 'package:base':
## 
## backsolve, forwardsolve

## Loading required package: maps

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

## $cor
## [1] 0.7728 0.0235
## 
## $names
## $names$Xnames
## [1] "read"  "write"
## 
## $names$Ynames
## [1] "math"    "science"
## 
## $names$ind.names
## NULL
## 
## 
## $xcoef
##          [,1]   [,2]
## read  -0.0633 -0.104
## write -0.0492  0.122
## 
## $ycoef
##            [,1]   [,2]
## math    -0.0670  0.120
## science -0.0482 -0.121
## 
## $scores
## $scores$xscores
##           [,1]     [,2]
##   [1,] -0.2636 -0.58956
##   [2,] -1.3042 -0.87790
##   [3,]  1.4945 -1.55654
##   [4,] -0.2492 -2.18757
##   [5,]  0.3690  0.44835
##   [6,]  0.5588  0.75972
##   [7,] -0.1655  0.99033
##   [8,]  1.4869  1.06618
##   [9,] -0.8894 -0.60276
##  [10,] -0.4113 -0.22384
##  [11,] -0.1579 -1.63238
##  [12,] -0.9038  0.99525
##  [13,] -1.6698 -1.27495
##  [14,] -0.6155  1.06280
##  [15,]  0.2493  1.26547
##  [16,]  0.8331  0.60158
##  [17,]  0.3690  0.44835
##  [18,] -0.5098  0.01998
##  [19,] -1.5997 -0.14645
##  [20,]  0.5032 -1.96679
##  [21,] -0.4954 -1.57803
##  [22,] -1.1849  0.12869
##  [23,]  0.7702 -1.32593
##  [24,] -0.4534 -0.90093
##  [25,]  1.3956  0.51099
##  [26,]  1.9302 -0.03100
##  [27,] -1.4099  0.16492
##  [28,]  0.1228  1.05789
##  [29,]  1.2483 -0.94700
##  [30,]  0.4467 -1.04587
##  [31,]  1.7196 -1.59277
##  [32,] -1.4656 -2.56159
##  [33,] -1.5084  0.40874
##  [34,]  1.2271 -0.37369
##  [35,] -0.2920  0.78275
##  [36,] -1.0936  0.68388
##  [37,] -1.0580 -1.48744
##  [38,] -1.2622 -0.20080
##  [39,]  1.4033 -2.11173
##  [40,]  1.9093 -1.28140
##  [41,]  0.6153 -0.16119
##  [42,] -0.4818  0.47138
##  [43,] -0.0458  0.17321
##  [44,]  1.2271 -0.37369
##  [45,] -1.4099  0.16492
##  [46,] -0.4818  0.47138
##  [47,]  0.7702 -1.32593
##  [48,] -1.1144 -0.56653
##  [49,]  0.0243  1.30171
##  [50,] -0.3621 -0.34574
##  [51,] -0.4538  0.92278
##  [52,]  1.8108 -1.03759
##  [53,]  0.9528 -0.21555
##  [54,] -0.9879 -0.35895
##  [55,] -1.7683 -1.03113
##  [56,]  1.5154 -0.30614
##  [57,]  1.7404 -0.34237
##  [58,]  1.3256 -0.61751
##  [59,] -0.8894 -0.60276
##  [60,]  0.4535 -0.02117
##  [61,]  0.4747 -0.59448
##  [62,] -0.1235  1.66743
##  [63,]  0.9528 -0.21555
##  [64,]  2.1272 -0.51863
##  [65,]  0.6717 -1.08211
##  [66,]  1.1005 -0.58127
##  [67,] -0.5519 -0.65712
##  [68,]  1.0093 -1.13646
##  [69,] -0.1999 -2.30948
##  [70,]  1.1150 -2.17928
##  [71,]  0.9528 -0.21555
##  [72,] -0.5519 -0.65712
##  [73,] -2.0145 -0.42159
##  [74,] -1.3042 -0.87790
##  [75,]  0.2077 -1.23534
##  [76,]  0.9600 -1.01455
##  [77,] -0.5803  0.71520
##  [78,] -1.3042 -0.87790
##  [79,]  2.1692  0.15847
##  [80,]  0.9108 -0.89265
##  [81,] -0.9879 -0.35895
##  [82,]  1.2126  1.22432
##  [83,] -1.3042 -0.87790
##  [84,] -1.2834  0.37250
##  [85,]  0.4047 -1.72297
##  [86,] -0.6296  0.83710
##  [87,]  0.5945 -1.41160
##  [88,]  1.3392  1.43190
##  [89,]  1.2135 -2.42310
##  [90,]  0.0107 -0.74770
##  [91,] -0.4398  1.14848
##  [92,] -0.4954 -1.57803
##  [93,] -1.4520 -0.51218
##  [94,]  1.2691  0.30341
##  [95,]  0.9528 -0.21555
##  [96,] -0.3133  1.35606
##  [97,] -1.7895 -0.45782
##  [98,] -1.2834  0.37250
##  [99,]  1.5854  0.82236
## [100,] -1.1849  0.12869
## [101,] -1.3535 -0.75599
## [102,]  0.0243  1.30171
## [103,]  0.6645 -0.28310
## [104,] -0.6432 -1.21231
## [105,] -0.2920  0.78275
## [106,] -0.2356 -0.13816
## [107,] -0.9459  0.31815
## [108,]  1.9654 -0.37861
## [109,]  0.2705  0.69216
## [110,] -1.7895 -0.45782
## [111,] -0.2636 -0.58956
## [112,]  0.6573  0.51590
## [113,] -1.1144 -0.56653
## [114,] -1.5997 -0.14645
## [115,] -1.7190 -1.15304
## [116,]  1.4589  0.61478
## [117,]  0.5236  1.10733
## [118,] -2.0145 -0.42159
## [119,] -0.1935  0.53893
## [120,]  0.9948  0.46155
## [121,] -0.5519 -0.65712
## [122,]  0.1792  0.13697
## [123,]  0.1792  0.13697
## [124,]  0.6645 -0.28310
## [125,] -0.1235  1.66743
## [126,] -0.3833  0.22756
## [127,]  0.7210 -1.20402
## [128,]  0.8259  1.40058
## [129,]  0.3270 -0.22875
## [130,]  2.0287 -0.27481
## [131,] -0.6083  0.26380
## [132,] -0.9038  0.99525
## [133,] -1.4520 -0.51218
## [134,]  0.5868  1.21112
## [135,] -0.8614 -0.15137
## [136,] -2.0073 -1.22059
## [137,]  0.0243  1.30171
## [138,]  0.4323  0.55214
## [139,]  1.4169 -0.06232
## [140,]  0.2005 -0.43633
## [141,]  1.8665  1.68892
## [142,]  0.5868  1.21112
## [143,]  0.8615 -0.77074
## [144,]  0.1228  1.05789
## [145,] -0.2920  0.78275
## [146,]  0.3690  0.44835
## [147,] -0.3133  1.35606
## [148,]  0.5588  0.75972
## [149,]  0.9108 -0.89265
## [150,]  0.3478  1.02165
## [151,]  1.1078 -1.38028
## [152,] -0.8682 -1.17607
## [153,]  0.3758  1.47305
## [154,]  0.2705  0.69216
## [155,] -0.7561  0.62952
## [156,] -1.3042 -0.87790
## [157,] -0.0950  0.29512
## [158,]  0.4391  1.57684
## [159,]  1.3256 -0.61751
## [160,] -1.5717  0.30495
## [161,] -0.1235  1.66743
## [162,] -0.1651 -0.83338
## [163,] -0.0742  1.54552
## [164,] -0.7561  0.62952
## [165,] -0.2920  0.78275
## [166,]  0.9528 -0.21555
## [167,] -0.1655  0.99033
## [168,]  0.7766  1.52249
## [169,] -0.7561  0.62952
## [170,] -0.6576  0.38571
## [171,]  0.4391  1.57684
## [172,]  0.6645 -0.28310
## [173,]  1.4733 -0.98323
## [174,] -0.7981 -0.04757
## [175,]  0.7066  0.39399
## [176,] -1.0371 -0.23704
## [177,] -1.5084  0.40874
## [178,]  0.7766  1.52249
## [179,]  0.1792  0.13697
## [180,] -0.5875  1.51420
## [181,] -0.9459  0.31815
## [182,]  0.7066  0.39399
## [183,] -0.6860  1.75802
## [184,] -0.7773  1.20283
## [185,] -0.5595  1.96560
## [186,] -1.4099  0.16492
## [187,] -0.0458  0.17321
## [188,]  0.7630 -0.52692
## [189,] -1.1356  0.00678
## [190,]  0.4747 -0.59448
## [191,]  0.5868  1.21112
## [192,]  0.8187  2.19959
## [193,]  0.1792  0.13697
## [194,]  0.4038  1.92445
## [195,] -0.2712  2.03316
## [196,] -0.4818  0.47138
## [197,]  0.9808  0.23585
## [198,]  0.2782 -1.93055
## [199,] -0.6296  0.83710
## [200,] -1.2834  0.37250
## 
## $scores$yscores
##            [,1]    [,2]
##   [1,]  1.01398 -0.8128
##   [2,] -0.56166 -1.3052
##   [3,] -0.38744 -0.5807
##   [4,]  0.32264 -0.8172
##   [5,] -0.34719  0.3842
##   [6,] -0.42770 -1.5455
##   [7,]  0.65755 -1.4179
##   [8,]  1.13197  0.6349
##   [9,] -0.38744 -0.5807
##  [10,]  0.13245  0.1461
##  [11,]  0.05471 -0.3367
##  [12,] -0.42770 -1.5455
##  [13,] -1.67087  1.0991
##  [14,] -0.44367  0.1424
##  [15,]  1.18299  2.2027
##  [16,]  0.73529 -0.9351
##  [17,]  0.19943  0.0260
##  [18,] -0.78934  0.1402
##  [19,] -0.77858  0.7431
##  [20,] -0.34719  0.3842
##  [21,]  0.49930 -3.8305
##  [22,] -2.46945  0.2499
##  [23,]  0.36012 -1.2993
##  [24,] -0.73311 -0.5829
##  [25,]  1.13197  0.6349
##  [26,]  1.06499  0.7550
##  [27,] -1.33596  0.4984
##  [28,] -0.58839 -0.2202
##  [29,]  0.86404  1.1155
##  [30,]  0.09219 -0.8187
##  [31,] -0.05774  1.1095
##  [32,] -1.34671 -0.1045
##  [33,] -1.37621 -0.4665
##  [34,] -1.26376 -1.9126
##  [35,] -0.26423 -1.4239
##  [36,] -0.80009 -0.4627
##  [37,] -2.18000  0.9752
##  [38,] -1.71112  0.1343
##  [39,]  1.34368  0.8774
##  [40,]  1.46689  0.0342
##  [41,]  1.25518 -0.2083
##  [42,] -0.92330  0.3805
##  [43,] -0.44367  0.1424
##  [44,]  0.73529 -0.9351
##  [45,] -0.22675 -1.9059
##  [46,] -1.52093 -0.8291
##  [47,]  1.05146 -1.2948
##  [48,] -1.70037  0.7372
##  [49,] -0.74908  1.1051
##  [50,] -0.19171  1.3498
##  [51,] -0.80808  0.3812
##  [52,]  1.21493 -1.1732
##  [53,] -0.47040  1.2274
##  [54,]  0.09219 -0.8187
##  [55,] -2.19076  0.3723
##  [56,]  1.82609  2.0863
##  [57,]  1.62237  0.9998
##  [58,]  0.71378 -2.1410
##  [59,] -0.45442 -0.4605
##  [60,]  0.42189  0.8715
##  [61,]  0.21540 -1.6619
##  [62,] -1.38697 -1.0694
##  [63,]  1.77507  0.5185
##  [64,]  1.54463  0.5170
##  [65,]  0.94178  1.5983
##  [66,]  0.93624 -1.2956
##  [67,] -0.64462  0.5029
##  [68,]  0.85329  0.5125
##  [69,] -1.06004 -0.8261
##  [70,]  0.62284  0.5110
##  [71,]  1.06499  0.7550
##  [72,] -0.65537 -0.1001
##  [73,] -1.76735  0.8573
##  [74,] -1.42722 -2.0343
##  [75,]  0.14842 -1.5418
##  [76,]  0.97650 -0.3307
##  [77,]  0.04672  0.5073
##  [78,] -0.76261 -0.9448
##  [79,]  1.06499  0.7550
##  [80,]  0.38441  1.3535
##  [81,] -0.44367  0.1424
##  [82,] -0.53216 -0.9433
##  [83,] -1.91207  0.4947
##  [84,] -0.22675 -1.9059
##  [85,]  1.22568 -0.5702
##  [86,] -1.29847  0.0163
##  [87,]  0.05471 -0.3367
##  [88,]  1.38915 -0.4486
##  [89,]  1.70809  0.6386
##  [90,] -1.00104 -0.1023
##  [91,] -0.66059  2.1908
##  [92,] -0.43845 -2.1485
##  [93,] -1.65490 -0.5888
##  [94,]  0.42189  0.8715
##  [95,]  0.67907 -0.2120
##  [96,] -1.09752 -0.3441
##  [97,] -1.97905  0.6148
##  [98,] -2.05679  0.1320
##  [99,]  1.46689  0.0342
## [100,] -1.53690  0.8588
## [101,] -1.58792 -0.7090
## [102,] -0.90733 -1.3075
## [103,]  1.15349  1.8408
## [104,] -0.00152  0.3864
## [105,] -0.46518 -1.0635
## [106,] -0.41938  2.7952
## [107,] -0.87229  1.9483
## [108,]  0.88800 -1.4164
## [109,]  0.53435 -0.5747
## [110,] -1.39218  1.2215
## [111,]  0.40559 -2.6253
## [112,]  1.39991  0.1543
## [113,] -0.00950  1.2304
## [114,] -0.70361 -0.2210
## [115,] -0.44367  0.1424
## [116,]  1.52311 -0.6889
## [117,] -0.30970 -0.0979
## [118,] -0.92330  0.3805
## [119,] -1.05727  0.6208
## [120,]  1.46689  0.0342
## [121,]  0.26641 -0.0941
## [122,]  0.53435 -0.5747
## [123,]  0.59611  1.5960
## [124,]  0.22893  0.3879
## [125,]  1.37318  1.2393
## [126,] -0.52141 -0.3404
## [127,]  0.89077  0.0305
## [128,] -0.00152  0.3864
## [129,]  0.00924  0.9894
## [130,]  1.88231  1.3632
## [131,] -0.00152  0.3864
## [132,] -1.40017  2.0655
## [133,] -0.13548  0.6267
## [134,]  0.61208 -0.0919
## [135,]  0.62284  0.5110
## [136,] -1.22350 -0.9478
## [137,] -0.38744 -0.5807
## [138,]  0.22094  1.2319
## [139,]  1.79104 -1.1695
## [140,]  0.62284  0.5110
## [141,]  1.02474 -0.2098
## [142,]  0.26641 -0.0941
## [143,]  0.66310  1.4759
## [144,]  0.68982  0.3909
## [145,] -0.41417  0.5043
## [146,]  0.83177 -0.6934
## [147,]  0.62806 -1.7798
## [148,]  1.02474 -0.2098
## [149,]  1.01675  0.6342
## [150,]  1.44016  1.1192
## [151,]  1.12122  0.0320
## [152,] -0.85632  0.2603
## [153,]  0.93624 -1.2956
## [154,]  0.18868 -0.5769
## [155,] -0.52141 -0.3404
## [156,] -0.71160  0.6230
## [157,]  0.07345 -0.5777
## [158,]  0.34415  0.3887
## [159,]  1.18820 -0.0882
## [160,] -1.40294  0.6185
## [161,] -0.07926 -0.0964
## [162,]  0.21817 -0.2150
## [163,] -0.42770 -1.5455
## [164,] -1.73785  1.2193
## [165,]  0.15918 -0.9389
## [166,]  1.41865 -0.0867
## [167,] -0.46518 -1.0635
## [168,]  1.14795 -1.0530
## [169,] -0.84556  0.8633
## [170,]  0.05471 -0.3367
## [171,]  0.60133 -0.6948
## [172,]  1.14795 -1.0530
## [173,]  1.71885  1.2416
## [174,] -1.06802  0.0178
## [175,]  1.39192  0.9983
## [176,] -0.93129  1.2245
## [177,] -0.84556  0.8633
## [178,] -0.14624  0.0238
## [179,]  0.21540 -1.6619
## [180,] -0.69286  0.3820
## [181,]  0.33340 -0.2143
## [182,]  0.93103  0.9953
## [183,] -0.82959 -0.8247
## [184,] -0.06850  0.5066
## [185,] -1.57716 -0.1060
## [186,] -1.05727  0.6208
## [187,] -0.21322  0.1439
## [188,]  1.18820 -0.0882
## [189,] -0.37668  0.0223
## [190,] -0.07926 -0.0964
## [191,]  1.25518 -0.2083
## [192,]  0.80228 -1.0553
## [193,] -0.17574 -0.3381
## [194,]  1.57413  0.8789
## [195,] -0.40341  1.1073
## [196,]  0.51837  1.1132
## [197,]  1.74558  0.1566
## [198,] -0.44367  0.1424
## [199,] -0.65537 -0.1001
## [200,] -0.88305  1.3453
## 
## $scores$corr.X.xscores
##         [,1]   [,2]
## read  -0.927 -0.375
## write -0.854  0.520
## 
## $scores$corr.Y.xscores
##           [,1]    [,2]
## math    -0.718  0.0087
## science -0.675 -0.0114
## 
## $scores$corr.X.yscores
##         [,1]     [,2]
## read  -0.717 -0.00879
## write -0.660  0.01222
## 
## $scores$corr.Y.yscores
##           [,1]   [,2]
## math    -0.929  0.371
## science -0.873 -0.487

Factor analysis

require(psych)

fa(r = cor(model.matrix(~read + write + math + science + socst - 1, data = hsb2)), rotate = "none", fm = "pa", 2)
## Factor Analysis using method =  pa
## Call: fa(r = cor(model.matrix(~read + write + math + science + socst - 
##     1, data = hsb2)), 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 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

Principal components analysis

princomp(formula = ~read + write + math + science + socst, data = hsb2)
## Call:
## princomp(formula = ~read + write + math + science + socst, data = hsb2)
## 
## 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.

Cite this article

stats writer (2024). What statistical analysis should I use in R?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/what-statistical-analysis-should-i-use-statistical-analyses-using-r/

stats writer. "What statistical analysis should I use in R?." PSYCHOLOGICAL SCALES, 28 Jun. 2024, https://scales.arabpsychology.com/stats/what-statistical-analysis-should-i-use-statistical-analyses-using-r/.

stats writer. "What statistical analysis should I use in R?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/what-statistical-analysis-should-i-use-statistical-analyses-using-r/.

stats writer (2024) 'What statistical analysis should I use in R?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/what-statistical-analysis-should-i-use-statistical-analyses-using-r/.

[1] stats writer, "What statistical analysis should I use in R?," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, June, 2024.

stats writer. What statistical analysis should I use in R?. PSYCHOLOGICAL SCALES. 2024;vol(issue):pages.

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