## inferr: Inferential statistics with R

Author: Aravind Hebbali

## Overview

Inferential statistics allows us to make generalizations about populations using data drawn from the population. We use them when it is impractical or impossible to collect data about the whole population under study and instead, we have a sample that represents the population under study and using inferential statistics technique, we make generalizations about the population from the sample.

The inferr package:

• builds upon the statistical tests provided in stats
• provides additional and flexible input options
• more detailed and structured test results

As of version 0.1, inferr includes a select set of parametric and non-parametric statistical tests which are listed below:

• One Sample t Test
• Paired Sample t Test
• Independent Sample t Test
• One Sample Proportion Test
• Two Sample Proportion Test
• One Sample Variance Test
• Two Sample Variance Test
• Binomial Test
• ANOVA
• Chi Square Goodness of Fit Test
• Chi Square Independence Test
• Levene’s Test
• Cochran’s Q Test
• McNemar Test
• Runs Test for Randomness

## Installation

# install inferr from CRAN
install.packages("inferr")

# the development version from github
# install.packages("devtools")
devtools::install_github("rsquaredacademy/inferr")

## Shiny App

Use launch_inferr() to explore the package using a shiny app.

## Usage

ttest(hsb$write, mu = 50, type = 'all') #> One-Sample Statistics #> --------------------------------------------------------------------------------- #> Variable Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] #> --------------------------------------------------------------------------------- #> write 200 52.775 0.6702 9.4786 51.4537 54.0969 #> --------------------------------------------------------------------------------- #> #> Ho: mean(write) ~=50 #> #> Ha: mean < 50 Ha: mean ~= 50 Ha: mean > 50 #> t = 4.141 t = 4.141 t = 4.141 #> P < t = 1.0000 P > |t| = 0.0001 P > t = 0.0000 ##### ANOVA owanova(hsb, 'write', 'prog') #> ANOVA #> ---------------------------------------------------------------------- #> Sum of #> Squares DF Mean Square F Sig. #> ---------------------------------------------------------------------- #> Between Groups 3175.698 2 1587.849 21.275 0.0000 #> Within Groups 14703.177 197 74.635 #> Total 17878.875 199 #> ---------------------------------------------------------------------- #> #> Report #> ----------------------------------------- #> Category N Mean Std. Dev. #> ----------------------------------------- #> 1 45 51.333 9.398 #> 2 105 56.257 7.943 #> 3 50 46.760 9.319 #> ----------------------------------------- #> #> Number of obs = 200 R-squared = 0.1776 #> Root MSE = 8.6392 Adj R-squared = 0.1693 ##### Chi Square Test of Independence chisq_test(as.factor(hsb$female), as.factor(hsb$schtyp)) #> Chi Square Statistics #> #> Statistics DF Value Prob #> ---------------------------------------------------- #> Chi-Square 1 0.0470 0.8284 #> Likelihood Ratio Chi-Square 1 0.0471 0.8282 #> Continuity Adj. Chi-Square 1 0.0005 0.9822 #> Mantel-Haenszel Chi-Square 1 0.0468 0.8287 #> Phi Coefficient 0.0153 #> Contingency Coefficient 0.0153 #> Cramer's V 0.0153 #> ---------------------------------------------------- ##### Levene’s Test levene_test(hsb$read, group_var = hsb$race) #> Summary Statistics #> Levels Frequency Mean Std. Dev #> ----------------------------------------- #> 1 24 46.67 10.24 #> 2 11 51.91 7.66 #> 3 20 46.8 7.12 #> 4 145 53.92 10.28 #> ----------------------------------------- #> Total 200 52.23 10.25 #> ----------------------------------------- #> #> Test Statistics #> ------------------------------------------------------------------------- #> Statistic Num DF Den DF F Pr > F #> ------------------------------------------------------------------------- #> Brown and Forsythe 3 196 3.44 0.0179 #> Levene 3 196 3.4792 0.017 #> Brown and Forsythe (Trimmed Mean) 3 196 3.3936 0.019 #> ------------------------------------------------------------------------- ##### Cochran’s Q Test cochran_test(exam) #> Test Statistics #> ---------------------- #> N 15 #> Cochran's Q 4.75 #> df 2 #> p value 0.093 #> ---------------------- ##### McNemar Test himath <- ifelse(hsb$math > 60, 1, 0)
#>            Controls
#> ---------------------------------
#> Cases       0       1       Total
#> ---------------------------------
#>   0        135      21        156
#>   1         18      26         44
#> ---------------------------------
#> Total      153      47        200
#> ---------------------------------
#>
#>        McNemar's Test
#> ----------------------------
#> McNemar's chi2        0.2308
#> DF                         1
#> Pr > chi2              0.631
#> Exact Pr >= chi2      0.7493
#> ----------------------------
#>
#>        Kappa Coefficient
#> --------------------------------
#> Kappa                     0.4454
#> ASE                        0.075
#> 95% Lower Conf Limit      0.2984
#> 95% Upper Conf Limit      0.5923
#> --------------------------------
#>
#> Proportion With Factor
#> ----------------------
#> cases             0.78
#> controls         0.765
#> ratio           1.0196
#> odds ratio      1.1667
#> ----------------------

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