Author: Keon-Woong Moon
Date: 2020-01-26

# Plot for distribution of common statistics and p-value

#### Keon-Woong Moon

#### 2020-01-26

To understand the concept of p value is very important. To teach the the distribution of common statistic( \(\chi^2\) for chisq.test() , t for Student’s t-test , F for F-test) and concept of the p-value, plot.htest() function can be used.

## Package Installation

You can install this package form the github. Currently, package `webr` is under construction and consists of only one function - plot.htest().

    #install.packages("devtools")
    devtools::install_github("cardiomoon/webr")

## Coverage of plot.htest()

The plot.htest() function is a S3 method for class “htest”. Currently, this function covers Welch Two Sample t-test, Pearson’s Chi-squared test, Two Sample t-test, One Sample t-test, Paired t-test and F test to compare two variances.

## For Chi-squared Test

You can show the distribution of chi-squre statistic and p-value.

     require(moonBook)
     require(webr)

     # chi-squared test
     x=chisq.test(table(acs$sex,acs$DM))
     x

        Pearson's Chi-squared test with Yates' continuity correction

    data:  table(acs$sex, acs$DM)
    X-squared = 3.1296, df = 1, p-value = 0.07688

     plot(x)

## For one sample t-test

You can show the distribution of t-statistic and p-value in one sample t-test.

    t.test(acs$age,mu=63)

        One Sample t-test

    data:  acs$age
    t = 0.77978, df = 856, p-value = 0.4357
    alternative hypothesis: true mean is not equal to 63
    95 percent confidence interval:
     62.52736 64.09574
    sample estimates:
    mean of x
     63.31155

    plot(t.test(acs$age,mu=63))

## Student t-test to compare means for two independent samples

Before performing a t-test, you have to compare two variances.

### F test to compare two variances

    x=var.test(age~DM,data=acs)
    x

        F test to compare two variances

    data:  age by DM
    F = 1.2383, num df = 552, denom df = 303, p-value = 0.0376
    alternative hypothesis: true ratio of variances is not equal to 1
    95 percent confidence interval:
     1.012416 1.505776
    sample estimates:
    ratio of variances
              1.238288

    plot(x)

### Use for Two Sample t-test for independence samples

Based on the result of var.test(), you can perform t.test with default option(var.equal=FALSE).

    x=t.test(age~DM,data=acs)
    x

        Welch Two Sample t-test

    data:  age by DM
    t = 0.58982, df = 682.36, p-value = 0.5555
    alternative hypothesis: true difference in means is not equal to 0
    95 percent confidence interval:
     -1.112568  2.068014
    sample estimates:
     mean in group No mean in group Yes
             63.48101          63.00329

    plot(x)

## Student t-test using pooled variance

To compare means of body-mass index between male and female patients, perform F test first.

    var.test(BMI~sex,data=acs)

        F test to compare two variances

    data:  BMI by sex
    F = 1.2078, num df = 254, denom df = 508, p-value = 0.07756
    alternative hypothesis: true ratio of variances is not equal to 1
    95 percent confidence interval:
     0.9794315 1.5008098
    sample estimates:
    ratio of variances
              1.207759

    plot(var.test(BMI~sex,data=acs))

Based on the result of F test, you can perform t-test using pooled variance.

    x=t.test(BMI~sex,data=acs,var.equal=TRUE)
    x

        Two Sample t-test

    data:  BMI by sex
    t = -0.50823, df = 762, p-value = 0.6114
    alternative hypothesis: true difference in means is not equal to 0
    95 percent confidence interval:
     -0.6348532  0.3737344
    sample estimates:
    mean in group Female   mean in group Male
                24.19492             24.32548

    plot(x)

## Paired t-test

You can show the distribution of t-statistic and p-value in paired t-test.

    x=t.test(iris$Sepal.Width,iris$Petal.Width,paired=TRUE)
    plot(x)

## Options for t-test

You can change the options of t.test.

    x=t.test(BMI~sex, data=acs,conf.level=0.99,alternative="greater",var.equal=TRUE)
    plot(x)