 ## Summary and Analysis of Extension Program Evaluation in R

Salvatore S. Mangiafico

# Sign Test for One-sample Data

The one-sample sign test compares the number of observations greater than or less than the default value without accounting for the magnitude of the difference between each observation and the default value.  The test is similar in purpose to the one-sample Wilcoxon signed-rank test, but looks specifically at the median value, and is not affected by the distribution of the data.

The test is conducted with the SIGN.test function in the BSDA package or the SignTest function in the DescTools package.  These functions produce a p-value for the hypothesis, as well as the median and confidence interval of the median for the data.

##### Appropriate data

•  One-sample data

•  Data are ordinal, interval, or ratio

##### Hypotheses

•  Null hypothesis:  The median of the population from which the sample was drawn is equal to the default value.

•  Alternative hypothesis (two-sided): The median of the population from which the sample was drawn is not equal to the default value.

##### Interpretation

Reporting significant results as e.g. “Likert scores were significantly different from a default value of 3” is acceptable.  As is e.g. “Median Likert scores were significantly different from a default value of 3”

### Packages used in this chapter

The packages used in this chapter include:

•  BSDA

•  DescTools

The following commands will install these packages if they are not already installed:

if(!require(BSDA)){install.packages("BSDA")}
if(!require(DescTools)){install.packages("DescTools")}

### One-sample sign test example

For appropriate plots and data frame checking, see the One-sample Wilcoxon Signed-rank Test chapter.

Input =("
Speaker           Rater     Likert
'Maggie Simpson'   1         3
'Maggie Simpson'   2         4
'Maggie Simpson'   3         5
'Maggie Simpson'   4         4
'Maggie Simpson'   5         4
'Maggie Simpson'   6         4
'Maggie Simpson'   7         4
'Maggie Simpson'   8         3
'Maggie Simpson'   9         2
'Maggie Simpson'  10         5
")

###  Check the data frame

library(psych)

str(Data)

summary(Data)

### Remove unnecessary objects

rm(Input)

### Sign test with the BSDA package

Note that Data\$Likert is the one-sample data, and md=3 indicates the default value to compare to.

library(BSDA)

SIGN.test(Data\$Likert,
md = 3)

One-sample Sign-Test

s = 7, p-value = 0.07031

alternative hypothesis: true median is not equal to 3

### Note the p-value in the output above

95 percent confidence interval:
3.000000 4.675556

sample estimates:
median of x
4

### Median value and confidence interval

### Sign test with the DescTools package

Note that Data\$Likert is the one-sample data, and mu=3 indicates the default value to compare to.

library(DescTools)

SignTest(Data\$Likert,
mu = 3)

One-sample Sign-Test

S = 7, number of differences = 8, p-value = 0.07031

### Note the p-value in the output above

alternative hypothesis: true median is not equal to 3

97.9 percent confidence interval:
3 5

sample estimates:
median of the differences
4

### Median value and confidence interval