The Sign Test for Paired Samples is a non-parametric analysis that uses plus and minus signs to evaluate whether there is a significant difference between two paired samples. In situations where the data do not meet the normality assumptions required for the Paired T-Test, the Sign Test offers a robust alternative. Using SmartstatXL, this analysis can be easily performed, providing valuable insights into differences between two different conditions or time periods within the same sample.
Example Case
Taken from: Handbook of Parametric and Nonparametric Statistical Procedures, Fifth Edition by David J. Sheskin
Example 18.1
A psychologist conducts research to determine whether people display more emotionality when exposed to sexually explicit words compared to when they are exposed to neutral words. Each of the ten subjects is shown a list of 16 randomly arranged words, projected onto a screen one at a time for a period of five seconds. Eight of the words on the list are sexually explicit, and the other eight are neutral. As each word is projected onto the screen, subjects are instructed to quietly say the word to themselves. While the subjects do this, a sensor attached to the palm of their hand records the galvanic skin response (GSR), which the psychologist uses as a measure of emotionality. The psychologist calculates two scores for each subject, one score for each experimental condition: Condition 1: GSR/Explicit — Average GSR score for the eight sexually explicit words; Condition 2: GSR/Neutral — Average GSR score for the eight neutral words. The GSR/Explicit and GSR/Neutral scores for the ten subjects are as follows. (The higher the score, the higher the level of emotionality.) Subject 1 (9, 8); Subject 2 (2, 2); Subject 3 (1, 3); Subject 4 (4, 2); Subject 5 (6, 3); Subject 6 (4, 0); Subject 7 (7, 4); Subject 8 (8, 5); Subject 9 (5, 4); Subject 10 (1, 0). Do subjects display differences in emotionality with reference to the two categories of words?
Analysis Steps
Here are the steps for the Sign Test for Paired Samples and further tests (PostHoc) using SmartstatXL, Excel Add-in:
- Activate the worksheet (Sheet) to be analyzed.
- Place the cursor on the dataset (to create a dataset, see the Data Preparation method). Datasets can be arranged in two layouts:
- Grouped by level (comparison between levels)
- Grouped by variable (comparison between variables)
- If the active cell is not on the dataset, SmartstatXL will automatically attempt to determine the dataset.
- Activate the SmartstatXL Tab
- Click the Non-Parametric menu. SmartstatXL will display a dialog box to ensure whether the dataset is correct or not (usually the cell address of the dataset is automatically selected correctly).
- If it is correct, click the Next Button
- Next, the Non-Parametric Test dialog box will appear:
- If the layout of the data used is based on a comparison between variables, the following dialog box will appear:
- Next, press the "OK" button
Analysis Results
Here is the Analysis Output for the Sign Test (Paired Samples):
Statistical Summary
Based on the analysis, it was found that 8 out of 10 subjects showed an increase in emotionality (indicated by the "+" sign) when exposed to sexually explicit words compared to neutral words, while only 1 out of 10 subjects showed a decrease in emotionality (indicated by the "-" sign).
The p-value obtained from the binomial approach is 0.039, while the normal approach yields a p-value of 0.046. Both of these p-values are less than 0.05, indicating that the results are significant at the 5% significance level.
Thus, based on the analyzed data, we can conclude that there is a significant difference in the emotionality of subjects when they are exposed to sexually explicit words compared to neutral words. This suggests that sexually explicit words affect the level of emotionality in subjects more than neutral words do.
Average Comparison
Table of average values, Mean Rank, Sum Rank, and Post hoc Test
From this data, we can see the average comparison of the emotional scores of subjects when exposed to sexually explicit words (Condition 1) and neutral words (Condition 2).
The average emotional score for Condition 1 is 4.70, while for Condition 2 it is 3.10. This suggests that subjects tend to have a higher level of emotionality when exposed to sexually explicit words compared to neutral words.
Thus, based on this average comparison, we can confirm that sexually explicit words affect the level of emotionality in subjects more than neutral words do. This is consistent with the statistical test results showing a significant difference between the two conditions.
