The Real Statistics **T Tests and Non-parametric Equivalents** data analysis tool supports the Mann-Whitney and Wilcoxon Signed-Ranks tests, while the **One Factor ANOVA** data analysis tool supports the Kruskal-Wallis non-parametric test. We now describe another data analysis tool which provides access to a number of non-parametric tests.

**Real Statistics Data Analysis Tool**: The Real Statistics Resource Pack provides the **Non-parametric Tests** data analysis tool which supports the following tests:

- Friedman’s Test
- One-Sample Runs Test
- Two-Sample Runs Test
- Two Sample Kolmogorov-Smirnov Test
- Cochran’s Q Test
- Moods’ Median Test
- Mann-Whitney Test
- Wilcoxon Signed-Ranks Test
- Kruskal-Wallis Test

These include the two sample version of the Moods’ Median Test and McNemar’s Test, which is the two sample version of Cochran’s Q Test.

We now show how to perform Example 1 of Two Sample Kolmogorov-Smirnov Test using the **Other Non-parametric Tests** data analysis tool.

Press **Ctrl-m** and double click on the **Other Non-parametric Tests** from the menu. Fill in the dialog box that appears as shown in Figure 1.

**Figure 1 – Non-parametric Tests data analysis tool**

Upon clicking on the **OK** button the output shown in range E3:F11 of Figure 2 appears.

**Figure 2 – Two Sample KS Test**

In this example the input data (range A3:C13) is in the form of a frequency table. The data analysis tool can also be used with data in raw format using the **Kolmogorov-Smirnov** (**raw**) option from Figure 1.

We next repeat Example 2 of McNemar’s Test using the **Non-parametric Tests** data analysis tool. In this example 1,000 people were surveyed with 705 in favor and 295 against a motion. After they listened to a debate 73 people changed their vote from against to in favor and 115 changed their vote from in favor to against. We want to test whether the debate affected peoples’ opinions.

We code the input data as shown in range A3:C8 of Figure 3, where 1 means in favor of the motion and 0 means against the motion.

**Figure 3 – McNemar’s Test**

We perform the test by pressing **Ctrl-m** and selecting the **Other Non-parametric Tests** data analysis tool from the menu. This time when the dialog shown in Figure 1 appears we insert A3:C7 in the **Input Range** (see Figure 3) and choose the **Cochran’s Q Test (freq) **option. The output appears on the right side of Figure 3.

The output is similar to that shown in Figure 1 of McNemar’s Test, except that the 0.5 correction factor is not employed in this version of the test.

**Observation**: To access the **Mann-Whitney** or **Wilcoxon Signed Ranks** test simply choose the appropriate option from the dialog box shown in Figure 1 and press the **OK **button (don’t fill in any other fields). You will then be redirected to the **T Test and Non-parametric Equivalents** data analysis tool, where you can further describe the test that you want.

Similarly, to access the **Kruskal-Wallis** test, choose this option and press the** OK** button without filling in any other fields and you will be redirected to the **Anova: Single Factor **data analysis tool to complete the test.

**Observation**: When choosing the **Two-Sample Runs Test with Ties** option, the number of distinct columns in the output is not completely determined. The software will assume there are 5 columns (plus one column for labels). If this is more than necessary then any unused columns will be filled with the values #N/A. If 5 isn’t enough, you will need to manually expand the range in the output which contains the array formula of form =RUNS2TEST(R1, R2, TRUE, 100) and press **Ctrl-Shft-Enter**. See Two-Sample Runs Test for more information about this formula.

Similarly if you want to use a number of iterations different from 100, you will need to highlight the =RUNS2TEST(R1, R2, TRUE, 100) formula in the formula bar, change the number of iterations and press **Ctrl-Shft-Enter**.

Hi,

Thank you very much for the available information. It is so helpful.

I got some issues with my research. My data is a paired dependent sample means I analyze the difference of the variable before and after implementation of a particular condition. However, this variable is an ordinal data. I rank the data from level 1 to level 10. I would like to analyze whether after the implementation the variable decreased or not. For example stress level before and after.

How I use data analysis package in excel for analyzing this variable? I checked for paired sample, there is only a paired t-test tool which is used for ratio data. I think I can’t use this tool for analyzing the condition of mentioned variable, is that right? If so, Can you recommend me how to analyze this particular data using excel?

Thank you very much. I hope you can help me.

If you believe that the rankings are evenly spaced; e.g. 5 is the same units above 1 as 10 is above 6, then you can assume that the data is interval data and so can use a paired t test (provided the other assumptions are met).

Charles

Please I need guide how to run a Data base on Statistical and Trend Analysis of Rainfall by Using non Parametric

Nass, Sorry but I don’t understand your question.

Charles

Hi,

So happy I found this page!! I am also conducting a survey study with Likert scale, my problem is:

1.) when I have made a regression calculation in SPSS, I have read one should pay attention to the statistical significans..however, I do not have any hypothesis. My research Q’s are formed to investigate the impact of one factor on another. Should I ignore tha stat significance then?

2.) I have both symmetrical and skewed data, how do I handle this? I am assuming that I can use these variables in a correlation?

3) Just to be clear, every factor in the questionnaire is one variable?

Many Thanks for your help!!

Kr’s

Hana,

1. Statistical significance in regression tests whether the regression model (or some part of the model such as a coefficient) fits the data. If the model is not a good fit, then any conclusion you make won’t be worth much.

2. It really depends on what you are trying to as to whether or not it is necessary to have data which is symmetric. In any case, when symmetry or normality is required, often you can transform the data to meet the assumption or use some other test which doesn’t require this assumption (e.g. a non-parametric test).

3. Not necessarily, although you can certainly view each question as representing one variable.

Charles

Sir Thank you very much for information on your website.

I am doing questionnaire survey with 5-point likert scale on 22 factors and my sample size is very small like 10 respondents from 2 diff groups which I want to analyze with statistical method can you please suggest some method i tried doing it with mann whitney u test but p-value is coming too small.

Shweta,

You probably shouldn’t expect too much (esp. regarding statistical power) from such a small sample. But in any case, what do you mean that the p-value is too small?

Charles