Data Analysis Tools for Non-parametric Tests

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:

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.

Non-parametric dialog box

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.

Two sample KS analysis

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.

McNemar's data analysis

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.

6 Responses to Data Analysis Tools for Non-parametric Tests

  1. Nass says:

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

  2. Hana says:

    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

    • Charles says:

      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

  3. Shweta says:

    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.

    • Charles says:

      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

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