# A non-parametric test for comparing variables belonging to the same group

#### mostafaibraheem

##### New Member
Situation:
I have a cell-plot chart (showing the means and standard deviations) of 9 domestic activities across a sample of 17 dwellings all belonging to one group (the same group).
The type of data is ordinal (ranking values). The purpose of this representation is to compare the relative ranking of 9 activities in relation to each other across the entire sample of 17 dwellings.
Request:
Kindly advise me on a non-parametric statistical test in order to compare the cell plots of just two (any two) of these activities against each other to find out whether there is a significant difference between them in terms of their ranking values (based on their means and standard deviations). My null hypothesis would be that there is no difference between the two compared activities.

Mostafa.

#### Bukenya Ivan

##### New Member
Hi Mostafa,
Kindly gid around these two Non-parametric tests;
Since your data is Ordinal, then consider
Kruskal-Wallis test OR Spearman's Rank Correlation.

#### Karabiner

##### TS Contributor
As far as I can see, you'll need the original values, not means and standard deviations.

Speaking in terms of a spreadsheet, then you have 17 cases (dwellings) i.e. 17 lines.
And you have 9 variables (activities) i.e. 9 columns.

Within the cells of this datasheet you have the rank of each activity in each dwelling.

You can globally compare the ranking of activities using the Fredman test, or pairwise
using the sign test.

With kind regards

Karabinber

#### mostafaibraheem

##### New Member
Thanks Karabiner,
Looking into the sign test, I am somehow confused about the fulfillment of some of the test assumptions.
A) first of all, in my situation, I am not sure about the types of variables I am using here. Is my dependant variable here the inhabitants' dwellings, and my independent variables the activities?
B) Secondly, how is the 2nd assumption fulfilled? [" ... the independent variable should consist of two categorical, 'related groups' or 'matched pairs'. 'Related groups' indicates that the same subjects are present in both groups"] (https://statistics.laerd.com/spss-tutorials/sign-test-using-spss-statistics.php).
Is this assumption fulfilled because - in principle - I have a respective rank value for each activity across the entire dwelling sample, although I am using this test here to compare the rankings of two different activities across the entire dwelling sample?
C) Also concerned about the 4th assumption; correct me if I am wrong: although my data is 'ordinal', the variable itself is treated as 'continuous' and in such respect the 4th assumption is fulfilled?

Thank you for your time and support

#### Karabiner

##### TS Contributor
Could you please describe in detail your study design and how data were collected?

With kind regards

Karabiner

#### mostafaibraheem

##### New Member
Could you please describe in detail your study design and how data were collected?

With kind regards

Karabiner
Sure Karabiner. I will explain this concisely below:

Across a sample of 17 selected dwellings, I have assessed various encounters/interactions between 9 different activities using a method I developed. Results were collected once, and there is no follow-up assessment. I was able to rank activities in terms of their degree of encounter/interaction for each dwelling, and across the entire sample. The latter I represented in the form of a cell-plot chart showing the mean and standard deviation for each activity across the entire sample. I did the same for another dwelling sample featuring the same activities. I was then able to compare activities across both samples by means of the non-parametric Mann Whitney U test where I was able to assess which of these activities have changed significantly (by referring to p values) and at the same time indicating which sample had increased or deceased in comparison to the other (by comparing the sum of mean ranks of each of the compared activities). Before conducting the Mann Whitney U test, I used the Friedman test to initially check that the variation of activities within each of the two investigated samples were not random.
Now the questions I have posed recently (2 days ago) were related to comparing the ranking values of any pair of activities within the same (only one) dwelling sample. I am not asking about comparing activities across different dwelling samples; this I have already completed. Now in spite of being able to visually compare ranking values of activities from different cell-plot charts by looking at the mean and standard deviations of its ranking values of interaction within one sample, I wanted to find an appropriate statistical method to indicate whether there is a statistically significant difference between these ranking values across any pair of activities in the same sample. Following your previous suggestion, I then attempted to use the sign test method, but came up with some queries and questions that I have outlined in my previous post; some of which are related to the fulfillment of the test assumptions as a condition for applying the sign test.
I look forward to your responses upon my previously posed questions.

Thank you for your time and support.

#### Karabiner

##### TS Contributor
Ok, then indeed the sign test can be used for pairwise comparisons.

meddles the Wilcoxon signed rank test with the sign test, which are markedly different tests. The upper part,
with the assumption #1 to #4 refers to the Wilcoxon signed rank test (which is inappropriate in your case,
due to #1). Only the last part refers to the sign test.

By the way, Laird statistic's claim that the sign test or the Wilcoxon signed rank test are about medians is wrong.

With kind regards

Karabiner

#### mostafaibraheem

##### New Member
Ok, then indeed the sign test can be used for pairwise comparisons.

meddles the Wilcoxon signed rank test with the sign test, which are markedly different tests. The upper part,
with the assumption #1 to #4 refers to the Wilcoxon signed rank test (which is inappropriate in your case,
due to #1). Only the last part refers to the sign test.

By the way, Laird statistic's claim that the sign test or the Wilcoxon signed rank test are about medians is wrong.

With kind regards

Karabiner
Good morning Karbiner,
I am impressed by your sincerity and capacity for support. Will not hesitate to contact you (provided you are available) should I have any further statistical issues in the future.
Thank you for your valuable time, support, and prompt response.

Much appreciated

Mostafa Ibraheem