# Which test (my goodness) shall I apply, please?

#### Libor

##### New Member
Can you pleaase kindly help me with my scholarly article? (I spent lots of time by solving this issue - to no avail):
I observed whether (and to what extent) the 52 SAME companies use their capacities across the years 2006, 2010, 2014, 2018.
-----
Here are the counts of companies (categorized by the extent of usage):
2006: none(35) partial(15) full(2) (=52 total)
2010: none(36) partial(11) full(5) (=52 total)
2014: none(26) partial(5) full(21 (=52 total)
2018: none(17) partial(3) full(32) (=52 total)
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(Explanation: In 2006, 35 companies did not use their capacities, 15 companies used their capacities only partially, and 2 companies used their capacities fully etc.
BUT: In 2010, observing the SAME COMPANIES as in the year 2006, 36 companies did not use their capacities, 11 companies used them only partially and 5 companies used them fully)

I want to ascertain whether the usage ACROSS the years has (significantly) changed.

Questions:
1) What statistical test shall I apply?
(categorical variables, paired samples; I tried Friedman test but it produces absurd results)

2) Can you please kindly give me a CONCRETE result for this test? (this is extremely important for me because I need to be sure that I understand the things properly)

Very many thanks,
Libor

Last edited:

#### obh

##### Well-Known Member
Hi Libor

I assume you use a sample of random 52 companies?
Did you try Chi-squared "my Goodness" of Fit contingency table? - (independence testing)

#### Libor

##### New Member
Hello, Many thanks.
Attached, is a graph.
black:no usage; greyartial usage; white:full usage In fact, I need to compare 3 proportions and to determin exactly whether they are accross the years statistically different or not. Can you please help? Many thanks. –

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#### Libor

##### New Member
Has the FULL usage (white bar) really increased in the course of the time? I need to prove it exactly. Many thanks.

#### Karabiner

##### TS Contributor
So you have n=52 companies, each observed 4 times (i.e. repeated measures).
The dependent variable is ordinal scaled. A global analysis of whether the level
of capacity use is (not) the same across years, can be performed using Friedman test.
If this turns out statistically significant, you can perform pairwise comparisons
between time points using the sign test. If you only want to compare full usage
against no full usage (partial and no use combined), you will have to create
4 new (binary) variables; global test would be Cochran's Q, pairwise comparisons
can be done using McNemar tests.

With kind regards

Karabiner

#### Libor

##### New Member
Very important: The 52 company are - across the years - always the same. This means that it will be a MATCHED (correlated) test. An extension of McNemar (but NOT Bowker test because Bowker applies to a situation where only 2 years are compared - but we compare 4 years)

#### Libor

##### New Member
So you have n=52 companies, each observed 4 times (i.e. repeated measures).
The dependent variable is ordinal scaled. A global analysis of whether the level
of capacity use is (not) the same across years, can be performed using Friedman test.
If this turns out statistically significant, you can perform pairwise comparisons
between time points using the sign test. If you only want to compare full usage
against no full usage (partial and no use combined), you will have to create
4 new (binary) variables; global test would be Cochran's Q, pairwise comparisons
can be done using McNemar tests.

With kind regards

Karabiner
Hello,
Many thank for the very QUALIFIED answer (Q-Cochran - yes, I used it if I want to restrict the test only to a binary variable)

Yes, I made Friedman (in SPSS), it gave me a highly INsignificant p-values ([asympt./exakt.: 0,1738/0,2731]), which meas that there is no difference between the proportions. But this is nonsense because FULL usage has increased evidently. Also, can you please see the graph, which I posted above? (this explains all) Can you please kindly make the Friedman for me and to find out the correct p-value? Many thanks.

#### Karabiner

##### TS Contributor
For Friedman, you need 52 lines (companies) and 4 columns for the yearwise measures of the dependent variable.
Did the output of the analysis indicate how many cases (companies) were included in the testing?

With kind regards

Karabiner

#### Libor

##### New Member
Many thanks. There were 52 companies altogether (each year, situation in the same 52 companies was reviewed).
Here is a Word file (friedman) with the data table.
Please, could you change the table - according to your own fancy, just please think anything out - so that the Friedman can be perfomed? (any solution chosen by you will be illustrative for me...) Many thanks and sincerely...

#### Karabiner

##### TS Contributor
That table cannot be re-arranged in order to permit a proper Friedman
test. The table displays aggregated data, but for the Friedman test
(as for any analysis with repeated measures) you need the individual
history of each company separately. I.e. in SPSS, you'd have 52 lines and
5 columns (one column for the company Id, 4 for the respective
measurements) in the data sheet, for example:
company1 / no / no / partial / full
company2 / no / partial / no /full
...
company52 / partial / partial /full /full

If the data are arranged that way, the Friedman test is easy.

With kind regards

Karabiner

#### Libor

##### New Member
Many thanks for the detailed explanation... I will try... so the problem was that I had the wrong data source, so the Friedman was performed in the wrong way...

#### Libor

##### New Member
Hello,
many thanks for your comment. I cannot judge of it. However, they are MATCHED samples. Can Goodness of Fit be applied?

#### Karabiner

##### TS Contributor
However, they are MATCHED samples.
That was my idea, too. Observations are not independent.

With kind regards

Karabiner

#### Libor

##### New Member
Yes, they are matched - correlated.
In fact, Cochran Q test is an extension of McNemar (McNemar does only 2 groups, but Cochran does any number of groups; however, the number of categories is in both cases restricted to 2 - binary)

Friedman is an extension of Cochran. The difference is that Friedman manages trinomic variable (but Cochran only binary)

#### obh

##### Well-Known Member
That was my idea, too. Observations are not independent.

With kind regards

Karabiner
Hi Karabiner,

Do you mean Goodness" of Fit contingency table? can't apply?

#### Karabiner

##### TS Contributor
No, it can't apply, since it requires independent observations.

#### Libor

##### New Member
Hello Karabiner,
just as a matter of interest and in order to make sure that Friedman is really appropriate for this job, I also contacted the technical support of NCSS and Minitab. Howerver, their statisticcians evidently do not know the things, because for example, I was recommended CHI2 test and similar nonsense. It is said if you consider that they are professionals...
Please note that I am NOT a statiscian but only a self-taught person in statistics (learning on the Internet...) I have no couch tutor etc.