# Three proportions

#### mizansiddiqis

##### New Member
Which test is use to identify significant group among three group of proportions? By doing individual chi square, z test for proportion or logistic regression using dummy variable?

#### hlsmith

##### Not a robit
Can you describe the data a little more, perhaps supply a table with the cell counts.

#### mizansiddiqis

##### New Member
Age group Male Female
<15 41 41
15-44 18 39
45+ 11 5
------------------------------------------------
70 85

#### mizansiddiqis

##### New Member
Can you describe the data a little more, perhaps supply a table with the cell counts.
Please find the table below:

Age group Male Female Total
<15 41 41
15-44 18 39
45+ 11 5
------------------------------------------------
70 85

#### hlsmith

##### Not a robit
Depends on your overall purpose, but you are probably fine running a single chi-sq, then looking for difference via the residuals from the test.

#### mizansiddiqis

##### New Member
The objective is to see if there is a difference by gender between these groups and find the group which is significantly different from others. I have sent you the table. Can you please run and show me the output and residuals to identify the significant one? Thanks for your help.

#### CamilleJosion

##### New Member
You can check this tutorial
https://help.xlstat.com/customer/en...-chi-square-and-fisher’s-exact-tests-in-excel

It might be more simple than the very accurate and complete article by Donald Sharpe quoted in the previous post.

As you have a cell with 5 individuals which is the known limit to use the chi-square test, you might want to use the Monte Carlo or Fisher exact tests. I let you run the tests, but the Fisher exact test gives a higher p-value.

#### mizansiddiqis

##### New Member
Thank you. But it does not answer my question which one is significant.

#### mizansiddiqis

##### New Member
Is this for a class or real-life project? Examples, https://pareonline.net/getvn.asp?v=20&n=8
Thanks. This is a real life project. The paper helped me to understand the concept and various tests involved. But not answering my question directly that is which group is significantly different from others? Practical help is appreciated.

#### mizansiddiqis

##### New Member
This is the SPSS output. How do I interpret the table below for residuals and p-value? Thanks.

Age group
<15 15-44 45+
Female
Count 41 39 5
Expected Count 45.0 31.3 8.8
Residual -4.0 7.7 -3.8
Standardized R -.6 1.4 -1.3
Adjusted R -1.3 2.6 -2.0

Male
Count 41 18 11
Expected Count 37.0 25.7 7.2
Residual 4.0 -7.7 3.8
Standardized R -.7 -1.5 1.4
Adjusted R 1.3 -2.6 -2.0

df p
Pearson Chi-Square 8.616 2 0.13
Likelihood Ratio 8.774 2 0.12

#### mizansiddiqis

##### New Member
This is the SPSS output. How do I interpret the table below for residuals and p-value? Thanks.

Age group
<15 15-44 45+
Female
Count 41 39 5
Expected Count 45.0 31.3 8.8
Residual -4.0 7.7 -3.8
Standardized R -.6 1.4 -1.3
Adjusted R -1.3 2.6 -2.0

Male
Count 41 18 11
Expected Count 37.0 25.7 7.2
Residual 4.0 -7.7 3.8
Standardized R -.7 -1.5 1.4
Adjusted R 1.3 -2.6 -2.0

df p
Pearson Chi-Square 8.616 2 0.13
Likelihood Ratio 8.774 2 0.12

#### mizansiddiqis

##### New Member
The adjusted residuals suggest that there are more females in the age group 15-44 (AR 2.6) and more male in the group 45+ (AR 2.0 its positive not negative as I have written in my previous reply). And the difference is significant at p is .013 and likelihood ratio is .012 (i made mistake with a decimal point). The Pearson Chi-square and Likelihood Ratio is applied to indicate significance for the entire table or between groups?

#### hlsmith

##### Not a robit
Concept of significance is over played. Above chi-sq is likely an omnibus test, meaning at least one level differs, that is where the residuals come into play, to understand where difference may be.

#### mizansiddiqis

##### New Member
In the manuscript which part of the spss output I should report. The adjusted residual or the whole output or just mentioned the level of significant and the level where AR become 2 or more?

#### Karabiner

##### TS Contributor
df p
Pearson Chi-Square 8.616 2 0.13
Likelihood Ratio 8.774 2 0.12
The p value is > 0.05. According to the common decision rule, this is considerd as not statistical significant,
meaning that one cannot reject the null hypothesis: "the distribution of sexes is the same in each age group"
(or "the distribution of age groups is the same for each sex", respectively). Therefore, post-hoc analyses
would usually not be performed.

By the way, it is unclear (at least for me) what you want to find out. Your analysis concerns whether the
distribution of sexes is the same over 3 age groups, irrespective of whether there are more men than women
(or vice versa). Your questions, though, seem to suggest that you want to know in which age groups there
are significantly more men than women (or more women than men). But maybe this is a misunderstanding
from my side.

With kind regards

Karabiner

#### mizansiddiqis

##### New Member
You are correct I am trying to find out which group is significant. I am mistaken with p value while writing. It is .013. That is significant. Now looking at the residuals I find 2 groups with adjusted residuals 2 or more. So these are significantly different from other groups? Do I need to do post hoc analysis? If so how do I do it? Thank you. Siddiqi

#### mizansiddiqis

##### New Member
<15 15-44 45+
Female
Count 41 39 5
Expected Count 45.0 31.3 8.8
Residual -4.0 7.7 -3.8
Standardized R -.6 1.4 -1.3
Adjusted R -1.3 2.6 -2.0

Male
Count 41 18 11
Expected Count 37.0 25.7 7.2
Residual 4.0 -7.7 3.8
Standardized R -.7 -1.5 1.4
Adjusted R 1.3 -2.6 -2.0

df 2
Pearson Chi-Square 8.616 2
p value .013
Likelihood Ratio 8.774 2 0.12

#### Karabiner

##### TS Contributor
Unfortunately, I still do not understand what you want to achieve.
"I am trying to find out which group is significant." is not a research
question. Do you want to find out in which age groups
there are significantly more men than women (or more women than men),
i.e. significant deviations from 50%/50%?
Or do you want to find out in which age group men are underrepresented
(or over-represented), i.e. in which certain age groups the proportion
of men is larger than overall?

With kind regards

Karabiner