Looking for guidance - statistical test to use for survey data Would like some guidance on what kind of statistical test to use for survey data
I want to look at two things:
•   Is there statistical difference between how groups have answered?
•   Is there a correlation between two questions?
For example, difference between how groups have answered. I have the demographic age group against favourite colour, I want to calculate if there is a significance difference in the colour chosen and if so which ones. This is random numbers below

I will also be running this on scale questions if this makes a difference. E.g. how satisfied are you with our products?

Finally, I am not sure if you would use the same test for this but I want to look at intra question analysis. For example, if one question is, Where did you first buy one of our products? And How satisfied are you with how products?
I want like to see any connections so it might be that people who first brought a product at a shopping centre are more satisfied with the products then those who brought online

I will be conducting the analysis in tableau but first want to ensure I use the right statistical tools
Thanks for your help
 A: Possibly subject to late night typing errors, I put your first
table into R:
g = c( 21, 321, 312, 335, 355)
b = c(354,  34,   3, 875, 345)
p = c(345, 635, 384,  53, 395)
TBL = rbind(g,b,p)
TBL
  [,1] [,2] [,3] [,4] [,5]
g   21  321  312  335  355
b  354   34    3  875  345
p  345  635  384   53  395

Here is output from chisq.test in R. Very highly
significant result with P-value near $0.$ So
colors are not selected homogeneously across age
groups.
chi.out = chisq.test(TBL);  chi.out

        Pearson's Chi-squared test

data:  TBL
X-squared = 1897.7, df = 8, p-value < 2.2e-16

The large chi-sq statistic 1898 is the sum of squares of
Pearson residuals. It's often useful to look at residuals
with absolute values greater than 3 as guidance towards
which ad hoc tests might be worthwhile.
round(chi.out$resi, 2)
    [,1]   [,2]   [,3]   [,4]  [,5]
g -12.77   2.51   8.19  -1.12  2.63
b   7.10 -16.43 -15.17  21.69 -1.30
p   4.31  13.34   7.26 -19.49 -1.04

Popularity of blue seems very low for ages 18-54, then very
popular at ages 55-74. Also 55 seems to be a time for changing
opinions on colors. And green seems unpopular overall.
[Maybe these are fake data for illustration
so I won't speculate why. Or suggest other patterns.]
I do wonder why there are so many subjects in older age groups.
Similar chi-squared tests seem appropriate for the other two tables.
Column headers are missing on last table.
Most statistical software does chi-squared tests on tables such
as the ones you show. But beyond showing the chi-squared statistic
and the P-value, there are differences in the details of output.
Note: If you have particular questions that you want answered for
the different tables you show, you might be more specific about
your goals. And that might prompt some useful comments and suggestions.
A: You seem to be looking at categorical data, so would need to be using a pearson chi-square test or similar (after checking for various assumptions). This is a good basic resource and includes a test of association example.
https://www3.nd.edu/~rwilliam/stats1/x51.pdf
I'm not familiar with Tableau-but any basic stats package should have this sort of test.
A: **@BruceET
Yes, it is fake data, but in saying that the responses will be weighted towards old age brackets
So I understand using chi-squared will give me an overall look
But I also want to look at the individual parts.
For example is there a colour that is being answered lower or higher in an age bracket, and is the difference statistically significant
The information you touched on regarding  Pearson residuals interests me
So in the original table I can see blue is lower for 35-54, with only three responses but is it a statistically significant difference, compared to the number of people in other age groups that selected blue?

Does the value you provide here of -15.17 define this?

I have put together some real data, demographic across the top, answer on the left

I want to identify if any answers are significantly higher or lower than expected
For example there seems to be a high number of 66-80 who have selected Q10 01, but is this significant?
Thanks
Toby
