# Comparing two means from the same respondents taken at the same time without confidence level

I have a question about comparing the means of two dimensions both relating to the concept reputation.

I have conducted a survey that measured three dimensions affecting the reputation of a brand using the RepTrak model as follows:

• 4 statements relating to the dimension Products/Services ...
• 3 statements relating to the dimension Governance ...
• 3 statements relating to the dimension Citizenship ...
• ... were proposed for respondents to give their opinion on.

All statements were measured using a high-precision slider with only two extremes shown: on the left completely disagree and on the right completely agree. The resulting value for every answer is a decimal value in between 0.000 (completely disagree) and 1.000 (completely agree).
For example, someone who sets the slider to three-quarters gets the value 0.750.

For every participant, all statements relating to one dimension were combined into a new column (in the program JASP) by calculating the mean of the participant's answers for the dimension. This means there are 3 new computed columns/variables to perform analysis on:

1. Products/Services
2. Governance
3. Citizenship

The resulting descriptive analysis for these variables are:

Products/Services Governance Citizenship
Valid 204 204 204
Missing 0 0 0
Mean 0.735 0.475 0.514
Standard deviation 0.111 0.172 0.161
Minimum 0.354 0.000 0.000
Maximum 0.949 1.000 1.000

#### Sampling

All 204 participants are sampled using a combination of voluntary response sampling and snowball sampling. I know the disadvantages of non-probability methods; unfortunately there was no other way to conduct the survey. Therefore, I do not have a confidence level to work with in my analysis.

Now I would like to test the following hypothesis: Governance scores the lowest of the three reputation dimensions.

In order to test this, I reckon it would be good to test if the difference between the means of, for example, Governance and Citizenship is significant enough. I have heard of the following types of tests:

• One sample t-test: select one variable in JASP (for example Citizenship) and enter the mean value of Governance (0.475) as a test value.
• Paired samples t-test: add Governance and Citizenship as a pair in JASP and test if they differ significantly.
• One sample z-test: select one variable in JASP (for example Citizenship) and enter the mean (0.475) and standard deviation (0.172) of Governance as test values.

Now I have some difficulty wrapping my head around the idea whether the dimensions, all affecting the overall reputation among customers of the brand, are paired or not, or whether a one sample t-test/z-test would be appropriate.

I have seen that analysts often compare the confidence intervals for two means. If those intervals overlap, they conclude that the difference between groups is not statistically significant. In my case that seems to be difficult, since I do not have a clear confidence level to work with.

What would be the best way to compare two means in order to test the hypothesis?