Do difference in two proportions by normal approx, chi sq .of CBT (wave 1 vs wave 2)

then stratify by confounding factors eg do diff in two proportions of CBT (wave 1 vs wave 2 ) for public only (in both waves) and then do the same for private only (in both waves).

When you choose to analyse your data using a chi-square test for independence, you need to make sure that the data you want to analyse "passes" two assumptions. You need to do this because it is only appropriate to use a chi-square test for independence if your data passes these two assumptions. If it does not, you cannot use a chi-square test for independence. These two assumptions are:

• Assumption #1: Your two variables should be measured at an ordinal or nominal level (i.e., categorical data). You can learn more about ordinal and nominal variables in our article: Types of Variable. Your responses are dichotomous (Yes/No) so this assumption holds true
• Assumption #2: Your two variable should consist of two or more categorical, independent groups. Example independent variables that meet this criterion include gender (2 groups: Males and Females), ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups: sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.
• If your response variable is continuous use ANOVA

thank you for the answers. using chi squared makes sense. so if i'm understanding this correctly i would merge the two files by adding data from wave 2(about 10k cases) to data from wave 1 (about 10k cases) as new cases creatinga a large combined data set (with about 20k total cases). I would create a new variable 'wave' where cases form wave 1 would have a value, let's say 0,' and cases from 'wave 2' would have a different value, let's say 1. i would then use chi-squared with independent variable being 'wave' and the dependent variable being CBT? Thanks so much!

Dear Stanislav

The answers above especially the one given by Christopher S Bova is quite detailed and fits your data. You need to review some standard text book(s) on statistics (Chi-squared test in particular.

Thank you for your answer. Chi squares makes sense. I just wanted to additionally clarify that I’m merging the two files of survey data correctly.

I would suggest that using a multilevel model or a generalized estimating equations approach (both available in SPSS v23) could be more effective because they allow for the inclusion of covariates. Multilevel modeling is also referred to as mixed effects modeling due to incorporation of both random and fixed effects.

Repeated cross sections present a challenge because of the presence of aggregate-level and individual-level effects. The use of multilevel modeling allows you to estimate both aggregate- and individual-level parameters simultaneously, and incorporate covariates at both levels.

Some argue that GEE is limited because it represents population average effects that are simply descriptive and influenced by the amount of heterogeneity in the population. There is evidence from Monte Carlo simulations, though, suggesting that the power for a GEE approach is greater than the multilevel/mixed effects model approach.

Thank you!