Solved – Comparison of before and after ordinal data across two groups

ordinal-datarepeated measuresscales

I would like to compare before-and-after "scores" on five quality of life questions across two groups. What I would like to know are:

Are the baseline scores across the two groups similar?
Is the change in scores significant (before and after) within each group?
Is the change in scores significant across both groups?

Will an independent t-test suffice to answer question number 1?

Will it be appropriate to perform a Wilcoxon signed rank test to answer question number 2? If not, what will be the more appropriate test?

On question 3, is Mann-whitney appropriate?

Thank you so much for the help.

Best Answer

If you can use a parametric test for one of these questions, you can use parametric tests for the others, and if not, not. Given that you say the data are ordinal, I would say that the t-test is not appropriate and you should use a test of the median for all three questions; it should probably be the same test for all three questions.

A different approach (and the one I would use) is to use ordinal logistic regression with score as the dependent variable.

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Solved – Comparison of Kaplan-Meier curves across ordered groups

Function comp in survMisc may be close to what you're after. From the docs:

Tests for trend are designed to detect ordered differences in survival curves.
That is, for at least one group: $$S_1(t) \geq S_2(t) \geq ... \geq S_K(t) \quad t \leq \tau$$ where $\tau$ is the largest $t$ where all groups have at least one subject at risk. The null hypothesis is that $$S_1(t) = S_2(t) = ... = S_K(t) \quad t \leq \tau$$ Scores used to construct the test are typically $s = 1,2,...,K$, but may be given as a vector representing a numeric characteristic of the group.
They are calculated by finding: $$Z_j(t_i) = \sum_{t_i \leq \tau} W(t_i)[e_{ji} - n_{ji} \frac{e_i}{n_i}], \quad j=1,2,...,K$$ The test statistic is: $$Z = \frac{ \sum_{j=1}^K s_jZ_j(\tau)}{\sqrt{\sum_{j=1}^K \sum_{g=1}^K s_js_g \sigma_{jg}}}$$ where $\sigma$ is the the appropriate element in the variance-covariance matrix (see COV).
If ordering is present, the statistic $Z$ will be greater than the upper $\alpha$-th percentile of a standard normal distribution.

For example:

library(survMisc)
data(larynx, package="KMsurv")
s4 <- survfit(Surv(time, delta) ~ stage, data=larynx)
comp(s4)

This will give tests for trend with various weights (as are used with the standard log-rank test):

$tests$trendTests
                                     Z       p
Log-rank                      3.718959 0.00010
Gehan-Breslow (mod~ Wilcoxon) 4.224765 0.00001
Tarone-Ware                   4.058010 0.00002
Peto-Peto                     4.129343 0.00002
Mod~ Peto-Peto (Andersen)     4.136319 0.00002
Trend F-H with p=1, q=1       2.396992 0.00827

The package has been changed slightly, and instead of tests or trendtests, use tft, which stands for... tests for trend. Furthermore, when using the comp() function, type it like this: comp(ten(<whatever your survival-fit object is>)).

Solved – Comparing the difference in change in repeated measures ordinal variables between two groups

If you are familiar with ordinal logistic regression models and mixed-effects models with lmer in the lme4 package in R, you may want to check out the clmm (cumulative link mixed models) function in the ordinal package. This function, built on lmer, may prove especially useful if you have covariates to control for.

I suppose this answer may be more relevant to Brian's problem than that of @user45094; I am not sure if SPSS has something like cumulative link mixed models.

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Related Solutions

Solved – Comparison of Kaplan-Meier curves across ordered groups

Solved – Comparing the difference in change in repeated measures ordinal variables between two groups

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