I am conducting a study on whether the visual outcomes differ before and after surgery in glaucoma patients depending on the type of intraocular lens (IOL) used. I am examining whether there are differences in visual field tests and visual acuity changes before and after surgery depending on the type of IOL used. The visual field is measured in dB, and visual acuity is measured in logMAR. I am wondering if it is appropriate to simply compare the differences between groups by subtraction in this case. I am seeking advice from experienced professionals on whether it is appropriate to conduct a t-test based on simple subtraction, or if numerical transformation or other statistical methods should be used.
Visual field measurements (in decibels, dB) and visual acuity (in logMAR) can be compared pre- and post-surgery by calculating the differences for each patient as you have stated. To compare these differences across groups defined by the type of IOL used, you can use paired t-tests within each group to determine whether significant changes occur before and after surgery. An independent t-test (for two groups of IOL) or ANOVA (for multiple groups of IOL) can be employed to compare differences between groups. These tests assume normality of the data and homogeneity of variances, you can check these assumptions using visual inspections (like histograms and Q-Q plots) and statistical tests (such as Shapiro-Wilk and Levene’s test). If the data do not meet these assumptions, non-parametric alternatives like the Wilcoxon signed-rank and Kruskal-Wallis tests should be considered.
To compare visual field measurements (in decibels, dB) and visual acuity (in logMAR) pre- and post-surgery across groups defined by the type of intraocular lens (IOL) used, follow these steps:
1. Calculate Differences for Each Patient:
Compute the difference in visual field measurements (dB) and visual acuity (logMAR) pre- and post-surgery for each patient.
2. Paired t-tests within Each Group:
· For each group of IOL, perform paired t-tests to determine if the changes in visual field measurements and visual acuity are statistically significant before and after surgery.
· The paired t-test is appropriate because it compares two related samples, accounting for the fact that measurements are taken from the same patients before and after surgery.
3. Independent t-test or ANOVA for Between-Group Comparisons:
· If comparing two groups of IOL, use an independent t-test to compare the differences in visual field measurements and visual acuity between the groups.
· If comparing more than two groups of IOL, use ANOVA to compare these differences across multiple groups.
A. Assumptions Checking:
· Normality: Use visual inspections (histograms, Q-Q plots) and statistical tests like the Shapiro-Wilk test to check if the data are normally distributed.
· Homogeneity of Variances: Use Levene’s test to assess if the variances are equal across groups.
B.Non-Parametric Alternatives:
· If the data do not meet the assumptions of normality or homogeneity of variances, use non-parametric tests:
· Wilcoxon Signed-Rank Test: As an alternative to the paired t-test for within-group comparisons.
· Kruskal-Wallis Test: As an alternative to ANOVA for between-group comparisons.
Detailed Steps:
1. Calculate Differences:
· For each patient, calculate:
ü Difference in Visual Field (dB)=Post-Surgery Visual Field (dB)−Pre-Surgery Visual Field (dB)
ü Difference in Visual Field (dB)=Post-Surgery Visual Field (dB)−Pre-Surgery Visual Field (dB)
ü Difference in Visual Acuity (logMAR)=Post-Surgery Visual Acuity (logMAR)−Pre-Surgery Visual Acuity (logMAR)
ü Difference in Visual Acuity (logMAR)=Post-Surgery Visual Acuity (logMAR)−Pre-Surgery Visual Acuity (logMAR)
2. Paired t-tests:
Perform paired t-tests for each IOL group separately to test if the mean difference in visual field and visual acuity is significantly different from zero.
3. Independent t-test or ANOVA:
For two groups:
ü Use an independent t-test to compare the mean differences in visual field and visual acuity between the two IOL groups.
For more than two groups:
ü Use ANOVA to compare the mean differences across multiple IOL groups.
4. Check Assumptions:
· Normality:
ü Plot histograms and Q-Q plots of the differences.
ü Perform Shapiro-Wilk test on the differences.
· Homogeneity of Variances:
ü Perform Levene’s test.
5. Non-Parametric Tests:
ü If the data are not normally distributed or variances are unequal:
ü Use the Wilcoxon signed-rank test for within-group comparisons.
ü Use the Kruskal-Wallis test for between-group comparisons.
By following these steps, you can rigorously compare the pre- and post-surgery visual outcomes across different IOL groups while ensuring the appropriate statistical methods are applied based on the data characteristics.