Hello everyone,
Currently, I am developing a longitudinal research applying psychometric questionaries in the same sample in two moments. However, I am looking bibliography or evidence about which is stronger statistical test: Paired Sample T-Test and Wilcoxon, and the assumptions behind the application of each test.
Hello Dante,
If all parametric assumptions are met, the paired t-test is slightly more powerful than the Wilcoxon signed ranks sum test (about 4.5-5% less for Wilcoxon). Otherwise, you can't be certain without running a simulation study of the specific data set characteristics.
Paired t-test: Requires that difference scores are normally distributed, and, therefore are of at least interval scale strength. Tests hypothesis that mean difference = constant (typically, zero). Virtually any software package will compute correct probability (under null hypothesis) of result as or more extreme than that observed in the data set.
Wilcoxon test: Requires that difference scores are at least ordinal strength, and therefore may be converted to ranks. Tests hypothesis that sum of the positive ranked differences = sum of the negatively ranked differences (which simplifies to median ranked difference = 0). Most textbooks will furnish exact critical values for N up to about 20 to 25, but then recommend a "large sample" approximation to the normal distribution thereafter. SPSS, I believe, uses the large sample approximation regardless of sample size.
Good luck with your work!
Dear Dante,
All explanation from Prof. David Morse is completely perfect, no doubt. I personally agree with all requirements and objectives of those tests.
I just want to share my research conducted lately, but not longitudinal one. I was observed prescribers' behavior and attitude in prescribing related errors. It is not Likert Scale, but closer to ratio/interval scale. I was found differences in tests between Wilcoxon and Paired t-test, but i choose Paired t-test since all assumptions met requirements and more that to the type of data scale.
I suggest text book from Philip Rowe in this link https://goo.gl/rNA7Eq and from Muth https://goo.gl/RcPctp.
Regards,
Dear Dante
Although normality assumption is important in using paired t-test but if the distribution of your data is symmetric instead of using Wilcoxon test you can still use paired t-test. Because t statistic is a robust statistic against normality assumption. To study symmetry assumption of your data you can use box-plot or skewness measures.
Paired t-test application implies that both measurements are on the same individuals. In the language of experimental design each individual is a block. It is a parametric test in which case the data must be at least of interval level and normally distributed. Wilcoxson test is nonparametric and can be ordinal.
I am not very strong in statistics but perhaps my little experience could help too. I faced a similar situation recently. I run a normality test and found that some data had low (0.43) Shapiro-Wilk values while others had 0.90. I, therefore, resulted to use Wilcoxon. But, on running both tests out on interest, I realized that both showed a significant result of 0.023 (W) and 0.03 (t). I guess the former is more reliable/accurate to handle my data than the latter.
Divya Agarwal No, you do the t-Test if you have interval level data, and the Wilcoxon if you have ordinal data.