Statistics Practical 2a

Comments on Z-tests and t-tests
1. You should have realized from the lectures that in practice, a z-test is seldom used, while the ‘default’ test for single sample or two-samples mean(s) is the ttest. This is because in most practical situations, the population variance is seldom known and therefore we need to estimate that by the sample variance, thus justifying a t-test rather than a z-test. It is always good to perform the standard exploratory data analysis before commencing any hypothesis testing involving t-tests. It is often useful to check through summary statistics (like the minimum and maximum of the data), as well as a quick plot of the data (box-plots), to check for any problematic data or outliers. The use of a t-test requires the assumption that the data is distributed like a normal distribution – essentially a bell-shaped curve for the histogram. Therefore it is extremely informative to look at the histogram of the data before commencing on testing, as this will indicate whether the use of the t-test is justified. Before commencing any testing, evaluate what are your hypotheses that you are interested in. If you are testing the mean for a single sample, are you testing the mean to be 0, or are you testing the mean against some non-zero value. If so, do remember to change the input in SPSS correspondingly. Similarly if you are testing the means for two samples, are you testing for the difference to be zero, or against a non-zero difference. Essentially, think through your hypotheses before doing any testings! When comparing between two groups, it is absolutely essential to note whether the groups are dependent (and therefore possibly requiring a paired-t test), or independent (and therefore allowing the use of the independent samples t-test). It is often useful to present the p-value of the hypothesis test, as well as the