Question

In what real life research situations would you use a z-score? t-score?

when would we know the population standard deviation? When would we not know the population standard deviation?

Answer 1

A z-score is a standardised score, which indicates the standard deviation units of a score. In other words, a raw score derived from a particular sample distribution can be transformed into a z score that indicates the precise location of the score with respect to the distribution. This transformation would allow the meaningful comparison of scores derived from different samples. For example, let’s assume a student scores 80 in English while scoring 70 in Psychology. On the face of it, it would appear that the student performed better in English. However, if an accurate comparison were to be made, it difficulty of the examination should also be assessed by measuring the average scores and the distribution of scores in both these subjects. In that case, the z score would be an important statistic as it is value derived after the mean and the SD of the sample is taken into consideration.

T-tests are used for comparison methods as well, however it indicates whether or not the difference between two means derived from a set of scores are statistically significant. In a one sample t-test, the sample mean is compared to the expected population mean, whereas in a two sample t-test, the means of the samples are compared against each other. The t-test is frequently utilised in many studies as a way to understand if an independent variable has produced differential effects on two groups.

Please post the other questions separately.