Non-Parametric Tests of Difference Flashcards
what is a test of difference?
used in an experiment to see if one set of data is significantly different to another set of data
what is the issue with non parametric tests?
they involve ranking data which loses some of the detail, making them less powerful than parametric tests at detecting differences
for each research design, what is the data involved?
in a repeated measures design, the two sets of data are related as they come from the same person
in a matched pairs design, the two sets of data are related as they come from matched pairs
in an independent groups design, the two sets of data are unrelated because they come from separate groups
which test is used for which sets of data?
the Wilcoxon test is used for related samples
the Mann-Whitney test is used for unrelated or independent samples
reasons for choosing the wilcoxon test
the hypothesis states a difference between two sets of data
the two sets of data are pairs of scores from one person (i.e. related data)
the data is ordinal because there are not equal intervals between ratings
reasons for choosing the mann whitney test
the hypothesis states a difference between two sets of data
the two sets of data are from separate groups of participants (i.e. unrelated data)
the data is ordinal because there are not equal intervals between ratings
steps to completing a wilcoxon test for related samples
1) state hypothesis — either an alternative hypothesis (directional or nondirectional) or a null hypothesis
2) collect and place raw data in a table — there should be two items for each participant
3) find the differences and rank — calculate the difference between each set of scores, ignore any differences of 0 and reduce N accordingly, rank the differences from low to high (ignoring the signs), the lowest number receives a rank of 1, the next lowest receives a rank of 2 and so on
if there are more than one of the same number, calculate the final rank by working out the mean (e.g. if 1 occurs 5 times it would have the ranks of 1, 2, 3, 4 and 5, the mean of this is 3 so it gets a rank of 3)
4) find the calculated value of T — T is the sum of the ranks of the less frequent sign
5) identify if the result is in the right direction in relation to your hypothesis
6) find the critical value of T — using significance level 5%, identify the kind of hypothesis (one tailed test if directional and vice versa), identify the N value which is total number of scores (ignoring zero values), locate the row in the statistical table that begins with this N value, the number in the box is the critical value of T
7) report the conclusion — if the calculated value is equal to or less than the critical value, the result is significant
steps to completing a mann whitney test for unrelated samples
1) state hypothesis — either an alternative hypothesis (directional or nondirectional) or a null hypothesis
2) collect and place raw data in a table — there should be data from each group of participants
3) rank each data set — rank all data items using the same steps as the wilcoxon test
4) add each set of ranks — total for column A is RA and total for column B is RB
5) find the calculated value of U — U is calculated using whichever total is smaller
6) identify if the result is in the right direction in relation to your hypothesis
7) find the critical value of U — using significance level 5%, identify the kind of hypothesis (one tailed test if directional and vice versa), identify the N value which is total number of scores for each group (ignoring zero values), locate the box in the statistical table where your NA and NB value intersect, the number in the box is the critical value of U
(NA is the number of scores in column A, NB is the number of scores for column B)
8) report the conclusion — if the calculated value is equal to or less than the critical value, the result is significant
how to report a conclusion
as the calculated value was not significant at P < 0.05, we must accept the null hypothesis and conclude that there is no difference in…. (hypothesis)
as the calculated value was significant at P < 0.05, we can reject the null hypothesis and accept the alternative hypothesis that concludes that…. (hypothesis)
