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# Non parametrics

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### Non parametrics

1. 1. Non-Parametric Tests<br />Ryan Sain, Ph.D<br />
2. 2. Non-parametric tests<br />These are used in the place of parametric stats<br />When your data is not normal<br />There are specific adjustments and procedures to not be affected by this<br />Typically do not use the mean to make comparisons<br />Most create rankings of the raw scores then analyze these rankings<br />
3. 3. Independent samples<br />Comparing two groups of independent samples<br />Equivalent to the t-test<br />Mann-Whitney<br />Wilcoxon rank-sum <br />
4. 4. Rank logic<br />Ignoring the specific groups<br />We rank all data from lowest (1st) to highest (nth)<br />If the groups are the same you would expect similar ranks in each group<br />The sums of these ranks will likely be similar if no difference between groups exist<br />If the groups ARE different – then you will expect a disproportionate set of ranks in one group compared to the other and the sums of those ranks would be different.<br />Same raw scores get an average of the ranks (tied ranks).<br />
5. 5. Standardizing and significance<br />We can calculate a mean using n for each group:<br />Wmean= n1(n1+n2+1)/2<br />SEWmean= SQRT (n1n2(n1+n2+1))/12<br />But we still need to get a standard error<br />convert raw to z<br />Using the mean calculated from above<br />Magical +/-1.96<br />
6. 6. Two related conditions<br />Wilcoxon signed rank test<br />Used when the data are related (repeated measures of the same individuals)<br />Is the same as the dependent t-test<br />Use a negative sign of the rank dropped for a given person between test 1 and 2.<br />Drop all people that did not change.<br />
7. 7. Testing multiple groups<br />Kruskal-Wallis<br />Uses the same ranking logic as the mann-whiteney<br />Is akin to an ANOVA<br />Omnibus test as well.<br />Post hoc tests of mann-whitney or Wilcoxon rank-sum.<br />
8. 8. Categorical Data<br />Categorical data is data that fits into only one category<br />Gender<br />Pregnancy<br />Voting<br />We have looked at using categorical data for predicting something (point biserial correlation) but now we want to examine the relationship between these variable types<br />
9. 9. The logic<br />There is no mean or median to work with<br />The values are arbitrary<br />All we can really look at are frequencies of occurrence<br />
10. 10. Chi square<br />Two categorical variables<br />Pregnant and contraception used.<br />What is the chance that our observations are not due to chance?<br />We cannot look at means, we can only look at frequencies – so we need to find the expected values<br />
11. 11. Contingency table<br />
12. 12. Expected distributions<br />So we look at what is expected in each cell. (cannot use n/cells to get this)<br />Because there is a different number of people in each condition. So we make an adjustment<br />Row total x column total / n<br />X2 = the sum of each (observed-expected)2/expected<br />This statistic is then able to be looked up on a probability table.<br />We can then decide if the distribution is expected or not.<br />Degrees of freedom (row-1)(column-1)<br />
13. 13. A sample<br />X2 = (20-70)2/70 + …..<br />X2 = 35.71 + 35.71 +31.25 + 31.25 <br />X2 = 133.92 with 2 df<br />
14. 14. assumptions<br />No repeated measures situations<br />Expected frequencies should be greater than 5<br />
15. 15. conclusion<br />If you have categorical data and you are wanting to see if the distributions are by chance – use the Chi Square analysis.<br />