# Non-parametric tests

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## Mann Whitney U Test

Step one: Rank (put in order from lowest to highest number) all scores together; ignore which groups the ranks are associated to. If there is a double set of score, add the values together and divide by two (or by how many values are the same). e.g rating score "2" has the rank order 1 and 2.

1+2=3 Divide by 2 =1.5

Step two: Add up all the ranks to get value of R1 (rank 1)

Step three: Repeat the same procedure as step two to get the value of R2.

Step four: Use formula

U1=R1-n1(n1+1) / 2              You must use the smallest total value for this

Step five: Using table of critical U values for Mann Whitney U Test match the number of participant in each group together. If the calculated value is smaller than the critical value, the results are significant and the probability of getting them by chance was less than 0.05.

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## The Wilcoxon signed rank test

Step one: Take the second set away from the first to get the difference

Step two: Rank the differences. Ignore any positive or negative signs and 0 values.

Step three: In the "difference" column, count how many positive and negative numbers there are.

Step four: Make calculation using the less frequent sign (postive or negative). Add scores in the ranked order of difference column which belong to either the postive or negative sign.

Step five: Calculate the n value. If there is a sample of e.g. 9, and one of them has a 0 difference, do not count them so n=8.

Step six: Match n value to the table of critical value. Values are found at the 0.05 significance level for two-tailed hypothesis.

Step seven: If the observed value is higher than the critical then the results are not significant, meaning the null hypothesis will be accepted. If the observed value was lower than the critical value the results were significant, meaning the null hypothesis would have been rejected.

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## Chi-square test

Step one: Add the totals for each column

Step two: The expected frequencies need to be calculated.

Expected Frequencies = row total x column total  /  overall total

Step three: Calculate the expected frequency for each cell.

Step four: Calculate Chi-Square

X^2 = sum of (observed - expected)^2  / expected

Step five: Calculation of degrees of freedom

(df)= (Number of rows -1) x (Number of columns -1)

Step six: Use the table of critical values. Always use 0.05 unless said.

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## Binomial Sign Test

Step one: Positive and negative signs need to be added. e.g. if condition A is yes and B is no then the flow of direction is plus but if opposite way round, it would be minus.

Step two: This step requires the counting of each postive and negative sign assigned to each participants scores.

Step three: The smallest of the total direction scores is the overall binomial test result.

Step four: Level of significance- look at critical values table. Level of significance is 0.05 for a 1 tailed test. If participants score the same in each condition, ignore.

In order for the study to be significant, the observed value has to be smaller or equal to the critical value. If it is not significant, the observed value is greater than the critical value so the null hypothesis is accepted.

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## Spearman's Rho

Step one: Ranking for the Spearman's Rho calucation - each column is ranked individually.

Step two: Rank the scores, give the lowest score, a rank of 1, the next, a rank of 2, and so on.

Step three: Repeat ranking calculations with other column(s)

Step four: Repeat step four using data from both columns (rank columns together).

Step five: Insert all values into final data table of ranks.

Step six: The difference between ranks for each dataset need to be calculated. Then the difference scores need to be squared.

Step seven: Use formula:

r=1- (6 x sum of D^2)  / n(n^2-1)

Look at critical value table. If the critical value is less than the observed the results are significant.

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