Inferential Statistical Tests How do you calculate the test Should this calculated value be greater / lesser than the critical value 3 reasons WHY the test is used

Mann Whitney

Inferential Statistical Tests: Mann Whitney U Checklist for using the Mann Whitney U Test: DV produces ordinal or interval type of data Independent Measures design Exploring a difference between each condition (levels of the IV). Calculated value (U) Critical value

Inferential Statistical Tests: Mann Whitney U Ranking the scores – ignore that there are 2 different groups Textbook (A) Textbook (B) Participant Rating 1 3 7 9 2 4 8 5 6 10 11 12

Inferential Statistical Tests: Mann Whitney U Rank order Rating scores of each participant (from the lowest value to the highest) 1 2 3 4 5 6 7 8 9 10 11 12 After ranking the scores, check if there are any repeated values. If there are any repeated values, average (mean) the rank

Inferential Statistical Tests: Mann Whitney U After averaging any ranks, add up all of the ranks in each group Textbook (A) Textbook (B) Participant Rating Rank 1 3 9 11 2 4 7 1.5 5 5.5 6 7.5 10 12 8   R1 23 R2 55

Inferential Statistical Tests: Mann Whitney U After adding up all of the ranks in each group, see which is the smallest Textbook (A) Textbook (B) Participant Rating Rank 1 3 9 11 2 4 7 1.5 5 5.5 6 7.5 10 12 8   R1 23 R2 55

Inferential Statistical Tests: Mann Whitney U Finally, use the formula given to work out the U The sum of the ranks already calculated The sum of the ranks already calculated

Wilcoxon

Inferential Statistical Tests: Wilcoxon Checklist for using the Wilcoxon Signed Ranks Test: DV produces ordinal or interval type of data. Repeated Measures design. Exploring a difference between each condition (levels of the IV). Calculated value (U) Critical value

Inferential Statistical Tests: Wilcoxon First, see what the difference is between the scores for the same participant Participant Left ear Right ear 1 5 33 2 10 26 3 31 32 4 20 6 27 30 7 25 8 9 15

Inferential Statistical Tests: Wilcoxon After finding the difference between every score, ignore whether it is positive or negative. Rank these differences Participant Left ear Right ear Difference (d) 1 5 33 -28 2 10 26 -16 3 31 32 -1 4 20 -12 6 27 30 -3 7 25 18 8 9 15

Inferential Statistical Tests: Wilcoxon After rank these differences, look back at the + / - signs, which is the least frequent Participant Left ear Right ear Difference (d) Ranked order of difference (d) 1 5 33 -28 8 2 10 26 -16 6 3 31 32 -1 4 20 -12 Ignore 27 30 -3 7 25 18 9 15

Inferential Statistical Tests: Wilcoxon After noting which is the least frequent sign, add the ranks which show this sign Participant Left ear Right ear Difference (d) Ranked order of difference (d) 1 5 33 -28 8 2 10 26 -16 6 3 31 32 -1 4 20 -12 Ignore 27 30 -3 7 25 18 9 15

Inferential Statistical Tests: Wilcoxon This calculation gives you T Participant Left ear Right ear Difference (d) Ranked order of difference (d) 1 5 33 -28 8 2 10 26 -16 6 3 31 32 -1 4 20 -12 Ignore 27 30 -3 7 25 18 9 15

Inferential Statistical Tests: Wilcoxon After finding T, you need to be able to calculate n to be able to find the critical value on the table of critical values N 0.05 6 7 2 8 4 9 10

Inferential Statistical Tests: Wilcoxon Next calculate n (which is the number of differences). This means how many Ps had a difference between their scores. Participant Left ear Right ear Difference (d) Ranked order of difference (d) 1 5 33 -28 8 2 10 26 -16 6 3 31 32 -1 4 20 -12 Ignore 27 30 -3 7 25 18 9 15

Chi2

Inferential Statistical Tests: Chi-square Checklist for using the Chi2 Test: DV produces nominal type of data. Independent Measures design. Exploring a difference between each condition (levels of the IV). Calculated value (U) Critical value

Inferential Statistical Tests: Chi-square Firstly, calculate the sum of each column and each row:   Male Female Row Total Earphones in Ears 16 15 31 No earphones in ears 6 12 Earphones dangling around neck 4 3 7 Column total 26 24 50

Inferential Statistical Tests: Chi-square Secondly, find out the expected frequencies for each cell using this formula: Expected frequencies = 𝑅𝑜𝑤 𝑡𝑜𝑡𝑎𝑙 ×𝐶𝑜𝑙𝑢𝑚𝑛 𝑇𝑜𝑡𝑎𝑙 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑡𝑜𝑡𝑎𝑙

Inferential Statistical Tests: Chi-square Apply the expected frequencies formula for the first cell: Expected frequencies = 𝑅𝑜𝑤 𝑡𝑜𝑡𝑎𝑙 ×𝐶𝑜𝑙𝑢𝑚𝑛 𝑇𝑜𝑡𝑎𝑙 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑡𝑜𝑡𝑎𝑙 Expected frequencies = 31 ×26 50   Male Female Total Earphones in Ears 16 15 31 No earphones in ears 6 12 Earphones dangling around neck 4 3 7 Column total 26 24 50

Inferential Statistical Tests: Chi-square Then apply the expected frequencies formula for all of the cells with results (not the totals!):   Male Female Total Earphones in Ears 16 EF = 16.12 15 EF = 14.88 31 No earphones in ears 6 EF = 6.24 EF = 5.76 12 Earphones dangling around neck 4 EF = 3.64 3 EF = 3.36 7 Column total 26 24 50

Inferential Statistical Tests: Chi-square After working out the expected frequencies, use the Chi2 formula

Inferential Statistical Tests: Chi-square This part has to be done for each cell Then they are all added up

Inferential Statistical Tests: Chi-square After working out the Chi2 formula, identify the degrees of freedom: df = (# of rows – 1) x (# columns – 1)

Inferential Statistical Tests: Chi-square After working out the degrees of freedom, the critical value can be found in the Critical Values table:

Binomial

Inferential Statistical Tests: Binomial Sign Test Checklist for using the Binomial Test: DV produces nominal data. Repeated Measures design. Exploring a difference between each condition (levels of the IV). Calculated value (U) Critical value

Inferential Statistical Tests: Binomial Firstly, add positive and negative signs to the data Participant Share French fries with celebrity (Condition A) Share French fries with students from another school (Condition B) 1 yes no 2 3 4 5 6 7 8 9 10 Flow of direction + – ignore Ignore

Inferential Statistical Tests: Binomial After assigning positive and negative signs, add these up Participant Share French fries with celebrity (Condition A) Share French fries with students from another school (Condition B) Flow of direction 1 yes no + 2 – 3 ignore 4 5 6 7 Ignore 8 9 10 # of + signs = 3 # of – signs = 5

Inferential Statistical Tests: Binomial Finally, the smallest of the total direction scores is the overall binomial test result (the calculated value) Smallest # of + signs = 3 # of – signs = 5

Spearman’s Rho

Inferential Statistical Tests: Spearman’s Checklist for using Spearman’s Test: At least ordinal data. Exploring a relationship between co-variables Correlational design. Calculated value (U) Critical value

Inferential Statistical Tests: Spearman’s Firstly rank each column separately Participant Years with a social media account Rating of whether social media profile is an effective tool for connecting with friends 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Inferential Statistical Tests: Spearman’s After ranking each column, insert these values into the data table Participant Years with a Social Media account Rank of years data Rating of whether Social Media profile is an effective tool for connecting with friends Rank of ratings data 1 2 3 8.5 9.5 5 4 12 5.5 14 6 7 8 9 10 15 11 13

Inferential Statistical Tests: Spearman’s After inserting the ranks into the data table, identify the difference between the ranks Difference between RANK of years and RANK of ratings -1 -4.5 6.5 -0.5 2.5 -3.5 1 3 -5.5 Participant Years with a Social Media account Rank of years data Rating of whether Social Media profile is an effective tool for connecting with friends Rank of ratings data 1 2 3 8.5 9.5 5 4 12 5.5 14 6 7 8 9 10 15 11 13

Inferential Statistical Tests: Spearman’s After identifying the difference between the ranks, square this difference (d2) Difference between RANK of years and RANK of ratings -1 -4.5 6.5 -0.5 2.5 -3.5 1 3 -5.5 Difference between RANK of years and RANK of ratings -1 -4.5 6.5 -0.5 2.5 -3.5 1 3 -5.5 Difference squared (d2) 1 20.25 42.25 0.25 6.25 12.25 9 30.25

Inferential Statistical Tests: Spearman’s After identifying d2, add up all of these values Difference squared (d2) 1 20.25 42.25 0.25 6.25 12.25 9 30.25

Inferential Statistical Tests: Spearman’s After calculating the sum of d2, use the formula