inferential tests

• How to do a sign test?

  step 1 - enter pairs of related data in a table.

  step 2 - for each pair score plus or minus (plus if item 1> item 2 or if the items are the same, minus if item 1< item 2 or if the items are different.

  step 3- S=the number of less frequent sign (plus or minus)

  step 4 - compare calculated value(S) with critical value.
• How to do a Mann-Whitney test?

  Step 1

  - rank all data list all the data from lowest to highest. lowest number has a rank of 1.

  - where two data items are the same, add up the ranks they would get and use the mean for those ranks.

  Step 2 - work out the calculated value of U.

  -Add total ranks of group A and total for Group B.

  -use the smaller value of R to calculate either Ua or Ub.

  -Ua=Ra-[Na(Na+1)]/2 (Na=number of participants in group A)

  Step 3 - compare calculated value (Ua or Ub) with the critical value.
• How to do a Wilcoxon Test?

  step 1 - calculate the difference between each pair of data and then rank the differences.

  step 2 - work out the calculated value of T. T is the sum of the less frequent sign.

  step 3 - compare calculated value (T) with the critical value.
• how to test for Spearman's rho?


  Step 1 - rank each set of scores separately.

  Step 2 - find the difference (d) between each pair of ranks, square it and add then up $(∑ d^2)$.

  Step 3 - work out the calculated value of rho.

  $rho=$$1- 6∑ d^6/N(N^2-1) Where ∑ =$$'sum of$

  Step 4 - compare calculated value (rho) with critical value.
• How to test Chi-Squared?

  Step 1 - fill data (observed values,O) in a contingency table (see left).

  Step 2 - calculate expected frequencies (E) for each cell (row total x column total and divided by overall total).

  Step 3 - work out the calculated value of $x^2$

  $x^2=$$∑ (0-E)^2/E)$

  Step 4 - Compare calculate value with the critical value
• How to test for Pearson's r - unrelated and related t-tests ?

  the formula for these tests is very complex and very unlikely to be used in an exam.

  you might be required to calculate the degrees of freedom (df):

  Pearson's r: $df=$$N-2$

  Unrelated t-test: df = Na +Nb-2

  Related t-tests:$df=$$N-1$
• Choosing a statistical test

  Nominal (categories) - Chi-squared test, sign test

  Ordinal (places in order, intervals are subjective)- Mann-Whitney U test, Wilcoxon, spearman's Rho

  Interval(Units of equal, precisely defined size) - Unrelated t-test, related t-test, Pearson's r