Statistical Tests

• Mann-Whitney is a test of difference between two groups of data. It is used when there is ordinal data collected using an independent group design, unrelated.
• Steps to complete Mann-Whitney

  1. Rank the data sets using both at the same time
  2. Calculate the sum of rank Ra and rank Rb
  3. Take the smallest rank value and find the calculated value
  4. Find the critical value using the numbers and the table
  5. Determine whether the results are significant
• Calculated value = $Ra - ((Na(Na+1))/2)$
• Wilcoxon is a test of difference when there is ordinal data and a design using repeated measures.
• Steps to complete Wilcoxon:

  1. work out the difference between score 1 and 2
  2. rank differences, ignore ones with no difference
  3. calculate T by adding all rank values of the less frequent sign
  4. Find the critical value using N and the table, not including the data with no difference.
  5. determine whether the results are significant
• If the results are significant, the critical value will be the same as or larger than the calculated value.
• Unrelated T-Test

  Requirements:

  • test of difference
  • interval data
  • independent group design/matches pairs
• Unrelated T-Test


  Steps:

  1. Calculate the sum of group A
  2. Calculate the sum of group B
  3. Square each value of group A and calculate the sum
  4. Square each value of group B and calculate the sum
  5. Calculate T using the equation
  6. Calculate critical value, ignoring signs, and compare
• Unrelated T-Test

  T = ((mean of A) - (mean of B))/ square root of ((Sa + Sb)/Na + Nb -2) x (Na+Nb)/Na x Nb

  e.g:

  • mean of a = 12
  • mean of b = 4
  • Sa = 54
  • Sb = 36
  • Na = 10
  • Nb = 10

  T = 103.28
• Unrelated T-Test

  Sa/Sb = sum of Xa^2 - (sum of Xa^2/Na)
• Related T-Test

  Requirements

  • Test of difference
  • Interval data
  • Repeated measures
• Related T-Test


  Steps

  1. Calculate difference between scores for condition A and B
  2. Square each difference
  3. Calculate the sum of the difference collum
  4. Calculate the sum of the d^2 collumn
  5. Calculate T using the equation
  6. Calculate critical value and determine significance
• Related T-Test

  T = sum of difference/ square root of ((N(sum of d^2) - (sum of d)^2)/N-1)
• Chi-Squared


  Requirements:

  • test of association
  • nominal data
• Chi-Squared


  Steps:

  1. Work out observed frequencies totals for rows and collums
  2. calculate expected frequencies: (total of row x total of column)/overall total
  3. Calculate E (expected) - O (unexpected) and (e-o)^2
  4. divide each (E-O)^2 by E
  5. find calculated value: sum of (E-O)^2
  6. Compare critical and calculated value
• Spearman's Rho


  Requirements

  • ordinal data
  • test of correlation
• Spearman's Rho


  Steps:

  1. Rank score in sets seperately, finding the mean for when there are more than 1 score
  2. calculate difference between ranks for each pair
  3. square each difference
  4. add up squared difference
  5. calculate Rho: 1 - ((6 x sum of d^2)/ N(N^2-1))