Inferential Statistical Tests

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  • Inferential Statistical Tests
    • Sign Test
      • Nominal Data
      • Not Frequency Data
      • Methods
        • 1. State the alternative and null hypothesis.
          • This is a non-directional hypothesis therefore requires a two tailed test.
        • 2. Record data and work out the "sign".
          • The "sign" is wether it is a + or - depending on wether the results are the same or diffrent
        • 3. Find the observed value of "S"
          • S= the number of times the less frequent value occurs
        • 5. State the conclusion.
          • If the observed value is smaller than the critical value we must accept the alternative hypothesis, and reject the null hypothesis.
    • Chi Square Test
      • Nominal Data (The level of data when they are in separate categories. Can includes numbers)
      • Frequency Data (occurrences in each category)
      • Example study:
      • Method:
        • 2. Draw up a contingency table. Include totals around it.
          • Example of a contingency table
        • 1. State the null and alternative non-directional hypothesis.
          • The alternative hypothesis is non directional, requiring a two tailed test.
        • 3. Compare the observed and expected frequencies (calculated by multiplying two totals, and diving that by the overall total)
        • 4.Find the observed value
        • 5. Add the critical value
        • 6. State the conclusion
          • If the observed value is more than the critical value, we accept the alternative hypothesis
    • Spearman's Rho Test
      • Correlation
        • Used to determine the correlation between two co-variables is significant or not.
      • Not nominal data
      • Method:
        • 2. Record and Rank the data.
        • 1. State the alternative and null hypothesis.
          • Null hypothesis (There will be no correlation) VS Alternative directional hypothesis. This makes Spearman's Rho a one tailed test.
        • 3. Calculate the rank difference.
        • 4.Find the observed value:    rho=1-(6?d²/ N(N² -1) )
        • 5. State the conclusion
          • If the observed value is greater than the critical value. It appears that you reject the null hypothesis.
            • However, if the sign is in the wrong direction (e.g. negative), and does not support the alternative hypothesis, the null hypothesis is accepted.
      • Pairs of scores: Repeated Measures
    • Mann Whitney U Test
      • Not Nominal Data
      • Not correlational
      • Independent Groups
      • Method
        • 3. Find the observed value of U.
          • U=(n_1×n_2 )+((n_1×(n_1+1))/2- T-1
        • 2. Record the data in a table and find the mean of each condition.
        • 4.Find the critical value of U.
        • 1. State the alternative hypothesis and null hypothesis.
          • The alternative hypothesis is a directional hypothesis therefore requires a one tailed test.
        • 5. State the conclusion.
          • When p?0.05 for a one tailed test the critical value is (U) and the observed value is (_) therefore the data is significant. This means that we must (reject/accept) the null hypothesis and (accept/reject) the alternate hypothesis.
            • If the observed value is smaller than the critical value we must accept the alternate hypothesis.
        • 3.Then rank both conditions (all together) from lowest to highest
        • 4. Add up all the ranks. (n1= the number of numbers)
      • Ordinal Data
      • Directional Hypothesis
    • Wilcoxon T Test
      • Not Nominal Data
      • Not correlation
      • Not Independent group
      • Method
        • 3. Rank
        • 2. Record, and calculate diffrence
        • 4. Find the observed valye of T
          • T = the sum of the ranks of the less frequent sign.
        • 1. State the alternative and null hypotheses
          • Directional. Requires one tailed test.
        • 5. Find the critical value of T
          • N=sum of participants - omit results.   Look up the critical value in the table
        • 6. State the conclusion
          • If the observed value is smaller than the critical value, we must accept the alternate hypothesis
      • Directional Hypothesis
      • At least Ordinal Data

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