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1. Inferential tests for Dummies 2. <ul><li>If your experiment needs statistics, you ought to have done a better experiment. (Rutherford)…
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  • 1. Inferential tests for Dummies
  • 2. <ul><li>If your experiment needs statistics, you ought to have done a better experiment. (Rutherford) </li></ul><ul><li>Do not put your faith in what statistics say until you have carefully considered what they do not say.  (William W. Watt) For example… The average human has one breast and one testicle.  (Des McHale) </li></ul><ul><li>The manipulation of statistical formulas is no substitute for knowing what one is doing. (Blalock Jr) </li></ul><ul><li>He uses statistics as a drunken man uses lampposts - for support rather than for illumination.  (Lang) </li></ul> words of wisdom
  • 3. Aim <ul><li>Understanding…. </li></ul><ul><li>Which inferential test to use and why </li></ul><ul><li>Levels of significance </li></ul><ul><li>Degrees of freedom </li></ul><ul><li>Critical and observed value </li></ul><ul><li>What ‘it is significant’ means </li></ul> aim
  • 4. <ul><ul><li>“ A statistical procedure that uses data from a sample to test an hypothesis about a population ” </li></ul></ul><ul><ul><li>In simple terms: If an interesting difference between treatment groups is seen in an experiment will this difference be reflected in the population generally? </li></ul></ul>hypotheses testing
  • 5. <ul><li>We use results of statistical tests to chose between the following: </li></ul><ul><li>null hypothesis H 0 ( loud noise has no effect on learning) and alterative/experimental hypothesis H 1 (loud noise disrupts learning) </li></ul>hypotheses testing
  • 6. <ul><li>Non-parametric </li></ul><ul><li>When we have nominal or ordinal data we use non-parametric tests: </li></ul><ul><li>Chi-squared, Sign test, Wilcoxon sign test, Spearman rank and Mann-whitney U test. They are not precise. </li></ul>Types of inferential tests
  • 7. <ul><li>Parametric </li></ul><ul><li>Independent t test, related t test, Pearsons product moment </li></ul><ul><li>To use a parametric test you need to: </li></ul><ul><li>have scores measured on an interval scale </li></ul><ul><li>scores must be normally distributed </li></ul><ul><li>variability of scores for each condition should be the same (homogeneity of variance). </li></ul>Types of inferential tests
  • 8. Tests of difference Participant design Level of measurement Nominal data Ordinal data Interval/ratio data Repeated measures or matched pairs Sign test Wilcoxon Matched Related t test* Independent groups chi-squared test Mann-Whitney Unrelated t test* Tests for relationship (correlations) Ordinal data Interval/ratio data Spearman’s Rank Correlation Co-efficient Pearson’s Product Moment Correlation Co-efficient*
  • 9. <ul><ul><li>State the Hypothesis </li></ul></ul><ul><ul><li>Set the significance level and the appropriate statistical tests to use </li></ul></ul><ul><ul><li>Collect data through experimentation and Compute Sample Statistics </li></ul></ul><ul><ul><li>Compare observed value and critical value in the statistical table </li></ul></ul><ul><ul><li>Make a Decision as to whether you accept your null or experimental hypothesis </li></ul></ul>Steps in hypotheses testing
  • 10. <ul><ul><li>State two hypotheses about the unknown population </li></ul></ul><ul><ul><li>NULL HYPOTHESIS: </li></ul></ul><ul><ul><ul><li>states that there is no effect, no difference, or no relationship or specific effect, difference or relationship </li></ul></ul></ul><ul><ul><ul><li>H 0 : loud noise has no effect on learning </li></ul></ul></ul><ul><ul><ul><li>ALTERNATIVE HYPOTHESIS: </li></ul></ul></ul><ul><ul><ul><li>states that there is an effect, there is a difference, or there is a relationship </li></ul></ul></ul><ul><ul><ul><li>H 1 : loud noise disrupts learning </li></ul></ul></ul>State the hypotheses
  • 11. <ul><ul><li>The significance level is the percentage of results that you would accept as being due to chance and still accept that your study worked. </li></ul></ul><ul><ul><li>If you are willing to accept that 5% (or lower) of your results are due to chance and 95% (or more) are due to your IV then your level of significance is 5%. This is what psychologists usually use. </li></ul></ul><ul><ul><li>α = .05 </li></ul></ul><ul><ul><li>If you are willing to accept only 1% due to chance then 1% is your level of significance. α = .01 </li></ul></ul>Set the significance level ( α level)
  • 12. <ul><ul><li>In other words, the probability (p) of your results being due to chance is: </li></ul></ul><ul><ul><li>p ≤ 0.05 </li></ul></ul>Set the significance level ( α level)
  • 13. <ul><ul><li>Collect data through experimentation, calculate sample statistic and compare it to the critical value. </li></ul></ul>Set the significance level ( α level)
  • 14. <ul><ul><li>E.g. A teacher records whether her 8 Year 13 students improved or got worse after she implemented a revision programme. </li></ul></ul><ul><ul><li>The probability of improvement is p and getting worse is q. </li></ul></ul><ul><ul><li>H 0 : p = .5 H 1 : p ≠ .5 </li></ul></ul><ul><ul><li>p + q = 1 </li></ul></ul><ul><ul><li>level of significance is α = .05 </li></ul></ul>An example of a statistical test: Sign Test
  • 15. <ul><ul><li>Lets pretend that 3 out of the 8 students got worse and 5 out of the 8 improved. </li></ul></ul><ul><ul><li>X = no. of positive changes </li></ul></ul><ul><ul><li>n = no. of participants </li></ul></ul><ul><ul><li>Z = X – pn = </li></ul></ul><ul><ul><li>√ npq </li></ul></ul>An example of a statistical test: Sign Test 0.71 observed value
  • 16. <ul><ul><li>Now compare your observed value of z = 0.71 to the critical value in the statistical table </li></ul></ul><ul><ul><li>N = 8 </li></ul></ul><ul><ul><li>2 tailed, level of significance 0.05 </li></ul></ul><ul><ul><li>Critical value is 0 </li></ul></ul><ul><ul><li>Your observed value must be equal or less than the critical value to be significant. </li></ul></ul>An example of a statistical test: Sign Test
  • 17. <ul><ul><li>So your observed value is not significant so you accept your null hypothesis that the revision programme had no effect. </li></ul></ul>An example of a statistical test: Sign Test
  • 18. Some statistical tables require you to work out the degrees of freedom, df. In the exam you will be told how to work this out. Sometimes it is simply n – 1 For some tests the observed value has to be greater than critical value in table and for some equal to or less. Other tests
  • 19. If your results were significant it means your experiment worked and you did find a difference. You reject your null hypothesis and accept your experimental/alternative hypothesis. What significance means
  • 20. <ul><li>Now do exercise 16 </li></ul>Any questions?
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