1. Lesson 5 DATA ANALYSIS

2. Am I using and independent groups design or repeated measures? Independent groups Mann- Whitney U test Repeated measures Wilcoxon test Experiments

3. Our raw data for today: Ppt12345678 No of words recalled Method 1651068598 Method 277887699 Independent groups or repeated measures?

4. Wilcoxon  Used to check for statistical significance when it’s a test of difference for related data. Repeated measures only.

5. Step 1  The difference between each participants’ two scores is calculated, you also need to state if it’s a positive or negative number Ppt12345678 No of words recalled Method 1651068598 Method 277887699 Difference Sign (+/-)

6. Step 2  The differences are given a rank to show their order – the lowest gets rank 1. Ignore +/- signs; and 0. If there are multiple scores which are the same, calculate their mean rank Ppt12345678 No of words recalled Method 1651068598 Method 277887699 Difference12221101 Rank Sign (+/-)--+-+-- Mean rank: We add up the ranks that these scores would have had, if they had been different from each other (the ranks of 1, 2,3 and 4), and then divide the sum of these (1+2+3+4 = 10) by the number of ranks involved (4). This gives us an "average" rank,

7. Step 3  Total the ranks for the positive differences and for the negative differences. The smallest is the observed value (T) Ppt12345678 No of words recalled Method 1651068598 Method 277887699 Difference12221101 Rank2.5666 Sign (+/-)--+-+--

8. Step 3  Total the ranks for the positive differences and for the negative differences. The smallest is the observed value (T)  Positive =  Negative =  So, the observed value of T is=  The observed value needs to be equal to or less than the critical value to be significant

9. Step 4  Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!)  Is it directional or non-directional  Does that mean it’s one-tailed or two-tailed?  What level of significance does Psychology use?  How many participants did we have in our experiment? Ignore scores of 0! N – the number of scores left ignoring those with those with 0 difference.

10. Step 4  Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!) Level of significance for two-tailed test 0.100.05170.020.01 Level o21f significance for one-tailed test N0.050.0250.010.005 50 620 7320 85320 98532 10 853

11. Step 4  Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!) Level of significance for two-tailed test 0.100.05170.020.01 Level of significance for one-tailed test N0.050.0250.010.005 50 620 7 3 20 85320 98532 10 853

12. Step 4  Observed value = 8.5  Critical value = 3  WILCOXON = Observed value equal to or less than Critical value to be significant

13. Step 5 How to write this up:  The results are not significant  suggesting there is no difference between method 1 and method 2 in terms of memory improvement.  The observed value (8.5) is greater than the critical value (3)  at p<0.05, one-tailed, N=7.  Therefore, we have to accept the null hypothesis, and reject the alternate hypothesis.

14. New set of a data Participant no.Condition ACondition BDifferenceRankSign +/- N=10 1811 277 3916 41112 51318 698 7816 8517 91311 10617

15. H/W  Make up a one tailed hypothesis  Make up a set of data (10 participants)  Work out the observed and critical value  Explain whether you would accept your hypothesis  Check you answer using the excel spreadsheet or calculator on line:  http://www.socscistatistics.com/tests/signedranks/Default2.aspx http://www.socscistatistics.com/tests/signedranks/Default2.aspx