2. Results, Descriptive and Inferential
A guide for the IB Psychology IA Results section (SL & HL)

3. Upcoming IB Psychology Webinars
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4. What the IB says regarding IA results sections
Students should
Apply descriptive statistics to analyse data (for example, mean, median, mode, range, standard deviation).
 Distinguish between levels of measurement (including nominal, ordinal, interval, ratio).
 Apply appropriate graphing techniques to represent data (for example, bar chart, histogram, line graph, frequency polygon).
 Apply an appropriately chosen statistical test (for example, Wilcoxon matched-pairs signed-ranks test, Mann–Whitney U test, sign test, chi-squared test) in order to determine the level of significance of data (HL only).
(Psychology guide p 51)

5. Concepts vital to the students’ understanding of the IA results section
Level of data: nominal, ordinal, interval, ratio
Measure of central tendency – which to use and why
Measure of dispersion – which to use and why
Probability
Significance

6. Easy ways to explain
Explain nominal quickly – not to be used for IA, because not possible to apply measures of CT and dispersion.
Ordinal = order, unequal distance between items (1st, 2nd, 3rd, etc. Likert scale for example)
Interval = equal distances between integers (numbers of items remembered, etc.) Note quasi-interval = where we cannot be sure that the items to be remembered were all of equal difficulty or value, like a list of words.
Ratio = equal distances between integers, on a scale with a true zero, and where 4 is twice 2 and 8 is twice 4, etc. (Time, speed, height, weight).

7. Measures of central tendency and dispersion
Data Level
Central tendency measure
Dispersion measure
Ordinal
Median
Range or inter-quartile range
Quasi-interval
Median (unless no reason to really presume different intervals, then mean)
Inter-quartile range or SD
Interval
Mean SD
Ratio

8. Probability and Significance
The probability measure that is used for social sciences, including psychology is usually p< This means that IF the difference between the results of two groups or conditions is 5% or less likely to have happened by chance, then it is significant at the p< 0.05 level. Tables of significance can show this. With the Mann-Whitney (independent samples) and the Wilcoxon (repeated measures) tests students can measure the significance of the difference in one direction (directional/one-tailed hypothesis) or in either direction (non-directional/two-tailed hypothesis).

9. Everyday Examples of Probability
Possible Questions:
What is the probability (p) that I will pick a red card?
What is the probability (p) that I will pick a club?
What is the probability (p) that I will pick picture card?
What is the probability (p) that I will pick an ‘Ace’?
Maths Hint:
Club = 13/52 = 0.25
Picture = 12/52
Ace = 4/52
Ace = 0.07
Club = 0.25
Red Card = 0.5
1 (Certain)
0 (Impossible)
0.5 (Even)
Picture = 0.23

10. What is significance?
What is significance? Significance is a statistical term which indicates that the association between two (or more) variables is strong enough for us to accept the experimental hypothesis.
Psychologists will only accept their experimental hypothesis if they are at least 95% sure that the results were caused by the IV.
P= ≤0.05 5%
95%
1 (Certain)
0 (Impossible)
0.5 (Even)

11. SL Results section
Statement of the measure(s) of central tendency, as appropriate
Statement of the measure(s) of dispersion, as appropriate
Justification of choice of descriptive statistic
Appropriate use of fully explained graphs and tables (may be computer generated)
Criterion E (4 marks)
Results are clearly stated and accurate and reflect the aim of the research.
Appropriate descriptive statistics (one measure of central tendency and one measure of dispersion) are applied to the data and their use is explained.
The graph of results is accurate, clear and directly relevant to the aim of the study.
Results are presented in both words and tabular form.
Problem with nominal data and chi-square as no measure of CT and dispersion

12. HL Results section
Descriptive statistics identical to SL, but out of 2 marks
PLUS, in a separate Results (Inferential) section:
Reporting of inferential statistics and justification for their use (calculations in appendix)
 Statement of statistical significance
Criterion F (3 marks)
An appropriate inferential statistical test has been chosen and explicitly justified.
Results of the inferential statistical test are accurately stated.
The null hypothesis has been accepted or rejected appropriately according to the results of the statistical test.
A statement of statistical significance is appropriate and clear.

13. Choosing the right inferential statistical test
Design
Type of data
Ordinal
Interval/ratio
Independent samples
Mann-Whitney U test
Unrelated t-test
Repeated measures
Wilcoxon
Related t-test
Matched pairs
In order to use a t-test, data must meet the requirements of a t-test. It is a parametric test. (Tests that assume the underlying source population(s) to be normally distributed; they generally also assume that the measures derive from an equal-interval scale.)
The level of measurement should be at least interval.
The data samples should have been drawn from a normally distributed population.
The samples should have similar variances.
Taken from the TSM at occ.ibo.org

14. Keeping it simple
With the opportunity sampling that the students are using it is unlikely that the requirements for a t-test will be met. HL Example 3 in the TSM on the OCC justifies use of an unrelated t-test by referring to normal distribution of data (not of sample); interval data; small SD – and still only gets 1 from the moderator with the comment that this is a parametric test and its use has not been justified. Strong advice: reduce interval or ratio data to ordinal by ranking and use non-parametric tests - Mann-Whitney (Independent samples) or Wilcoxon (Repeated measures). Do not accept an experiment that generates nominal data because this creates problems when it comes to measures of CT and dispersion. Example follows

15. Summary of experiment
The experiment was a partial replication of Diemand-Yauman’s (2011) research into disfluency of font and memory. It was an independent measures (independent samples) design, with one group of participants remembering a list of 25 two-syllable words written in an italicized font (disfluent condition) and the control group remembering the same list of words written in a normal font (fluent condition). The hypothesis was directional in that it was predicted that those in the disfluent group would remember significantly more words. The results showed that the disfluent font group recalled more words from the list, but the difference between the two groups was not significant at the p< 0.05 level. Here is an example of how the results section(s) and data appendices should be laid out. This can be used as the basis for any SL or HL IA.
We suggest that you look at how the material here allows students to meet the highest descriptor band of the Results criteria. This layout will work for any experiment that uses mean and SD. Obviously some adaptations would be needed for repeated measures design, and use of Wilcoxon test, but the principles remain the same.

16. Results (Descriptive) WORDS (HL & SL)
The data obtained was quasi-interval. There was no way of telling if each word was equally difficult to remember, and therefore no certainty that the raw data is equally spaced. However, because the words were two-syllable nouns in common use in the English language, they should have been equally well remembered, and there were no extreme outliers, the mean was used. The standard deviation was calculated to show the dispersion around the mean, being the measure of dispersion that is best used with the mean. Group A (disfluent group) remembered a mean of 19.6 words, with a SD of Group B (fluent group) remembered a mean of 17.5 words, with a SD of (For raw data and calculations, see Appendices A, B & C).
Level of data
Measure of CT justified
Measure of dispersion justified
Results stated
[Note – calculations and raw data go in Appendices]

17. Results (Descriptive) TABLE (HL & SL)
Table of results showing the differences in the mean number of words recalled between the disfluent and fluent groups
Group
Mean no. of words recalled SD
A (disfluent)
19.6
2.76
B (fluent)
17.5
2.17
3 x 3 cell table. Should identify the groups, the measure of CT and the measure of dispersion. Title needed.
[Calculation of SD for each group from

18. Results (Descriptive) GRAPH (HL & SL)
Bar chart created in Excel using a suitable scale, labelled axes, groups identified, title.

19. HL IA Results (Inferential) (HL only)
As the experimental design was independent samples, and we could not be certain of a normal distribution of our population, our quasi-interval data was ranked as ordinal and the non-parametric Mann-Whitney U-test of statistical significance was applied. For n1 = 10 and n2 = 10, the critical value of U is 27 for a one-tailed test at the p < 0.05 level. To be significant, the calculated U has to be equal to or less than this critical value. The calculated U was 28.5 (see Appendix D) and therefore the difference between the two groups was not significant. The null hypothesis, that any increase in recalled words from the 25-word list written in a disfluent (italicized) font will not be significant and will be due to chance, must be accepted. There was no significant increase in words remembered by Group A (disfluent condition). [Calculations done using ]
Calculations go in the Appendices.
You will probably want to use this site – I do!
Explanation, using exp design and data level, for using Mann-Whitney U-test.
Numbers in groups
Critical value
Found value
Statement of statistical significance

20. Appendices
Raw data and calculations

21. Appendix A
All appendices should have a heading.

22. Appendix B Calculation of mean Group Total A (disfluent) 17 21 19 1624 20 23
196
B (fluent) 15 18 14
175
Mean for each group= Total/n (no. of participants in the group)
Group A mean = 19.6 words remembered
Group B mean = 17.5 words remembered
Show how the mean was arrived at. Include the formula.

23. Appendix C Calculation of standard deviation
Calculation of SD for each group from
Formula used:
Include formula in Appendices

24. Appendix C (continued)
Calculation of SD Group A (disfluent)
Group A SD = 2.76

25. Appendix C (continued)
Calculation of SD Group B (fluent)
Group B SD = 2.17
Summary: Group A (disfluent): Mean no. of words recalled = 19.6 SD = 2.76
Group B (fluent): Mean no. of words recalled = 17.5 SD= 2.17

26. Appendix D
Calculation of inferential statistics Mann-Whitney U-test calculated with help from
It is important to paste the sheet of calculations into the appendices.

27. Check with the Mann-Whitney table of significant values

28. Appendix D (continued)
Therefore, the increase in the words remembered by Group A (disfluent) was not significant.
Plus the results of the calculations.

29. Upcoming IB Psychology Webinars (again )
Brain & behaviour: More than genetics? Fri 4 Nov 4.30pm GMT
Cognitive Psychology: How to use theories of memory. Wed 9 Nov 4.30pm GMT
Social Psychology: Stereotype formation and effects. Thu 10 Nov 4.30pm GMT
Quality answers for Qualitative Methods papers. Wed 16 Nov 8.30pm GMT

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