Correlation, Anova, and SPSS

1. Correlation, Anova, and SPSS 774/801 Sept 8, 2004 John Hattie & Tony Hunt

2. Test the Nation: The NZ IQ test • Do males and/or females over estimate their IQs?

3. Some findings • Nearly all of us estimate that our IQ is above 100 (the average IQ scores from reputable tests). • Males give a higher mean self-estimate of IQs than do females (113 vs. 106). • Males estimates were significantly higher than their actual IQ, and females estimates were significantly lower than their actual IQ • Females attribute higher IQs to others than they claimed for themselves, whereas males attribute lower IQs to others than for themselves. • There is only a modest correlation between self-estimated IQ and actual IQ score. • Fathers are estimated as having higher IQs than mothers (114 vs. 107) • Females, unlike males, estimated higher IQs onto their fathers than their methods

6. Why??? • It has been noted that males have a slightly larger brain size advantage (of .78 sd units), and the correlation between brain size measured by magnetic resonance imaging and intelligence is .35, hence the male advantage for intelligence accruing from greater brain size is .78 * .35 = .27 sd = 4 IQ points. • Males tend to have more general knowledge than females, particularly on current affairs, physical health and recreation, science, and arts.

7. Concept of Correlation • Strength and Direction • But how high is high? • We know from sampling what the distribution looks like?

8. 1. PARE: Power • Is your study POWERFUL enough to detect the effect you are investigating Do chickens have lips?

10. 2. PARE: Chance • Did the effect/conclusion occur by chance • E.g., That two means are the same – the hypothesis of no difference • Setting a rejection level, say a =.05

11. 3. PARE: Type II errors Type I errors – Rejecting a claim when it is true (a =.05) Type II errors – Accepting a claim when it is false (e.g., chickens do not have lips, if it is indeed true)

12. How big does a correlation need to be? Two answers – Greater than chance Large enough to be meaningful

13. Greater than chance … • If we r = .20, is it really different from a chance (r=0) effect? • Given N, we could sample 1000’s of times to see what a distribution of r’s would be • And then see what probability of obtaining the actual r (=.20) we found

14. When would be satisfied? • If I said, that there is a 99% chance it will rain tomorrow, would you be reasonable certain it would rain tomorrow? • 95%? 90%. 80%. 50% • 10%. 5%. 1%?? • The traditional claims

15. For correlation … • z = Zr / 1 * (1-r) • We have probabilities in SPSS MAGNITUDE Effect-size = 2r/ (1-r2)

16. Differences between means • What are the differences in levels of WELL-BEING among males and females, and between Australia and New Zealand

17. What are the differences in levels of WELL-BEING among males and females, and between Australia and New Zealand well-being? SAMPLE SIZES Country * GENDER Cross tabulation GENDER MALE FEMALE Total Country New Zealand 516 644 1160 Australia 421 694 1115 Total 937 1338 2275

19. GRAPH Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph

21. anova

22. Interaction

23. off to the lab …. 774/801 Sept 8, 2004 John Hattie & Tony Hunt