Correlation, Anova, and SPSS

774/801 Sept 8, 2004

John Hattie & Tony Hunt

Test the Nation: The NZ IQ test

Do males and/or females over estimate their IQs?

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

92

94

96

98

100

102

104

106

108

110

18-25 26-40 41-59 60+

Fem

ale

Fem

ale

Fem

aleMal

e

Fem

ale

Mal

e

Mal

e

Mal

e

50

55

60

65

70

75

80

Language Spatial Arithmetic* Memory Reasoning* Learning

Fem

ale

Mal

e

Mal

e

Mal

e

Mal

e

Mal

e

Mal

e

Fem

ale

Fem

ale

Fem

ale

Fem

ale

Fem

ale

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.

Concept of Correlation

Strength and Direction But how high is high? We know from sampling what the distribution

looks like?

1. PARE: Power

Is your study POWERFUL enough to detect the effect you are investigating

Do chickens have lips?

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 =.05

3. PARE: Type II errors

Type I errors – Rejecting a claim when it is true (=.05)

Type II errors – Accepting a claim when it is false (e.g., chickens do not have lips, if it is indeed true)

How big does a correlation need to be?

Two answers –

Greater than chance

Large enough to be meaningful

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

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

For correlation …

z = Zr / 1 * (1-r) We have probabilities in SPSS

MAGNITUDE

Effect-size = 2r/ (1-r2)

Differences between means

What are the differences in levels of

WELL-BEING among males and

females, and between Australia and

New Zealand

What are the differences in levels of WELL-BEING among males and females, and between Australia and New Zealand well-being?

Country * GENDER Cross tabulation

GENDERMALE FEMALE Total

CountryNew Zealand 516 644 1160Australia 421 694 1115

Total 937 1338 2275

SAMPLE SIZES

Australia Mn sd Effect-size

Male 45.7 10.6

OZ Male-Female

Female 46.2 10.6 .??

Total 46.0 10.6

New Zealand

Male 53.6 7.5

NZ Male-Female

Female 54.3 7.4 .??

54.0 7.5

NZ – Australia= .??

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

Australia Mn sd Effect-size

Male 45.7 10.6

Female 46.2 10.6 .04

Total 46.0 10.6

New Zealand

Male 53.6 7.5

Female 54.3 7.4 .08

54.0 7.5

NZ - Australia .89

anova

Source df MS F p

Country 1 35211.9 416.71 <.001

Gender 1 151.8 1.80 .180

Country * Gender 1 6.1 0.07 .787

Error 2271 84.5

Interaction

45

46

47

48

49

50

51

52

53

54

55

Australia New Zealand

FEMALE

MALE

off to the lab ….

774/801 Sept 8, 2004

John Hattie & Tony Hunt