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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
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Language Spatial Arithmetic* Memory Reasoning* Learning
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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
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Australia New Zealand
FEMALE
MALE
off to the lab ….
774/801 Sept 8, 2004
John Hattie & Tony Hunt