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

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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

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 = Z r / 1 * (1-r) We have probabilities in SPSS MAGNITUDE Effect-size = 2r/ (1-r 2 )

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 GENDER MALEFEMALETotal CountryNew Zealand5166441160 Australia4216941115 Total93713382275 SAMPLE SIZES

Australia MnsdEffect-size Male45.710.6 OZ Male- Female Female46.210.6.?? Total46.010.6 New Zealand Male53.67.5 NZ Male- Female Female54.37.4.?? 54.07.5 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

AustraliaMnsdEffect-size Male45.710.6 Female46.210.6.04 Total46.010.6 New Zealand Male53.67.5 Female54.37.4.08 54.07.5 NZ - Australia.89

anova SourcedfMSFp Country135211.9416.71<.001 Gender1151.81.80.180 Country * Gender16.10.07.787 Error227184.5

Interaction

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

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