Correlation: A & B tend to occurtogether more frequently than onewould expect by random chanceMultiple Regression: Above is truewhen comparing those otherwisesimilar in certain ways
CorrelationHigher educationand charitable givingtend to occurtogether (morefrequently than onewould expect byrandom chance)
Multiple RegressionHigher educationand charitable givingtend to occurtogether (morefrequently than onewould expect byrandom chance)comparing thosewith otherwisesimilar incomeand wealth
Explaining Associations: 1. Random chance 2. A causes B 3. B causes A 4. Something else causes both A & BMultiple regressionallows us to excludespecific items from#4, unless we can’t ordidn’t measure it.
Nature says kids’ nightlights cause myopia “Although it does not establish a causal link, the statistical strength of the association of night-time light exposure and childhood myopia does suggest that the absence of a daily period of darkness during early childhood is a potential precipitating factor in the development of myopia.”G.E. Quinn, C.H. Shin, M. Maquire, R. Stone (University of Pennsylvania Medical School), 1999,Myopia and Ambient Lighting at Night, Nature, 399, 113.
Nature says kids’ nightlights cause myopia 1. Random chance 2. A causes B 3. B causes A 4. Something else causes both A & BG.E. Quinn, C.H. Shin, M. Maquire, R. Stone (University of Pennsylvania Medical School), 1999,Myopia and Ambient Lighting at Night, Nature, 399, 113.
Rebuttal: Maybe parents’ myopia causes both nightlights and child’s myopia? “…we find that myopic parents are more likely to employ night-time lighting aids for their children. Moreover, there is an association between myopia in parents and their children…” “…Quinn et al.’s study should have controlled for parental myopia.”J. Gwiazda, E. Ong, R. Held, F. Thorn (New England College of Optometry), 2000, Myopia andAmbient Night-Time Lighting, Nature, 399, 113.
Statistics tests a small sample topredict the whole population Significance shows how likely our result might have been due to an unusual random sample, rather than an actual difference in the population
Most papers report some measure of statisticalsignificance (chance that the association wasdue to a weird random sample) • p-value • confidence interval
How likely is it to randomly drawthese five fruits from a truckloadwith as many apples as oranges? p-value
p-valuep<.05 = there is less than a 5% chance that the result was caused by an unusual random sample where there was no actual (population) difference
Was there a significant gender difference in planned givers with a will v. a trust? No
This (sample) difference could haveeasily occurred even if the two(population) groups were the same
It DOES NOT mean the two(population) groups do not differ,only that WE CAN’T TELL.
No “*” means we can’t confidently tell the effect of this item
95% Confidence intervalIf you kept taking random samples, 95%of the time the true (population) valuewould appear inside the confidenceinterval associated with each sampleSampleAverageStrength Population Average Strength Confidence Interval
Dashed line is a 95% confidence intervalS. Huck and I. Rasul (2008) Testing consumer theory in the field: Private consumption versus charitable goods
Multiple Comparisons Problem How likely is it to randomly draw these five fruits from a truckload with as many apples as oranges? Would your answer change if I got to draw 20 times to find this group?
If all variables are random, about oneout of 20 will have a p-value<.05
“We tested 100 items and found 5 to be significant at p<.05.”
Significance v. MagnitudeIt is possible to be highly confident of avery small effect. This may be publishable,but not practically important.
Numbers(coefficients) resulting from complex statistical techniques may not be directlyinterpretable in terms of real world magnitude
The impact of children on the probability of exclusively secular giving is“-0.089”, butthe meaning of that number is not easily translated
Even with complex techniques, we can easily compare sign andmagnitude relative to other variables
Race and education factors are3-4 times as large. More children have an oppositerelationship compared with more education.
Odds ratios are differentUsually you cancompare sign andsize, but odds ratiosare always positive
Odds ratios: the odds of an event occurringin one group over the odds of it occurring in another group <1 negative; >1 positive; =1 none
Odds ratios <1 correspond with negative coefficient numbers in other reportingPamala Weipking (2008) Giving to particular charitable organizations: Do materialists support local organizations and do Democrats donate to animal protection?
Finding academic research articles ISI ranked academicIncludes everything, journals articles onlyeven workingpapers andindustry literature
How to read academic research (even if you’re not an expert)Dr. Russell James III, Texas Tech University www.EncourageGenerosity.com