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Digression - HypothesesMany research designs involve statistical tests involve accepting or rejecting a hypothesisNull (statistical) hypotheses assume no relationship between two or more variables. Statistics are used to test null hypothesesE.g. We assume that there is no relationship between weight and fast food consumption until we find statistical evidence that there is123

ProbabilityProbability is the odds that a certain event will occurIn research, we deal with the odds that patterns in data have emerged by chance vs. they are representative of a real relationshipRemember inference is the keysamples and populationsAlpha () is the probability level (or significance level) set, in advance, by the researcher as the odds that something occurs by chance1234

ProbabilityAlpha levels (cont.)E.g. a = .05 means that there will be a 5% chance that significant findings are due to chance rather than a relationship in the data12

ProbabilityMost statistical tests produce a p-value that is then compared to the a-level to accept or reject the null hypothesisE.g. Researcher sets significance level at .05 a priori; test results show p = .02. Researcher can then reject the null hypothesis and conclude the result was not due to chance but to there being a real relationship in the dataHow about p = .051, when a-level = .05?1

ErrorSignificance levels (e.g. a = .05) are set in order to avoid errorType I error = rejection of the null hypothesis when it was actually trueConclusion = relationship; there wasnt one (false positive) (= a)Type II error = acceptance of the null hypothesis when it was actually falseConclusion = no relationship; there was one 1234

Error Truth TableNull TrueNull FalseAcceptType II errorRejectType I error1234

Back to Our ExampleConclusion: No relationship exists between weight and fast food consumption with this group of respondents1

2Really?Conclusion: We have found no evidence that a relationship exists between weight and fast food consumption with this group of subjectsDo you believe this? Can you critique it? Construct validity? External validity?Thinking in this fashion will help you adopt a critical stance when reading research1

Another ExampleNow lets see if a relationship exists between weight and the number of piercings a person hasWhats your guess (hypothesis) about how the results of this test will turn out?Its fine to guess, but remember that our null hypothesis is that no relationship exists, until the data shows otherwise1

Another Example (continued)What can we conclude from this test?

Does this mean that weight causes piercings, or vice versa, or what?1

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Correlations and causalityCorrelations only describe the relationship, they do not prove cause and effectCorrelation is a necessary, but not sufficient condition for determining causalityThere are Three Requirements to Infer a Causal Relationship1

CausalityA statistically significant relationship between the variablesThe causal variable occurred prior to the other variableThere are no other factors that could account for the causeCorrelation studies do not meet the last requirement and may not meet the second requirement (go back to internal validity 497)1

If there is a relationship between weight and # piercings it could be becauseweight # piercingsweight # piercingsweight some other factor # piercingsWhich do you think is most likely here?4Correlations and causality123

Other Types of CorrelationsOther measures of correlation between two variables:Point-biserial correlation=use when you have a dichotomous variableThe formula for computing a PBC is actually just a mathematical simplification of the formula used to compute Pearsons r, so to compute a PBC in SPSS, just compute r and the result is the same1

Other Types of CorrelationsOther measures of correlation between two variables: (cont.)Spearman rho correlation; use with ordinal (rank) dataComputed in SPSS the same way as Pearsons rsimply toggle the Spearman button on the Bivariate Correlations window

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Coefficient of DeterminationCorrelation Coefficient SquaredPercentage of the variability among scores on one variable that can be attributed to differences in the scores on the other variableThe coefficient of determination is useful because it gives the proportion of the variance of one variable that is predictable from the other variableNext week we will discuss regression, which builds upon correlation and utilizes this coefficient of determination123

Correlation in excel

Use the function correlThe arguments (components) of the function are the two arrays1

http://www.stat.uiuc.edu/courses/stat100/java/GCApplet/GCAppletFrame.htmlhttp:// www.stat.tamu.edu /~west/applets/clicktest.htmlhttp://www.stat.tamu.edu/~west/applets/rplot.html

2Applets (see applets page)1