PowerPoint Presentation
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
2
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
1
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