07 - inferential statistics.pptacfoos/courses/465/07 - inferential... · • descriptive...

Inferential StatisticsInferential Statistics

Experimental Psychology

Arlo Clark‐Foos

Descriptive vs. Inferential StatsDescriptive vs. Inferential Stats

• Descriptive InferentialDescriptive Inferential

Inferential StatisticsInferential Statistics

• Did your IV have an effect?Did your IV have an effect?

• By chance alone

• Large vs Small values• Large vs. Small values

Null vs. Alternative HypothesesNull vs. Alternative Hypotheses

• Ho = Null HypothesisHo   Null Hypothesis– Any differences between groups are due to chance alone

• H (or H1, H2, etc.) = Alternative (ExperimentalHa (or H1, H2, etc.)   Alternative (Experimental Hypothesis– Any differences between groups are due to the IV

By chance alone…By chance alone…

• When is something rare enough?g g

30 times in every 100? 5 times in every 100?

Significance level (α)= .30  Significance level (α)= .05

Differences between groupsDifferences between groups

• Independent Samples t‐testIndependent Samples t test

– Independence?

– Is there another type?

Detroit Tigers exampleDetroit Tigers example

1984 20031984 2003

104‐58 43‐119

37    38   44 50   46   62

47    49   49 52   74   69

54 69 77 7654    69 77    76

M =   48.38 M = 63.25

t = 2.61

Sampling DistributionsSampling Distributions

Critical ValuesCritical Values

Number of ParticipantsNumber of Participants

• Relationship between number of participants andRelationship between number of participants and variability– Effect on sampling distribution (t‐distribution)

– What does this mean about conducting a t‐test?What does this mean about conducting a t test?

Degrees of FreedomDegrees of Freedom

• In the context of making an estimate (e.g., Mean)In the context of making an estimate (e.g., Mean)

• df = # of scores that are free to take on any valuedf = # of scores that are free to take on any value

• Examples• Examples

• Back to the Tigers• Back to the Tigers…

One Tail or Two Tail Test?One Tail or Two Tail Test?

• Directional vs. Nondirectional HypothesesDirectional vs. Nondirectional Hypotheses

– Which test makes it easier to reject the null?Which test makes it easier to reject the null?

– Valid?

Student’s t‐distributionStudent s t distribution

• Calculated t‐value vs. Critical t‐valuesCalculated t value vs. Critical t values

Back to our Tigers exampleBack to our Tigers example

• 1984:M = 48.381984: M  48.38

• 2003: M = 63.25

• df = (N1984 ‐ 1) + (N2003 ‐ 1)

df = 14df = 14

• t(14) 2 61• t(14) = 2.61

Statistical ErrorsStatistical Errors

• Recall assumptions of significance (α) levelRecall assumptions of significance (α) level – 5 out of every 100 replications

– Implications?

New Fad: Effect SizeNew Fad: Effect Size

• Statistical Significance vs. Effect Size

• Effect Size not affected by sample size

Paired‐Samples t‐testPaired Samples t test

• Paired‐samples, Repeated‐measures, Within‐Paired samples, Repeated measures, WithinSubjects, Dependent…

– Refers to a contrast between groups of participants who were assigned to groups through matched pairs, natural pairs or repeated measurespairs, or repeated measures.

• We are essentially comparing scores within the same participants (subjects).

• Test‐Retest, Time1‐Time2, Trial Types

Paired‐Samples t‐testPaired Samples t test

• Advantages of correlated groups designsAdvantages of correlated groups designs– Control issues

• The three methods for creating correlated‐groups designs give us greater certainty of group equality.

– Statistical issues

• Correlated‐groups designs can help reduce error variation.

• Error variability– Variability in DV scores that is due to factors other than the IV –

individual differences measurement error and extraneous variationindividual differences, measurement error, and extraneous variation (also known as within‐groups variability).

Independent Samples t‐testIndependent Samples t test

• Advantages of independent‐groups designsAdvantages of independent groups designs– Simplicity

– Use of correlated‐groups designs is impossible in some situations.

Interpreting Your StatsInterpreting Your Stats

• The t‐test for independent samplesThe t test for independent samples– Translating statistics into words

• If two equal groups began the experiment and they are now unequal, to what can we attribute the difference?

• If our controls have been adequate, our only choice is to assume that the difference between the groups is due to the IV.

• For example, if you were writing an interpretation of the results from the sample experiment in your text, you might write something like the following:

– Salesclerks who waited on well‐dressed customers (M = 43.38, SD = 10.11) took significantly less time, t(14) = 2.61, p = .021, to respond to customers than salespeople who waited on customers dressed in sloppy clothing (M = 63 25 SD = 12 54) The effect size estimatedsloppy clothing (M = 63.25, SD = 12.54).  The effect size, estimated with Cohen’s d,  was .92.

Interpreting Your StatsInterpreting Your Stats

• The t‐test for correlated samplesThe t test for correlated samples– Translating statistics into words

– Example from the text:• Salespeople who waited on well‐dressed customers (M = 48.38, SD= 10.11) took significantly less time, t(7) = 5.47, p = .001, to respond to the customers than when they waited on customers dressed in sloppy clothes (M = 63.25, SD = 12.54).  The effect size, estimated with Cohen’s d,  was 1.93.