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Inferential Statistics Inferential Statistics Experimental Psychology Arlo ClarkFoos

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Page 1: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

Inferential StatisticsInferential Statistics

Experimental Psychology

Arlo Clark‐Foos

Page 2: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

Descriptive vs. Inferential StatsDescriptive vs. Inferential Stats

• Descriptive InferentialDescriptive Inferential

Page 3: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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

Page 4: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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

Page 5: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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

Page 6: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

Differences between groupsDifferences between groups

• Independent Samples t‐testIndependent Samples t test

– Independence?

– Is there another type?

Page 7: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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

Page 8: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

Sampling DistributionsSampling Distributions

Critical ValuesCritical Values

Page 9: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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?

Page 10: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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…

Page 11: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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?

Page 12: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

Student’s t‐distributionStudent s t distribution

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

Page 13: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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

Page 14: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

Statistical ErrorsStatistical Errors

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

– Implications?

Page 15: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

New Fad: Effect SizeNew Fad: Effect Size

• Statistical Significance vs. Effect Size

• Effect Size not affected by sample size

Page 16: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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

Page 17: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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).

Page 18: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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.

Page 19: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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.

Page 20: 07 - Inferential Statistics.pptacfoos/Courses/465/07 - Inferential... · • Descriptive Inferential. Inferential Statistics • Did your IV have an effect? • By chance alone •

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.