Final Test InformationFinal Test Information The final test is Monday, April 13 at 8:30 am The final test is Monday, April 13 at 8:30 am

GRH102: Last name begins with A - IGRH102: Last name begins with A - I GRH106: Last name begins with K - ZGRH106: Last name begins with K - Z

The exam is out of 40: 15 multiple choice The exam is out of 40: 15 multiple choice (worth 15); 5 short answer (worth 25)(worth 15); 5 short answer (worth 25)

It will cover material from the entire course, It will cover material from the entire course, but the focus will be on ANOVA and correlationbut the focus will be on ANOVA and correlation

You will need to be able to identify when to do You will need to be able to identify when to do a z-test, t-test, ANOVA, and correlationa z-test, t-test, ANOVA, and correlation

Not all of the short-answer questions require Not all of the short-answer questions require calculationscalculations

Statz Statz RappersRappers

The Basics of Hypothesis The Basics of Hypothesis TestingTesting

1.1. State the null and research hypotheses in State the null and research hypotheses in words and symbolswords and symbols

2.2. Determine the level of significanceDetermine the level of significance

3.3. Identify the critical valueIdentify the critical value

4.4. Calculate the test statisticCalculate the test statistic

5.5. Evaluate the test statistic in light of the Evaluate the test statistic in light of the critical valuecritical value

6.6. Make a decision about the null hypothesisMake a decision about the null hypothesis

7.7. State your conclusions in plain languageState your conclusions in plain language

Statistical Tests: Single sample Statistical Tests: Single sample meanmean

Used to compare a single sample to a Used to compare a single sample to a populationpopulation Is the sample significantly different from the Is the sample significantly different from the

population?population?

HH00: µ = X: µ = X

HH11: µ ≠ X: µ ≠ X

If you know the population standard If you know the population standard deviation, then use a z-testdeviation, then use a z-test

If you do not know the population If you do not know the population standard deviation, then use a t-teststandard deviation, then use a t-test

Statistical Tests: T-test for two Statistical Tests: T-test for two related samplesrelated samples

Used to compare two groups that are related Used to compare two groups that are related in some wayin some way Are the two groups significantly different from Are the two groups significantly different from

each other?each other?

HH00: µ: µDD = 0 = 0

HH11: µ: µDD ≠ 0 ≠ 0

Could be a pre/post (i.e., before/after) designCould be a pre/post (i.e., before/after) design Could be two groups whose participants are Could be two groups whose participants are

related in some way (couples, twins, siblings related in some way (couples, twins, siblings etc).etc).

Statistical Tests: T-test for two Statistical Tests: T-test for two independent samplesindependent samples

Used to compare two groups that are Used to compare two groups that are independent of each otherindependent of each other Are the two groups significantly different from Are the two groups significantly different from

each other?each other?

HHoo: : µµ11 = = µµ22

HH11: : µµ11 ≠ ≠ µµ22

Statistical Tests: Analysis of Statistical Tests: Analysis of variancevariance

Used to compare three or more groupsUsed to compare three or more groups Are the groups significantly different from Are the groups significantly different from

each other?each other?

HHoo: : µµ11 = = µµ22 = = µµ33

HH11: : µµ11 ≠ ≠ µµ22 ≠ ≠ µµ33

If you If you rejectreject your null hypothesis and your null hypothesis and conclude that there conclude that there isis a difference a difference between the groups, you need to conduct between the groups, you need to conduct post hoc (Tukey HSD) tests to determine post hoc (Tukey HSD) tests to determine whichwhich groups are different groups are different

ANOVA Summary TableANOVA Summary Table

SourceSource dfdf SSSS MSMS FF

BetweenBetween K-1K-1 MSMSBB*df*dfBB SSSSBB/df/dfB B

MSMSBB/MS/MSWW

WithinWithin N-KN-K MSMSWW*df*dfWW SSSSWW/df/dfWW

TotalTotal N-1N-1 SSSSBB + SS + SSWW

Statistical Tests: CorrelationStatistical Tests: Correlation

Used to determine if there is a relationships Used to determine if there is a relationships between two variablesbetween two variables Are the variables significantly correlated with each Are the variables significantly correlated with each

other?other?

HH00: r = 0: r = 0

HH00: r ≠ 0: r ≠ 0 There are three ways to describe the relationship There are three ways to describe the relationship

between the variables:between the variables: The direction and strength of the relationship (i.e., is r The direction and strength of the relationship (i.e., is r

positive or negative, and how close is it to 1.0?)positive or negative, and how close is it to 1.0?) Is r significant (compare obtained value of r to critical Is r significant (compare obtained value of r to critical

value)?value)? The amount of variance in one variable explained by the The amount of variance in one variable explained by the

other (i.e., rother (i.e., r22, the coefficient of determination), the coefficient of determination)

Study DesignsStudy Designs

ExperimentalExperimental

Looks for differences Looks for differences between groups of between groups of scoresscores

Uses terms like Uses terms like “effect”, “difference”, “effect”, “difference”, “cause”“cause”

Use z-test, t-test or Use z-test, t-test or ANOVA to analyze ANOVA to analyze datadata

CorrelationalCorrelational

Looks for relationships Looks for relationships between groups of between groups of scoresscores

Uses terms like Uses terms like “relationship”, “relationship”, “correlation”“correlation”

Use correlation to Use correlation to analyze dataanalyze data

Data Analysis Decision Tree Data Analysis Decision Tree for Experimental Designsfor Experimental Designs

How many groups?How many groups?

2 groupsDo a t-test2 groupsDo a t-test

3 or moregroupsDo an ANOVA

3 or moregroupsDo an ANOVA

Are the scores related?Are the scores related? Is Fobt ≥ Fcrit?Is Fobt ≥ Fcrit?

NoT-test for

independent samples

NoT-test for

independent samples

YesT-test for related

samples

YesT-test for related

samples

NoDo not reject H0

NoDo not reject H0

YesReject H0

Conduct HSD post hoc test

YesReject H0

Conduct HSD post hoc test

1 group (comparesample to population)1 group (compare

sample to population)

Do you know the populationstandard deviation?

Do you know the populationstandard deviation?

NoT-test for

single samples

NoT-test for

single samples

YesZ-test for

singlesamples

YesZ-test for

singlesamples