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Chi-square & T-test

Comm 420.8Fall 2007

Nan Yu

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Warming up

Please download practice 1, practice 1 answer, ChisquareData, Ttestdata

Use ChisquareData to complete the questions of practice 1.

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Effect Sizes

Statistical Significance vs. Strength of Effect

• Strength of Effect: 0 to 10 = Least Effect1 = Maximum Effect

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Strength of Association for Chi-Squares:

Cramér’s V

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Effect size for Chi-square

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Influence of Sample Size on

Statistical Significance (p-value) versus

Strength of Association (Cramer’s V)

Sample size will not affect the strength of association, only significance level.

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Vote

Yes No

Yes

No

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Chi-Square Value = 1.72Degrees of Freedom = 1Significant? No, p = .19Cramér’s V =.17

Chi-Square Value = 17.14Degrees of Freedom = 1Significant? Yes, p < .001Cramér’s V =.17

Yes

No 100 200

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Vote

Yes No

Note: The number in each cell is mean.

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Run Chi-square to test the following question

People from different race will have a different opinion on the selection of countries that represent a great danger to the U.S.. (race, q36).

Chi-Square:_17.46_ DF _5_ p _<.01_

Cramer’s V: _.44_

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The Chi-square test showed that people from different race have a different opinion on the selection of countries that represent a great danger to the U.S., 2 (6, N=45) = 17.46, p<.01, Cramer’s V=.44.

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T-test: Testing Differences in Means

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I. The Issue of Variability

Variability withinwithin Groups Variability betweenbetween Groups

mean 1 mean 2

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Different Groups: Large Between-Group Variability Small Within-Group Variability

Similar Groups: Small Between-Group Variability Large Within-Group Variability

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Which one represents similar groups?

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Independent Sample t-test

Independent Sample t-test is used to test differences between only 2 groups.

Ex. Female test scores will differ from male test scores.

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T-test assumptions

IV is nominal and has two categoriesDV is interval/ratioDV is normally distributed.T-test will robust with larger samplesCases represent a random sample

(representative).Cases are independent of one another.

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Example: Males likes TV sports more than females

Put the interval orratio-level variablehere. (DV)

Put the variablerepresenting thegroups here. (IV)

Click “Define Groups"

IV? DV?

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Define your groups by the values.

In this case, it is “0” for males and “1” for females.

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Compare the means.

T-test statistic

Degrees of freedom p-value

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T-test statistic

Degrees of freedom p-value

Are these two groups similar or different (within-group) ?If p >.05, means they are similar, use the top rowIf p<.05, means they are different, use the bottom row.

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Report: Males (M=3.04, SD=1.89) do like TV sports more than females (M=1.97, SD=.88), t(34)=2.66, p<.05.

T-test statistic

Degrees of freedom p-value

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- Paired Sample t-test is used to test differences between 2 scores.

- Variables must be interval or ratio-level and measured on the same metric.

Ex. Aggression scores will be higher after viewing a violent film than before viewing a violent film.

Variables: Before Film Stimulus After

- Here, IV has only one level, but there are two DVs: before aggression, after aggression

Paired Sample t-test

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Paired Sample t-test

Place your “before” and “after” variables here.

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T-test statistic

Degree of freedom P-value

Report: Aggression scores after viewing the film (M=3.95, SD=.96) were significantly higher than were scores prior to viewing the film (M=2.55, SD=1.11), t(57)=6.89, p<.001.

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Directional and non-directional hypotheses

Females and males have different levels of liking toward dramas.

Females likes to watch dramas more males.

Liking toward dramas will be different as a result of gender.

Which one is a directional hypothesis?

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One-tailed or two-tailed test

Non-directional hypothesis: one-tailed test

Directional hypothesis: two-tailed test

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Probability Distribution

95% of chances thatwe found the two means are different.

5% of chances thatdidn’t found the difference.

Females and males have different levels of liking toward sitcom.

Mean of females is not equal to mean of males

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Two-tailed tests—split the alpha

Females likes to watch sitcom more males.

Mean of females > Mean of males

2.5% of chances thatdidn’t found means offemales is higher thanthat of males.

2.5% of chances thatdidn’t found means offemales is lower thanthat of males.

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In-class practice 1 (Ttestdata.sav)

H1:Males likes to watch TV reality crime more than females.

(gender, tvrcrime)

Please use t-test to test the H1 and answer the following questions:

Males: Mean _____ SD _____Females: Mean______ SD ______t(__)=____, p______

Can we reject the null here?

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Answers to practice 1

Males: Mean _2.58_ SD _1.17_Females: Mean _3.32_ SD _1.49_t(_55_)=_2.11_, p_<.05_

Can we reject the null here?No. We proposed males > females, but we

found males < females

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In-class practice 2

H2:Happiness scores will be higher after viewing a sad film than

before viewing a sad film.

Please use t-test to test the H2 and answer the following questions:

Before: Mean _____ SD _____

After: Mean______ SD ______

t(__)=____, p______

Can we reject the null here?

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Answers to practice 2

Before: Mean _2.53_ SD _1.13_

After: Mean _4.02_ SD _.83_

t(_57_)=_-7.70_, p_<.001_

Can we reject the null here?

Yes