# Hypothesis Tests: Two Independent Samples - PowerPoint PPT Presentation

1 / 26

Hypothesis Tests: Two Independent Samples. Violent Videos Again. Bushman (1998) Violent videos and aggressive behavior Doing the study Bushman’s way--almost Bushman had two independent groups Violent video versus educational video

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Hypothesis Tests: Two Independent Samples

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

Hypothesis Tests: Two Independent Samples

### Violent Videos Again

• Bushman (1998) Violent videos and aggressive behavior

• Doing the study Bushman’s way--almost

• Bushman had two independent groups

• Violent video versus educational video

• We want to compare mean number of aggressive associations between groups

### Analysis

• These are Bushman’s data, though he had more dimensions.

• We still have means of 7.10 and 5.65, but both of these are sample means.

• We want to test differences between sample means.

• Not between a sample and a population mean

Cont.

### Analysis--cont.

• How are sample means distributed if H0 is true?

• Need sampling distribution of differences between means

• Same idea as before, except statistic is (X1 - X2)

### Sampling Distribution of Mean Differences

• Mean of sampling distribution = m1 - m2

• Standard deviation of sampling distribution (standard error of mean differences) =

Cont.

### Sampling Distribution--cont.

• Distribution approaches normal as n increases.

• Later we will modify this to “pool” variances.

### Analysis--cont.

• Same basic formula as before, but with accommodation to 2 groups.

• Note parallels with earlier t

### Degrees of Freedom

• Each group has 100 subjects.

• Each group has n - 1 = 100 - 1 = 99 df

• Total df = n1- 1 + n2 - 1 = n1 + n2 - 2 100 + 100 - 2 = 198 df

• t.025(198) = +1.97 (approx.)

### Conclusions

• Since 2.66 > 1.97, reject H0.

• Conclude that those who watch violent videos produce more aggressive associates (M = 7.10) than those who watch nonviolent videos (M = 5.65), t(198) = 2.66, p < .05 (one-tailed).

## Conclusions

Since -.88 < 1.97, fail to reject H0.

Conclude that those who took the IQ pill did not score significantly higher (M = 102.4) on an IQ test than those who did not take the IQ pill (M = 99.4), t(8) = -.88, p > .10.

### t value for related samples

Larger t value for same data

### Assumptions

• Two major assumptions

• Both groups are sampled from populations with the same variance

• “homogeneity of variance”

• Both groups are sampled from normal populations

• Assumption of normality

• Frequently violated with little harm.

### Pooling Variances

• If we assume both population variances are equal, then average of sample variances would be better estimate.

Cont.

### Pooling Variances--cont.

• Substitute sp2 in place of separate variances in formula for t.

• Will not change result if sample sizes equal

• Do not pool if one variance more than 4 times the other.

• Discuss

### Heterogeneous Variances

• Refers to case of unequal population variances.

• We don’t pool the sample variances.

• We adjust df and look t up in tables for adjusted df.

• Minimum df = smaller n - 1.

• Most software calculates optimal df.

### Effect Size for Two Groups

• Extension of what we already know.

• We can often simply express the effect as the difference between means (=1.45)

• We can scale the difference by the size of the standard deviation.

• Gives d

• Which standard deviation?

Cont.

### Effect Size, cont.

• Use either standard deviation or their pooled average.

• We will pool because neither has any claim to priority.

• Pooled st. dev. = √14.8 = 3.85

Cont.

### Effect Size, cont.

• This difference is approximately .38 standard deviations.

• This is a medium effect.

• Elaborate

Cont.

### Confidence Limits--cont.

• p = .95 that interval formed in this way includes the true value of 1 - 2.

• Not probability that 1 - 2 falls in the interval, but probability that interval includes 1 - 2.

• Comment that reference is to “interval formed in this way,” not “this interval.”