Hypothesis Tests: Two Independent Samples
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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

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Hypothesis Tests: Two Independent Samples

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Hypothesis tests two independent samples

Hypothesis Tests: Two Independent Samples


Violent videos again

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


The data

The Data


Analysis

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

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

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

Sampling Distribution--cont.

  • Distribution approaches normal as n increases.

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


Analysis cont1

Analysis--cont.

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

  • Note parallels with earlier t


Our data

Our Data


Degrees of freedom

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

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).


Iq pill independent samples

IQ PillIndependent Samples


Iq pill independent samples1

IQ PillIndependent Samples


Computing t

Computing t


Conclusions1

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

t value for related samples

Larger t value for same data


Assumptions

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

Pooling Variances

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

Cont.


Pooling variances 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

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

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

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 cont1

Effect Size, cont.

  • This difference is approximately .38 standard deviations.

  • This is a medium effect.

  • Elaborate


Confidence limits

Confidence Limits

Cont.


Confidence limits 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.”


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