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Sampling Distributions and Hypothesis Testing. 2 Major Points An example An example Sampling...

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Sampling Distributions and Hypothesis Testing
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Sampling Distributions and Hypothesis Testing

    

2

Major Points

An example Sampling distribution Hypothesis testing

The null hypothesis Test statistics and their distributions The normal distribution and testing

Important concepts

3

The chance that something can happen may depend on…

Fate Probability Gambling Error Likelihood Expected variability in a sample

4

Media Violence

Does violent content in a video affect later behavior? Bushman (1998)

Two groups of 100 subjects saw a video Violent video versus nonviolent video

Then free associated to 26 homonyms with aggressive & nonaggressive forms. e.g. cuff, mug, plaster, pound, sock

Cont.

5

Media Violence

Results Number of aggressive free associates to the

homonym as a function of video: saw violent video mean = 7.10 saw nonviolent video mean = 5.65

Is this difference large enough to conclude that type of video affected results?

6

A Simplified Version of Study One-group study is easier to start with

than two-group study. Convert to one-group study

People normally give 5.65 aggressive associates to homonyms. (a pop. parameter)

A group who watched violent videos give 7.10 aggressive associates. (a sample statistic)

Is this sufficiently more than expected to conclude that violent video has effect?

7

What is the Question?

Is the difference between 7.10 and 5.65 large enough to lead us to conclude that it is a real difference? Would we expect a similar kind of difference with

a repeat of this experiment? Or...

Is the difference due to “sampling error?”

8

Sampling Error = variability due to chance The normal variability that we would expect

to find from one sample to another, or one study to another

Random variability among observations or statistics that is just due to chance

9

How Could we Assess Sampling Error?

Take many groups of 100 subjects who did not see a violent video.

Record the number of aggressive responses to 26 homonyms.

Plot the distribution and record its mean and standard deviation.

This distribution is a “Sampling Distribution.”

10

Sampling Distribution

The distribution of a statistic over repeated sampling from a specified population.

Possible result for this example. See next slide. Shows the kinds of means we expect to find when

people don’t view a violent video.

11

Mean Number Aggressive Associates

7.257.00

6.756.50

6.256.00

5.755.50

5.255.00

4.754.50

4.254.00

3.75

Sampling Distribution

Number of Aggressive AssociatesF

req

ue

nc

y

1400

1200

1000

800

600

400

200

0

Std. Dev = .45

Mean = 5.65

N = 10000.00

In this case the sd is the standard error, not sample sd

12

What Do We Conclude?

When people don’t view violent video, they average between about 4.5 and 6.5 aggressive interpretations of homonyms.

Our violent video group averaged 7.10 aggressive interpretations. Our subjects’ responses were not like normal.

Conclude that the violent video increased aggressive associations.

13

Hypothesis Testing A formal way of doing what we just did, compare sample statistic to

population parameters State research question Assumptions Null and Alternative Hypotheses Sampling Distribution of Test Statistic Decision Rule Sample and Test Statistic Decision

Start with hypothesis that subjects are normal. The null hypothesis:

The is no difference…. There is no association….

Find what normal subjects do. Compare our subjects to that standard.

14

The Null Hypothesis

The hypothesis that our subjects came from a population of normal responders.

The hypothesis that watching a violent video does not change mean number of aggressive interpretations.

The hypothesis we usually want to reject.

15Chapter 8 Sampling Distributions

Steps in Hypothesis Testing condensed: p. 151 Define the null hypothesis. (because we can rarely

test the research H) Sample and decide what you would expect to find if

the null hypothesis were true (given random sampling, what is the sampling distribution).

Look at what you actually found and compare to the sampling distribution. What’s the probability of getting that statistic by chance?

Reject the null if what you found is not what you expected given the sampling distribution.

16

Important Concepts

Concepts critical to hypothesis testing Decision Type I error Type II error Critical values One- and two-tailed tests

17

Decisions

When we test a hypothesis we draw a conclusion; either correct or incorrect. Type I error

Reject the null hypothesis when it is actually correct. Type II error

Retain the null hypothesis when it is actually false.

18

Type I Errors

Assume violent videos really have no effect on associations

Assume we conclude that they do. This is a Type I error

Probability set at alpha () usually at .05

Therefore, probability of Type I error = .05

19

Type II Errors

Assume violent videos make a difference Assume that we conclude they don’t This is also an error

Probability denoted beta () We can’t set beta easily. We’ll talk about this issue later.

Power = (1 - ) = probability of correctly rejecting false null hypothesis.

20

REJECT THE NULL HYP.

FAIL TO REJECT THE NULL HYP.

NULL IS FALSE

1. Correct decision

4. TYPE II ERROR

NULL IS TRUE

3. TYPE I ERROR

2. Correct decision

Four possible outcomes when testing null hypotheses:

21

Critical Values

These represent the point at which we decide to reject null hypothesis.

e.g. We might decide to reject null when (p|null) < .05. Our test statistic has some value with p = .05 We reject when we exceed that value. That value is the critical value.

22

One- and Two-Tailed Tests

Two-tailed test rejects null when obtained value too extreme in either direction Decide on this before collecting data.

One-tailed test rejects null if obtained value is too low (or too high) We only set aside one direction for rejection.

Cont.

23

One- & Two-Tailed Example

One-tailed test Reject null if violent video group had too many

aggressive associates Probably wouldn’t expect “too few,” and therefore no

point guarding against it.

Two-tailed test Reject null if violent video group had an extreme

number of aggressive associates; either too many or too few.

24

Review Questions

Define a sampling distribution. How would you create sampling distribution

of mean number of aggressive associates if the null were true?

What is sampling error? What does sampling error have to do with all

of this?

Cont.

25

Review Questions--cont.

What are the steps in hypothesis testing? What is the probability we’d conclude violent

videos cause aggression if they really don’t? Distinguish between Type I and Type II

errors. Distinguish between one-tailed and two-tailed

tests.


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