Hypothesis Testing in SPSS Using the T Distribution

Lab: Chapters 11, 12 and 13

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The Sampling Distribution

2Z-Scores

3.02.01.00.0-1.0-2.0-3.0

Distribution of Cases in a Normal Distribution

2.5% of cases 13.5% 34% 34% 13.5% 2.5% of cases

Using the T Sampling Distribution• Interval estimation (confidence intervals)• Hypothesis Testing

• Single (One) sample t-test• Paired sample t-test• Independent samples t-test

– Degrees of freedom:• Single and Paired df=n-1• Independent df= n1 + n2 - 2

– Criteria for significance tests:• If n < 1000, alpha = .05• If n =/> 1000, alpha = .01 3

Hypothesis Testing Steps• Four steps in hypothesis testing

1. State the research and the null hypothesis.2. Are the sample results consistent with the null

hypothesis or the research hypothesis?• if consistent with the null hypothesis, go to step 4• if consistent with the research hypothesis, go to step 3

3. What is the probability of getting the sample results if the null hypothesis is true?

4. Reject or do not reject the null hypothesis.• reject null (results are significant)• do not reject null (results are not significant)

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One-tailed and two-tailed hypotheses• Will depend on your research question

– two-tailed hypothesis• Does not specify direction• Only asks “Is there a significant difference?”

– one-tailed hypothesis• Question specifies a direction • “Is the difference significantly greater?”• “Is the difference significantly less?” etc.

– The one-tailed probability is the two-tailed probability from SPSS divided by 2

One Sample T-test

• To test hypotheses about the mean of one variable for one group to the population

• Example: Did the average household size of 1980 GSS young adults differ significantly from three (the population or “test” value)?

1. State the research and the null hypothesis.• null hypothesis: In the population of 1980 young adults,

the average household size was three.• research hypothesis: In the population of 1980 young

adults, the average household size was not three.6

One sample (cont.)2. Are the sample results consistent with the null

hypothesis or the research hypothesis?Analyze | Compare Means | One-Sample T Test

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One sample (cont.)3. What is the probability of getting the sample

results if the null hypothesis is true?

4. Reject or do not reject the null hypothesis.Note: one-tailed significance = .598/2 = .299

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Paired-Samples t Test• To test hypotheses about the means on two

variables for one group• Example: Were 1980 GSS young adults (one

group) significantly more willing (one-tailed) to let controversial persons give public speeches than to let them teach college?1.State the research and the null hypothesis.

• research hypothesis: The average willingness to let controversial persons give public speeches was greater than their willingness to let them teach college.

• null hypothesis: The average willingness to let controversial persons give public speeches was the same or less than their willingness to let them teach college.

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Paired (cont.)2. Are the sample results consistent with the null

hypothesis or the research hypothesis?Analyze | Compare Means | Paired-Samples T Test

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Paired-Samples Output for OKSPEECH and OKTEACH3. What is the probability of getting the sample results if the null hypothesis is true?4. Reject or do not reject null hypothesis.

one-tailed significance = .000/2 = .000

Independent-Samples t Test• To test hypotheses about the mean on one

variable for two groups• Example: Was the number of hours worked per

week by employed 1980 GSS young adults significantly higher for males than for females?1.State the research and the null hypothesis.

• research hypothesis: The average number of hours worked per week by employed males was higher than by employed females.

• null hypothesis: The average number of hours worked per week by employed males was the same or lower than by employed females.

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Independent (cont.)2. Are the sample results consistent with the null

hypothesis or the research hypothesis?Analyze | Compare Means | Independent-Samples T Test

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Independent: Output for HOURS by SEX (0, 1)

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3. What is the probability of getting the sample results if the null hypothesis is true?

one-tailed significance = .041/2 = .0205

4. Reject or do not reject null hypothesis.