Statistical Analysis Study Notes

FINAL EXAM PRACTICE NOTES

Paired T-Test Output for Smoking Cessation Program

  • Context and Purpose: The paired T-test compares the number of cigarettes smoked per day before and after participation in a smoking cessation program.

Questions and Answers

  1. On average, when did individuals smoke the most cigarettes per day?

    • Pre-program: The mean number of cigarettes smoked per day before the program was 20.72.

  2. How many individuals were in the study?

    • Total Participants (N): 50 individuals.

  3. Provide the null and research hypotheses for the Paired T-test using the notation discussed in class:

    • Null Hypothesis (H0): extµD=0ext{µD} = 0 (the mean difference in the number of cigarettes smoked before and after the program is zero).

    • Research Hypothesis (H1): extµD≠0ext{µD} ≠ 0 (the mean difference in the number of cigarettes smoked is not zero).

  4. Provide the value of the observed t-statistic for the Paired T-test and the degrees of freedom associated with the t-statistic:

    • Observed t-statistic: t=2.783t = 2.783

    • Degrees of Freedom (df): 49.

  5. Report the p-value (two-sided) for the Paired T-test:

    • Two-sided p-value: p=.008p = .008.

  6. Would you choose to reject or fail to reject the null hypothesis for the Paired T-test?

    • Decision: Reject the null hypothesis (H0).

  7. What other piece of information on the output (other than the p-value) provides evidence to support the answer you gave for question #6?

    • Evidence: The 95% Confidence Interval for the difference (lower bound: 0.5398, upper bound: 3.34102) does not include zero, indicating a significant difference.

Paired Samples Statistics

  • Summary of Results:

    • Mean pre-program: 20.7200

    • Mean post-program: 18.7800

    • Standard Deviation pre-program: 11.15208

    • Standard Deviation post-program: 10.47308

    • Standard Error Mean pre-program: 1.57714

    • Standard Error Mean post-program: 1.48112

Paired Samples Correlation

  • Correlation Details:

    • N: 50

    • Correlation Coefficient: 0.898

    • Significance: p < .001 (both one-sided and two-sided).

Oneway ANOVA Output for Caffeine Consumption and Cigarette Smoking

  • Context and Purpose: This analysis assesses whether caffeine consumption is associated with the number of cigarettes smoked.

Questions and Answers

  1. On average, which group of individuals smoked the fewest number of cigarettes per day?

    • Group: Individuals categorized as "Occasionally" consuming caffeine smoked the fewest cigarettes per day (Mean = 12.5833).

  2. Provide the null and research hypotheses for the Single Factor Between Subjects ANOVA:

    • Null Hypothesis (H0): extµ<em>extnever=extµ</em>extoccasionally=extµextfrequentlyext{µ}<em>{ ext{never}} = ext{µ}</em>{ ext{occasionally}} = ext{µ}_{ ext{frequently}} (the means are equal).

    • Research Hypothesis (H1): Not all means are equal (significant differences exist among groups).

  3. Was the assumption of homogeneity of variances met for these data?

    • Answer: Yes.

    • Levene's Statistic: 1.138, p-value: 0.326.

  4. Would you choose to report the ANOVA F-statistic or the Welch Statistic in your results?

    • Choice: Report the ANOVA F-statistic.

  5. Provide the value of your selected test statistic, the two relevant degrees of freedom associated with it, and the associated p-value:

    • F-statistic: 1.136

    • Degrees of Freedom: 2 (between groups), 71 (within groups)

    • p-value: 0.327.

  6. Would you choose to reject the null hypothesis?

    • Decision: Fail to reject the null hypothesis (H0).

  7. Which post-hoc test for pairwise comparisons would you use? Were there any significant pairwise comparisons found?

    • Test: Bonferroni;

    • Result: No significant pairwise comparisons found.

Chi-Square Test for Association Output for Gender and Caffeine Consumption

  • Context and Purpose: This test assesses the association between gender and caffeine consumption.

Questions and Answers

  1. How many females consume caffeine frequently?

    • Count: 12 females.

  2. If there was no association between the two variables, how many males would we expect to never consume caffeine?

    • Expected Count: 13.8 males.

  3. Was the expectation that all expected cell frequencies have a value of 5 or greater met?

    • Answer: Yes.

  4. Is there a significant association between gender and caffeine consumption?

    • Answer: Yes.

    • Chi-Square Statistic: 10.561, Degrees of Freedom: 2, p-value: 0.005.

  5. What was the value of the Effect Size for this test?

    • Effect Size: Cramer’s V = 0.357.

Multivariate Linear Regression Analysis Output

  • Context and Purpose: Studying factors influencing recidivism in offenders preparing for release from prison.

Questions and Answers

  1. Is the overall model significant?

    • Answer: Yes.

    • F-statistic: 6.837, p-value: 0.002.

  2. What percentage of variation in likelihood of recidivism can be explained by the model?

    • Percentage Explained: Adjusted R Square = 19.2%.

  3. Which independent variable(s) in the model is/are significantly associated with the dependent variable?

    • Significant Variable: Number of Rule Violations;

    • t-statistic: 3.399, p-value: 0.001.

  4. Provide the predicted likelihood of recidivism for a female who had 12 rule violations.

    • Predicted Likelihood: 56.299.

Selecting the Appropriate Statistical Test

Research Scenarios and Corresponding Statistical Tests

  1. Levels of entitlement change over time: Paired Samples T-test

  2. Significant association between gender and drug use: Chi-Square Test for Association

  3. Impact of gender and family history of artistic talent on creativity: Multivariate Linear Regression

  4. Impact of current offense on sentence length: Oneway ANOVA

  5. Average hours of exercise over the past 15 years: Z-test for One Sample Mean

  6. Type of car affecting commuting willingness: Independent Samples T-test