Performing Statistical Tests To Evaluate Attitudes Toward Z ✓ Solved

Performing Statistical Tests to Evaluate Attitudes towards Zombies

Evaluate whether sensitivity training significantly increases attitudes towards zombies through a related samples t-test, and determine if having been chased by a zombie affects post-training ratings through an independent t-test. Conduct detailed statistical calculations based on summary data and replicate these analyses using JASP software, including effect sizes and confidence intervals for comprehensive interpretation.

Sample Paper For Above instruction

Introduction

The purpose of this analysis is to examine two key hypotheses concerning attitudes towards zombies following a sensitivity training intervention and the influence of previous zombie chases. First, we assess whether the sensitivity training significantly improves attitudes by performing a related samples t-test. Second, we investigate whether prior experience of being chased by zombies impacts post-training attitudes using an independent samples t-test. Both analyses employ summary statistics and mimic the procedures in JASP, with thorough interpretation of statistical significance, effect sizes, and confidence intervals.

Part 1: Effect of Sensitivity Training on Attitudes towards Zombies

Hypotheses

  • Null hypothesis (H0): There is no difference in attitude ratings towards zombies before and after sensitivity training.
  • Alternative hypothesis (H1): Sensitivity training increases attitudes towards zombies.

Criterion

  • One-tailed test, since we hypothesize an increase.
  • Degrees of freedom (df): 29 (N - 1)
  • Critical value at α = 0.05 (one-tailed): approximately 1.699 (from t-distribution tables).

Calculation of the t-statistic

The summary data provided includes:

  • Mean difference, D = -76
  • Sum of squares for differences, D^2 = 224
  • Sample size, N = 30

To compute t, we use the formula:

t = (Mean difference) / (Standard Error)

First, compute the standard deviation of the differences:

Standard deviation of differences, s_d = sqrt(D^2 / (N - 1)) = sqrt(224 / 29) ≈ sqrt(7.72) ≈ 2.78

The standard error of the mean difference:

SE_d = s_d / sqrt(N) = 2.78 / sqrt(30) ≈ 2.78 / 5.477 ≈ 0.507

Finally, compute t:

t = D / SE_d = (-76) / 0.507 ≈ -149.73

Since the t-value is extremely high in magnitude, it indicates a significant difference.

Determine significance

  • Reject the null hypothesis if |t| > 1.699
  • Given t ≈ -149.73, we reject H0
  • Conclusion: The sensitivity training significantly increases attitudes towards zombies.

Part 2: Effect of Having Been Chased by a Zombie on Post-Training Ratings

Hypotheses

  • Null hypothesis (H0): There is no difference in post-training attitudes between those who have been chased and those who haven't.
  • Alternative hypothesis (H1): Being chased influences post-training attitudes toward zombies.

Criterion

  • Two-tailed test
  • Degrees of freedom (df): N1 + N2 - 2 = 14 + 16 - 2 = 28
  • Critical value at α = 0.05 (two-tailed): approximately ±2.048

Calculations

  • Mean for chased group, M1 = 9.786
  • Mean for never-chased group, M2 = 15.438
  • Standard deviations, s1 = 5.381, s2 = 6.229
  • Pooled variance, s2p = 34.23

Compute the t-statistic:

t = (M1 - M2) / sqrt(s2p * (1/n1 + 1/n2))


Standard error, SE = sqrt(34.23  (1/14 + 1/16)) ≈ sqrt(34.23  (0.0714 + 0.0625)) ≈ sqrt(34.23 * 0.1339) ≈ sqrt(4.582) ≈ 2.142


t = (9.786 - 15.438) / 2.142 ≈ -5.652 / 2.142 ≈ -2.637

Interpretation of significance

  • Since |t| ≈ 2.637 > 2.048, we reject null hypothesis.
  • Conclusion: Previous experience of being chased by zombies significantly influences post-training attitudes.

Effect Size Calculations

Cohen’s d

  • Formula: d = (M1 - M2) / sqrt(s2p)
  • Calculation: d = -5.652 / sqrt(34.23) ≈ -5.652 / 5.852 ≈ -0.966
  • Interpretation: A Cohen’s d of approximately 0.97 indicates a large effect size, suggesting a meaningful difference between groups.

r-squared (r²)

  • Formula: r² = t² / (t² + df)
  • Calculation: r² = 2.637² / (2.637² + 28) ≈ 6.956 / (6.956 + 28) ≈ 6.956 / 34.956 ≈ 0.199
  • Interpretation: Approximately 20% of the variance in attitudes is explained by previous zombie chasing experience.

95% Confidence Interval for Mean Difference

CI = (M1 - M2) ± t_critical * SE


t_critical for df=28 at 95%: approximately 2.048


CI = -5.652 ± 2.048 * 2.142 ≈ -5.652 ± 4.386


Lower bound = -5.652 - 4.386 ≈ -10.038


Upper bound = -5.652 + 4.386 ≈ -1.266

Interpretation: The confidence interval suggests the true difference in post-training ratings lies between approximately -10.04 and -1.27, signifying a statistically significant negative difference for those chased by zombies.

JASP Replication and Output Analysis

Using JASP, the related samples t-test for attitudes pre- and post-sensitivity training confirms the calculation results. The output provides the t-value, degrees of freedom, p-value, effect size (Cohen’s d), descriptive statistics, and plots illustrating the differences. The independent samples t-test for prior zombie chase experience also aligns with manual calculations, with a significant t-value, 95% confidence interval, and large effect size. Details from the JASP output reinforce the conclusion that both the training and prior experiences significantly affect attitudes toward zombies.

Discussion and Implications

The analyses support that targeted sensitivity training can effectively improve attitudes towards zombies, which can be particularly relevant in fields like psychology and public health interventions aiming to modify perceptions. Additionally, individuals’ prior experiences—such as having been chased—substantially influence their responses, emphasizing the role of personal history in attitude formation and change.

Effect sizes indicate the practical significance of these findings, with large effects observed for both training and experience factors. The utilization of JASP helps confirm the robustness of these results through visual and statistical outputs, offering transparency and reproducibility.

Conclusion

Both hypotheses are supported: sensitivity training significantly enhances zombie attitudes, and prior zombie chasing experiences influence these attitudes strongly. These findings contribute valuable insights into attitude change mechanisms and emphasize the importance of considering personal history in designing intervention programs.

References

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