session5.Final

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Session 5 Final Tracy Cuffia Colorado Christian University MAT-250A-35001-SP24 Intro to Research and Applied Statistics Professor Pierre Williams April 28, 2024

Final Paper 2 For the final paper in this course, we were asked to analyze whether there was a difference in the effectiveness of the treatment of participants and which was most successful for a study concerning those with an intense fear of snakes. For this problem we used ANOVA to evaluate the data. A single factor or one-way ANOVA is needed because there are more than two groups of data and require a more complex test. In ANOVA we have two variables, one is still independent, and the other is dependent. There are more than two groups of data, so a test is required that can handle this complex set of data and “among social and behavioral scientists, it is used more frequently than any other inferential statistical technique” (Spatz, 2007, p. 222). The study conducted for this problem does show there is significant difference in the effectiveness of the treatments given to the participants who have a fear of snakes. The results from the AVONA show that those who held the model and required to imitate the snake did show the most improvement and was the most successful treatment of the four variables. The model group had the highest sum and average. The control group of course was the least the least effective with its average and variance the same. Using the t-test we can determine that the model is the better than the three other groups. When compared with film which is better than desensitization and control, the p–value is less than .05, which means we reject the alternative and conclude that model is the best group. As for how these results can help someone live a biblically focused life, I can’t help but think when Moses was told by God to throw down his staff in Exodus 4:3, which turned into a snake. Just as the folks in this study did, they overcame their fear through the model. Faith is required and trusting God is in control is lot like the study. God will often provide a model for faith throughout the Old Testament to show us how faith works.

Model Film Desensitization Control 29 22 21 13 27 18 17 12 27 17 16 9 21 15 14 6 Anova: Single Factor Summary Groups Count Sum Average Variance Model 4 104 26 12 Film 4 72 18 8.6666666 Desensitization 4 68 17 8.66666667 Control 4 40 10 10 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 515 3 171.666667 17.4576271 0.00011279 3.49029482 Within Groups 118 12 9.83333333 Total 633 15 t-Test: Two-Sample Assuming Equal Variances Control Desensitization Mean 10 17 Variance 10 8.666666667 Observations 4 4 Pooled Variance 9.33333333 Hypothesized Mean Difference 0 Df 6 t Stat -3.2403703 P(T<=t) one-tail 0.00883933 t Critical one-tail 1.94318028 P(T<=t) two-tail 0.01767867 t Critical two-tail 2.44691185 p value is less than .05 reject the null. Desensitization is better than control.

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t-Test: Two-Sample Assuming Equal Variances Desensitiza Tion Film Mean 17 18 Variance 8.66666667 8.666666667 Observations 4 4 Pooled Variance 8.66666667 Hypothesized Mean Difference 0 df 6 t Stat -0.4803845 P(T<=t) one-tail 0.32398341 t Critical one-tail 1.94318028 P(T<=t) two-tail 0.64796681 t Critical two-tail 2.44691185 P value is greater than .05 We accept the null There is no difference between these two groups. t-Test: Two-Sample Assuming Equal Variances Film Model Mean 18 26 Variance 8.66666667 12 Observations 4 4 Pooled Variance 10.3333333 Hypothesized Mean Difference 0 Df 6 t Stat -3.5195308 P(T<=t) one-tail 0.00626284 t Critical one-tail 1.94318028 P(T<=t) two-tail 0.01252568 t Critical two-tail 2.44691185 p value is less than .05 reject the null. Model is better than film.

References Spatz, C. (2007). Basic statistics: Tales of distributions. Cengage Learning

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