Research Statistics: MAT-250A Assignment on T-tests and ANOVA

This assignment analyzes research statistics using T-tests and ANOVA. It presents four hypotheses, each tested with relevant statistical outputs, including test statistics, p-values, and conclusions based on a 5% significance level. The analysis includes comparisons between different groups (film, desensitization, model, and control) to determine significant differences. The first hypothesis examines the difference between film and desensitization, the second between film and model, and the third between desensitization and control. The final hypothesis utilizes a single factor ANOVA to compare all four variables. The results are interpreted to determine the acceptance or rejection of null hypotheses, providing insights into the relationships between the variables. The assignment concludes with a bibliography of relevant sources.

Running head: RESEARCH STATISTICS
Research Statistics
Name of the Student
Name of the University:
Author note:

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RESEARCH STATISTICS
Table of Contents
Solution......................................................................................................................................1
Hypothesis 1...........................................................................................................................2
Hypothesis 2...........................................................................................................................2
Hypothesis 3...........................................................................................................................3
Hypothesis 4...........................................................................................................................4
Bibliography...............................................................................................................................6
Solution

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T-test Output 1
Hypothesis 1
Null hypothesis: There is no differences between the film and desensitization.
Alternative hypothesis: There is a differences between the film and desensitization.
Result:
Test statistic = 0.48
P-value = 0.65
Alpha= 0.05 (at 5% significance level)
Conclusion:
It has been seen that P-value > alpha at 5% significance level. Hence the null
hypothesis of the test is not significant and the alternative hypothesis is rejected. Therefore it
may be concluded that there is no differences between the film and desensitization.
Hypothesis 2

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T-test Output 2
Null hypothesis: There is no differences between the film and model.
Alternative hypothesis: There is a differences between the film and model.
Result:
Test statistic = -3.520
P-value = 0.013
Alpha= 0.05 (at 5% significance level)
Conclusion:
It has been seen that P-value < alpha at 5% significance level. Hence the null
hypothesis of the test is significant and the alternative hypothesis may not be rejected.
Therefore it may be concluded that there is a differences between the film and model.
Hypothesis 3

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T-test Output 3
Null hypothesis: There is no differences between the desensitization and control.
Alternative hypothesis: There is a differences between the desensitization and control.
Result:
Test statistic = 3.240
P-value = 0.018
Alpha= 0.05 (at 5% significance level)
Conclusion:
It has been seen that P-value < alpha at 5% significance level. Hence the null
hypothesis of the test is significant and the alternative hypothesis may not be rejected.
Therefore it may be concluded that there is a differences between the desensitization and
control.
Hypothesis 4

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Single Factor ANOVA output
The study conducted only four variables. These are model, film, desensitization and
control. It has been seen that the average of model group is 26 which shows the highest
average rest of others. The smallest average is 10 which has been shown by control group.
Moreover in case of control group the mean and variance are same. Similarly the variance of
film and desensitization is also same and the variability is 8.6667.
Null Hypothesis: There is no differences between the model, film, desensitization and
control.
Alternative hypothesis: There is a differences between the model, film, desensitization and
control.
Result:
Test statistic = 17.458
P-value = 0.0001

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Alpha = 0.05 (at 5% significance level)
It is clear that the P-Value < alpha at 5% significance level. Hence the null hypothesis
of the test is significant and the alternative hypothesis may not be rejected. Therefore it may
be concluded that there is a differences between the model, film, desensitization and control.
Thus it may be concluded from the study that all the relationship shows a significant
relationship except the relationship between film and desensitization.

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Bibliography
Campbell, D., & Lele, S. (2014). An ANOVA test for parameter estimability using data
cloning with application to statistical inference for dynamic systems. Computational
Statistics & Data Analysis, 70, 257-267.
De Winter, J. C. (2013). Using the Student's t-test with extremely small sample sizes.
Practical Assessment, Research, and Evaluation, 18(1), 10.
Mrkvicka, T., Myllymaki, M., Jilek, M., & Hahn, U. (2016). A one-way ANOVA test for
functional data with graphical interpretation. arXiv preprint arXiv:1612.03608.
Zholud, D. (2014). Tail approximations for the Student $ t $-, $ F $-, and Welch statistics for
non-normal and not necessarily iid random variables. Bernoulli, 20(4), 2102-2130.

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