Example of a Paper on Statistical Techniques

Independent sample t-test

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It has been shown by various researches that the decision usually made by people to behave either morally or immorally depends on the past occurrences. In some cases, it has been assumed that people usually undergo rationalization that ends up releasing them of the guilt they had. There are individuals who will try and compensate the bad behavior done by doing good in the future so as to do away with the sense of guilt. On the other hand, there are those who will always keep doing bad deeds as a way of justifying their deeds.

Studies also show that there are two ways in which people reflect the misdeeds they took part in in their mindset. The first approach is the factual approach which involves the events replaying just like they transpired. The second approach is the counterfactual which involves the individuals imagining how the events should have turned out rather than how they turned out. This is known as the what if or the only if scenario.

We were provided with a dataset consisting of 75 people with at least one of the two conditions. The first category is the factual group that took things literary as they happened. The other group is the counterfactual, who think there is a different way in which they should have done what they did. The levels of guilt were measured on a scale of 1 to 10.

We analyzed the data using independent sample t-test. This is a test usually used to investigate if there is a significant difference between two unrelated groups ((Weinberg, Abramowitz, 2008). In this case we check if the guilt rating for the factual category differed significantly from the counterfactual category.

The results were as shown below

The hypothesis to be tested is:

H0: There is no significant difference in the guilt rating between the two groups.

H1: There is a significant difference in the guilt rating between the two groups.

From the above results, we fail to reject the null hypothesis and conclude that there is no significant difference between the guilt rating of the factual and counterfactual group. This is seen from the fact that the p-value or the significance code is 0.778. This value is greater than 0.05.

Paired sample t-test

This is a technique used in comparing means of two samples with an aim of checking if the two samples are correlated. It is used in before-after studies. We are provided with a dataset consisting of the working memory of 45 participants before and after 10 weeks of adaptive computerized memory training. We are interested in testing the hypothesis:

H0: There is no significant difference in the memory of participant before and after the test.

H1: The working memory of participants is better than it was after the test.

We conducted a paired sample t-test and obtained the following results.

From the results above, we reject the null hypothesis. We thereafter conclude that there is no significant difference in the memory of participant before and after the test. This is due to the fact that the p-value which is our significance code is 0.00 which is less than 0.05. The above results therefore indicate that it is necessary for individuals to participate in computerized memory training tests because they are helpful.

One way ANOVA

This is a statistical technique that is used to compare three or more means in a given dataset. One way ANOVA is usually used to test the hypothesis that the mean of one group is significantly different from the other group means (Weinberg, Abramowitz, 2008). In this case, we are interested in testing if there is a significant difference between the mimicry based on the category of the individual; ie the individuals goal status. We need to check if at least one group differs in the mimicry level. That is the conscious, non-conscious and the no goal category.

We test the hypothesis:

H0: There is no significant difference in the mean times for the 3 groups.

H1: At least one group is significantly different.

The results are as shown below:

From the results above, we reject the null hypothesis. This is because the p-value which is our significance code is 0.02 which is less than 0.05. We thereafter conclude that there is a significant difference between the three groups when it comes to mimicking.

Correlation

Correlation is a statistical measure that shows the extent to which two variables in a dataset depend on each other. In this case, we investigate the correlation between the number of hours a student sleeps and the final exam scores. We use the dataset of a sample of 35 medical students. We test the hypothesis:

H0: There is no association between the exam score and the hours of sleep.

H1: There is association between the exam score and the hours of sleep

The results are as shown below

The above output indicates a strong correlation between the hours of study and the exam score. There exists a correlation of 0.961 between the exam score and the length of sleep.

Regression

It is a statistical technique that usually measures the strength of relationships between one or more predictor variables and the response variable. In this case, we conduct a multiple linear regression analysis to check for the association between the sleep-wake cycle of 35 medical students and other predictor variables such as the length of sleep, academic performance, social activities and work demands. The data was obtained for Pitsburg Sleep Quality Index, and sleep a wake diary. We perform multiple linear regression to check for the factors affecting the time it takes before a student falls asleep (sleep latency). The results are as shown below.

From the output above,

Sleep latency=48.895+3.904Gender-0.682 Sleep irregularity-0.20Length of sleep-0.354 Academic performance

However all these predictors are not significant predictors since their p-values are all greater than 0.05.

We also conducted multiple linear regression to check for the factors that can be used to predict the academic performance of the various students. The out

From the analysis above, we find that:

Academic performance=-1.5962-1.018Gender+0.5583 Sleep Irregularity+0.23Length of sleep-1.5Sleep onset latency

We find that the only significant predictor of exam scores in this case is the length of sleep.

The model is significant as seen in the ANOVA table above. This is since the p-value is less than 0.05.

References

Weinberg, S. L., & Abramowitz, S. K. (2008). Statistics using SPSS: An integrative approach.

Cambridge: Cambridge University Press.