**Examine a research article which incorporates t tests or its nonparametric analogs. Briefly summarize and report the statistic and discuss whether the assumptions of the test were met and if the type of data was appropriate for the statistical test. Include the following in your paper:**

**Description of the statistic you intend to examine in the article**

**Brief description of the study portrayed in the article**

**Description of how the statistic was used in the study.**

**Explanation of how this is appropriate or inappropriate**

**Explanation of how assumptions of the test were met or not met**

**Identification of the levels of measurement of variables in the study**

**Description of the appropriateness of the level of measurement**

**Discussion of how the data was displayed (i.e. graphs, tables)**

**Discussion examining the appropriateness of the data displays (Strengths and weaknesses? Were they appropriate? Why or why not?)**

**Your paper must be composed using Microsoft Word and must be typed in Times New Roman, font size 12. This and all papers should be written in APA format and follow standard rules of grammar and formatting. 5- pages excluding cover page and references are required.**

**ASSESSING T-TESTS 1**

**Introduction**

A t-test is the most commonly used statistical test which incorporates statistical examinations of two population means (Moore 2008). Due to its simplicity, it is not only easy to use but can be adapted to a wide range of situations. A t-test is crucial to every statistics carried out because it leads to conclusive results when used. A t-test is used to examine whether or not two samples are different and is highly effective when variances of two distributions are unidentified or when a certain experiment uses small sample sizes (Moore 2008). Scientific research is used by researchers to examine the nature and phenomena surrounding two variables at a particular time. Researchers, therefore, use the t-test to answer some basic questions as to whether variables are related or what will happen to the level of one variable if the level of the other variable is raised (Moore 2008). The t-statistic is the test statistic in the t-test which means that the t-test will look at the t-statistic, the t-distribution and the degree of freedom. This determines the probability value that researchers use to determine whether group means differ. Incase the number of variables being compared are more than three, then (ANOVA) an examination of variances is used (Moore 2008). A z-test is used when the sample size being examined is large.

**Description of statistic and study**

Depression is a medical condition that affects many individuals worldwide. This medical condition affects the well being of an individual whereby the individual experiences mood disorders (Lam 2011). The individual exhibits activities that directly affect his or her behavior, feelings, thoughts and a sense of well-being. According to Lam (2011), some of the symptoms that a depressed person exhibits are anxiety, hopelessness, worry and guilt. Since the condition affects the way the individual thinks, he or she may have suicidal thoughts and therefore depression should be treated with immediate effect (Beck 2009). There are many drugs that doctors use to cure individuals that are affected by depression. One of these drugs is Prozac. It would be best to test hoe effective Prozac is in treating depressed individual. A well-being scale is highly effective since it will show the level of depression of an individual before taking Prozac and the successive depression level after taking the drug. In the study, a total of nine people took part whereby they were subjected to a well-being scale of between 0 and 20 (UoE 2000). A high score would indicate a greater well-being than a low score. The statistic used in this article was the difference between the post-mood and pre-mood of the individual. This statistic was obtained by subtracting the time of the pre-mood from the post-mood. The difference (change score) would therefore be used to find how effective Prozac is.

**Use of statistic and its aptness**

The change score was first calculated in all the nine individuals. This was done by obtaining the difference of the post-mood score and the pre-mood score of all the nine individuals. The data was computed and put in a table.

Retrieved from http://www.une.edu.au/WebStat/unit_materials/c6_common_statistical_tests/example_paired_sample_t.html

According to the University of England (2000), calculation of the pre-mood mean took place and was found to be 3.33 while that of the post-mood was 7.0. The increase of the pre-mood mean of 3.33 to that of a post-mood mean of 7.0 would be determine if Prozac was effective or not (UoE 2000). The difference would also show how much effective the drug is. The statistic was later used and the means were compared (paired sample T-test) in a bid to find the effectiveness of Prozac on the well-being of people suffering from depression. This took place by finding the standard deviation, correlation and standard error mean of the two paired samples. This was appropriate in that it would better show the results of the change score. It was necessary to compute the data in this way to find the standard deviation and the standard error mean because it would show the error found in the change score thereby leading to concise and appropriate results. According to the University of England (2000), through the paired sample t-test, a confidence interval of the difference was computed and found to be at 95 percent. This showed without a doubt that the results of the change score were significant and concise.

**Levels of measurements and its appropriateness**

In the paired sample statistic, the variables that were compared were the mean, number of people that took part in the study, standard deviation and the standard error of mean for all the variables. The next step was the paired sample correlation whereby all the correlations of the given variables were found. In this level of measurement there is a repeated measures analysis and therefore all the participants were measured twice. The paired sample correlations showed that there was a high degree of correlation between for the two scores (pre-mood and post-mood). The measurement showed that a person who had a well-being score that was fairly low before treatment would still have a fairly low well being score after treatment in relation to the other members who took part in the study. A person who had a well being score that was high before the treatment would have a high well being score after the treatment. The pattern of change in this group of scores is inconsistent.

The paired sample test on table one shows the descriptive statistics for the score difference of each pair of a given variable. The mean difference (3.67) was tested against zero to show if the number was small or large or if the difference is real or one that could be expected due to chance (UoE 2000). The information given on this table also reveals that the true population mean is between 6.357 and -0.9763. The table also reveals that there is a 95 percent probability to this. The paired sample test on table two shows that the probability of the number occurring by chance given the null hypothesis would be 1.4 percent (0.014)

Retrieved from http://www.une.edu.au/WebStat/unit_materials/c6_common_statistical_tests/example_paired_sample_t.html

**Assumptions**

The assumptions of the repeated samples in the t-test are comparable to the one sample t-test but they refer to the different scores in the pre-mood and post-mood. Some major assumptions made in the t-test are that all observations are independent and therefore one observation does not affect the other (Utts 2007). Another assumption in the test is that the dependent variable is always measures and computed on an interval scale. All the differences in the t-test which arise from the pre-mood value and the post-mood value are normally distributed. All the measures in the pre-mood and the post-mood value are interval scale numbers also referred to as self-report scores (Utts 2007). This leads to the assumption that no one’s particular score had been influenced by the score of another person. Another assumption that is easy to support is that the values of the pre-mood and post-mood have no extremes and are not unusually distributed.

**Conclusion**

There was a significant increase in the well of the individuals who were suffering from depression. There was an increase in the well being score upon administration of the Prozac drug. This proven hypothesis shows that it is possible to cure a person suffering from depression (t (9) = -3.14, p = .012,^{2} = .52). The results of the t-test show that there is strong evidence that link the increase of a person’s well-being to the administration of Prozac to the individual. According to the University of England (2000), the result of the t-test is significant (t(9) = -3.143, p = .012) which means that there is a rejection of the null hypothesis and thus favoring the alternative hypothesis. The results of the test show that only once or twice for every one hundred times that the experiment was conducted was the only time that a t-statistic of the found size was given. This was the only time that null hypothesis was true. The likely possibility was that there was some deliberate and systematic cause that made this to be true. This systematic and deliberate cause that made the results to be how they are is because of the Prozac drug. The test also shows that 52.3 percent of the varying scores in the well-being of the participants are attributed to the use of Prozac or not using the drug (UoE 2000). It is also true that all the data computed and used was appropriate. This is because the method of computing the data was accurate, concise and correct.

**References**

Beck, A. T., & Alford, B. A. (2009). Depression: Causes and treatment. Philadelphia: University of Pennsylvania Press.

Lam, R. W. (2011). *Depression*. Oxford: Oxford University Press.

Moore, D. S. (2008). The basic practice of statistics. New York: W.H. Freeman and Co. University of New England. (2000). *Common Statistical tests: Example of Paired Sample T-test.* Retrieved on 26^{th} August 2013