*PUB 550 Application of the t-Test*

PUB 550 Application of the t-Test

**Introduction **

Student t-test is often applied in the statistical analysis to test hypothesis. In the SPSS output, the results of t-test can be translated in different ways. In other words confidence interval can be applied as well as the significant values obtained. T-test is a form of inferential statistics that is always applied to determine if there is a significant different between the means of two variables or two groups in a dataset (Kim, 2015). The two variables may be related in certain features. While performing t-test, there are always assumptions that have to be made. For example, there is always assumption of equality of variance. Some other assumptions that are always made include normality of data distribution, adequacy of sample size, the data is also assumed to be randomly sampled. The independent sample t-test or two sample t-test is always performed when one variable being considered is categorical while the other is continuous. The continuous variable must have a normal distribution (Delacre et al., 2017).

**Assumptions in t-test**

T-distribution is always considered to be a continuous probability distribution that often arise from the estimation of the mean of a given population with a normal distribution. In most cases t-test is applied in proving hypothesis (Champely et al., 2017). There are different approaches that can be applied in either rejecting or accepting null hypothesis (Test et al., 2018). In t-test, there is always the testing of the difference between the two samples under consideration when the variances of the two variables are unknown. Assumptions of normality are essential in ensuring accurate or effective processes in the statistical analysis. There is always the need to consider the scale of measurement in the process of undertaking t-test. In most cases, the scale of measurement applied to the data under analysis should always follow an ordinal or continuous scale. Homogeneity of variance is another assumption that is always made regarding t-test (Kim & Park, 2019). In other words, the variance of data under each variable should be equal to ensure that there is effective outcomes in the process of comparing the means using t-test.

**t-tests Selected**

Two sample t-test or the independent sample t-test is often used in data analysis to compare the means of two independent groups to test whether there is a statistical evidence that the associated population means have a significant difference. Just like any other t-test, the independent t-test is a parametric test. The independent sample t-test is always recommended when one variable is categorical while the other variable is continuous and normally distributed. In this case, weight is a continuous variable while sex is a categorical variable (Jeanmougin et al., 2018). The independent sample t-test is most commonly applied in testing the statistical difference between the means of the given two groups. It can also be applied in the determination of the statistical difference between the means of two interventions. Finally, independent sample t-test can be applied in the determination of statistical difference between the means of two change scores. The independent sample t-test can only be applied in comparing the means for two and only two groups (Kruschke, 2018).

**Null and Alternative Hypotheses**

The null hypothesis is always stated in a negative statement while alternative hypothesis is stated in a positive format. The null hypothesis is normally involve an accepted fact, in other words, it is the opposite of alternative hypothesis. In most cases, researchers or data analysis often work to disapprove, nullify or reject the null hypothesis. In the above case, when null hypothesis is rejected, it means that the weight of the participants does not differ by sex. On the other hand, when null hypothesis is rejected, it would mean that the weight of individuals involved in the study does not differ by sex. Null and alternative hypothesis are important in the statistical analysis since they are used to guide the research outcomes. The formulation of the null and alternative hypothesis often depend on the variables involved in the study process. In other words, the variables ought to be carefully selected to ensure effective outcomes (Krois et al., 2019).

**The Decision Rule**

Decisions rules are important in the hypothesis test, they enable data analysis to make effective decisions on the outcomes of the results of analysis. While conducting t-test, it is necessary for the researcher to observe the significant value under 2-tailed. From SPSS analysis, there is always the options for the equality of variance and cases where equal variances are not assumed. When the equality of variances was assumed at the beginning of the data analysis, data analysis would only check for the value under the equality of variance to determine effective outcome or the determination of the decision rule on the hypothesis (De Winter, 2018). The decision can also be based on the upper and lower limits. In other words, when the mean difference is within the lower and upper limit, then we fail to reject the null hypothesis. On the other hand, when the value is outside this limit, we can reject the null hypothesis.

**Test Statistic ****and ****p-value**

Decisions rules are important in the hypothesis test, they enable data analysis to make effective decisions on the outcomes of the results of analysis. While conducting t-test, it is necessary for the researcher to observe the significant value under 2-tailed. From SPSS analysis, there is always the options for the equality of variance and cases where equal variances are not assumed. When the equality of variances was assumed at the beginning of the data analysis, data analysis would only check for the value under the equality of variance to determine effective outcome or the determination of the decision rule on the hypothesis. The decision can also be based on the upper and lower limits. In other words, when the mean difference is within the lower and upper limit, then we fail to reject the null hypothesis. On the other hand, when the value is outside this limit, we can reject the null hypothesis. P-value can be applied while conducing independent sample t-test to make meaningful conclusion. The independent sample t-test is most commonly applied in testing the statistical difference between the means of the given two groups. It can also be applied in the determination of the statistical difference between the means of two interventions (Love et al., 2019).

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**Interpretation of The T-test Results**

SPSS often provide a better approach of undertaking t-test. When setting the variables during test, there is always

the consideration of the grouping variable which has to be defined according the coding that was done in the processes of defining variables. In this case, the grouping variable was sex. With 1-representing male and 2-representing female. Grouping variable 1 was therefore set as 1 while the grouping variable 2 was set as 2. The dependent variable used was weight. The data under this variable was continuous. Before undertaking statistical test, there was the analysis of descriptive statistics to determine the attributes of the variable under consideration. . In the SPSS output, the results of t-test can be translated in different ways. In other words confidence interval can be applied as well as the significant values obtained. T-test is a form of inferential statistics that is always applied to determine if there is a significant different between the means of two variables or two groups in a dataset.

### Findings and Meaning

From the result obtained, the data was analyzed at 95% confidence interval. The mean difference was 11.333. The 2-tailed significant value was 0.522 which is greater than 0.05. Therefore, when the equality of variance is assumed, we fail to reject the null hypothesis meaning that there is no signigificant different in the means. In other words, the weight of the individuals selected does not differ by sex. From the analysis, there was also the determination of both the upper and lower limits which were then compared to the mean obtained. When the mean difference is within the lower and upper limit, then we fail to reject the null hypothesis. On the other hand, when the value is outside this limit, we can reject the null hypothesis. P-value can be applied while conducing independent sample t-test to make meaningful conclusion. From the test, we fail to reject the null hypothesis and use it to make conclusion.

### **Conclusion**

The results can be applied in the research processes to determine the best interventions that can be applied in the management of obesity and the related conditions. The outcome of the research as well as the methodologies that have been applied are essential in guiding different research processes and statistical analysis. Student t-test is often applied in the statistical analysis to test hypothesis. In the SPSS output, the results of t-test can be translated in different ways. In other words confidence interval can be applied as well as the significant values obtained.

**References**

´Kim, T. K. (2015). T test as a parametric statistic. *Korean journal of anesthesiology*, *68*(6), 540. Retrieved from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4667138/

´Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch’s t-test instead of Student’s t-test. *International Review of Social Psychology*, *30*(1). Retrieved from: https://www.rips-irsp.com/articles/10.5334/irsp.82/

´Krois, J., Ekert, T., Meinhold, L., Golla, T., Kharbot, B., Wittemeier, A., … & Schwendicke, F. (2019). Deep learning for the radiographic detection of periodontal bone loss. *Scientific reports*, *9*(1), 1-6. Retrieved from: https://www.nature.com/articles/s41598-019-44839-3

´Love, J., Selker, R., Marsman, M., Jamil, T., Dropmann, D., Verhagen, J., … & Wagenmakers, E. J. (2019). JASP: Graphical statistical software for common statistical designs. *Journal of Statistical Software*, *88*(2), 1-17. Retrieved from: https://dergipark.org.tr/en/pub/jegys/article/574275

´Kim, T. K., & Park, J. H. (2019). More about the basic assumptions of t-test: normality and sample size. *Korean journal of anesthesiology*, *72*(4), 331. Retrieved from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6676026/

´Test, N., Plot, T. S., & Plot, I. V. (2018). One-sample t-test. Retrieved from: https://www.minitab.com/en-us/uploadedfiles/documents/sample-materials/mortgageprocesstime-en.pdf/

´Jeanmougin, M., De Reynies, A., Marisa, L., Paccard, C., Nuel, G., & Guedj, M. (2018). Should we abandon the t-test in the analysis of gene expression microarray data: a comparison of variance modeling strategies. *PloS one*, *5*(9), e12336. Retrieved from: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012336

´Kruschke, J. K. (2018). Bayesian estimation supersedes the t test. *Journal of Experimental Psychology: General*, *142*(2), 573. Retrieved from: https://psycnet.apa.org/record/2012-18082-001

´Champely, S., Ekstrom, C., Dalgaard, P., Gill, J., Weibelzahl, S., Anandkumar, A., … & De Rosario, H. (2017). pwr: Basic functions for power analysis. Retrieved from: https://nyuscholars.nyu.edu/en/publications/pwr-basic-functions-for-power-analysis

´De Winter, J. C. (2018). Using the Student’s t-test with extremely small sample sizes. *Practical Assessment, Research, and Evaluation*, *18*(1), 10. Retrieved from: https://scholarworks.umass.edu/pare/vol18/iss1/10/