**T-Test Nursing assignment**

### Topic 4: The t-Test

- Differentiate the use of three types of t-tests.
- Explain the assumptions of the t-test.
- Interpret t-test results to determine the difference in means.

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## Application of the t-Test |

## Topic 4 DQ 1 |

Compare the three types of t-tests by discussing when each is most appropriate to use and which types of questions each type of t-test best answers. Include specific examples to illustrate the appropriate use of each test. T-Test Nursing assignment

**Topic 4 DQ 1**

The t-test is one type of inferential statistics that are used to determine whether there is a significant difference between the means of two groups (Glen, 2020). The three main types of the t-test are:

One sample t-test tests whether the mean of a single population is equal to a target value. An example is testing whether the mean heights of female college students are greater than 5.5 feet. The second t-test type is the two-sample t-test which tests whether the difference between the means of two independent populations is equal to a target value. And an example of this is testing whether the mean height of female college students significantly differs from the mean height of male college students (Glen, 2020) T-Test Nursing assignment. Another type of t-test is paired t-test, this tests whether the mean of the differences between dependent or paired observations is equal to a target value. When measuring paired t-test, two measurements are usually taken on the same item, person or thing. This test is chosen if two items that are being measured are in the same unique condition. An example is measuring the weight of male college students before and after each student takes a weight-loss pill. This is to determine the mean weight loss is significant enough to conclude that the pill works or not (Glen, 2020). T-Test Nursing assignment.

Reference:

Glen, S. (2020). The t-Test (Student’s T-Test): Definition and Examples. Retrieved from

https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/t-test/

## Topic 4 DQ 2 |

Step 2 of hypothesis testing involves reviewing the assumptions of the test you selected. Discuss the three assumptions of the t-test. Provide an example of the assumption that is not robust to violations and a situation when the assumption is violated.

** Topic 4 DQ 2**

Assumptions are (Harvard University, n.d.):

- Not always true
- Important conditions that should hold in order for the t-test to work accurately

If you look in the textbook, based on what type of t-test you are doing the assumptions vary slightly. To combine them all, regardless of the type of t-test, there are common assumptions including random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation. T-Test Nursing assignment.

The t-test relies on a set of assumptions for it to be interpreted properly and with validity. Based on these assumptions, the data must be randomly sampled from the population of interest and that the data variables follow a normal distribution (Maverick, 2020).

As mentioned above that based on the t-test the assumptions may vary, that is the same for understanding if the test is robust for violations or not – see below (Emory University, n.d.)

- One-sample t-tests are considered “robust” for violations of normal distribution. This means that the assumption can be violated without serious errorbeing introduced into the test.
- The t-test for dependent means is considered typically “robust” for violations of normal distribution. This means that the assumption can be violated without serious errorbeing introduced into the test in most circumstance. T-Test Nursing assignment
- The t-test for independent means is considered typically “robust” for violations of normal distribution. This means that the assumption can be violated without serious errorbeing introduced into the test in most circumstance.

Potential assumption violations include (Emory University, n.d.)

- Implicit factors – the lack of independence within the sample
- Lack of independence: the lack of independence between samples
- Outliers – the apparent non-normality of the entire samples
- Unequal population variances
- Patterns in plot of data – detecting violation assumptions through graphics

Reference

Harvard University (n.d.) The important assumptions for using the t-test. Harvard Canvas. Retrieved from. canvas.harvard.edu › courses › files › download

Maverick, J. B. (2020). What assumptions are made when conducting a t-test? Retrieved from https://www.investopedia.com/ask/answers/073115/what-assumptions-are-made-when-conducting-ttest.asp

Emory University. (n.d.). Test Assumptions. http://www.psychology.emory.edu/clinical/bliwise/Tutorials/TOM/meanstests/assump.htm

**Topic 4 DQ 2**

Step 2 of hypothesis testing is to check the assumptions. In hypothesis testing, all statistical tests have assumptions, circumstances that need to be satisfied before the completion of the test (Corty, 2016). If this does not happen, the test results will be uncertain (Corty, 2016). There are three assumptions that can be made of the t-test:

**Random Sample: **The sample is random from the population, robust if violated (Corty, 2016).

**Independence of observations: **Cases within the sample don’t influence each other, not robust if violated (Corty, 2016).

**Normality: **The dependent variable is normally distributed in the population, robust to violations if the sample is large (Corty, 2016) T-Test Nursing assignment.

Whether or not the sample is a random sample from the population is the first assumption (Corty, 2016). This assumption is robust, meaning if it is violated, the analysis can still be completed (Corty, 2016). For example, a researcher is using the mean of a sample of adults with ADHD in comparison to the mean of a population of adults with ADHD to perform a single- sample t test (Corty, 2016). If she takes a random sample from a population of adults with ADHD from one state, the researcher should only generalize her results from that particular state (Corty, 2016. However, if the researcher chose participants not at random, the first assumption would be violated. Although, the test can still be completed.

The next assumption is that the observations in the sample are independent, the assumption is not robust (Corty, 2016). This means, if the assumption is violated, the t test cannot be completed (Corty, 2016). Using the same example as before, each subject appears in the sample one time and the reaction times of each case does not influence one another (Corty, 2016). These cases are tested individually and randomly selected, making them independent, not violating the second assumption (Corty, 2016). If the cases were tested as a group and the samples were not random, they become dependent to one another and the second assumption is violated. The test cannot be completed. T-Test Nursing assignment

Reference

Corty, E.W. (2016). *Using and Interpreting Statistics: A Practical Text for the Behavioral, Social, and Health Sciences. (3 ^{rd} Ed.)* New York, NY: Worth Publishers T-Test Nursing assignment