Question 1
The following is a definition and description of some of the commonly used statistics for categorical and continuous variables to test for a statistically significant difference between two-samples or measures.
Chi-Square: Chi-square refers to any statistical hypothesis test within which the sampling distribution associated with the test occurs as a chi-squared distribution if the null hypothesis being tested is true (McDonald, 2014). The tests are used in the testing of existing relationships between categorical variables, which is essential towards building on overall progression in maximizing on the general understanding of the variables as they relate to the statistical measure. The development of this test arises from sample variance, which allows for an adequate analysis of the overall variability of the hypothesis being considered.
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T-tests: T-tests are a type of statistical test used as part of determining whether there exists a significant difference between two or more variables (McDonald, 2014). In this test, one of the critical aspect to note is that it is expected to assume that the variables can be considered within normal distribution. That would help towards examining some of the essential factors that would assist in the identification of the exact factors that are contributing to the significant difference.
Binomial Proportions: Typically, the use of binomial proportions is used in the overall process of assessment focusing on a true proportion concerning a given population (McDonald, 2014). That would help in ensuring that the results gathered from a given sample of a population are accurate to help build on overall progress in examining the statistical variables. However, it must be noted that these tests rely on two key factors, which are a normal distribution and reasonable approximation.
Question 2
The main difference between the one-sample t-test, the two-sample t-test, and the paired-sample t-test can be seen from their applicability during the overall process of sample testing and analysis. When dealing with one-sample t-test, the main focus is on using results from one sample, which are compared to results from a known population (McDonald, 2014). That means that it becomes much easier to identify any variations that can be considered as being statistically significant or those that can be deemed to have occurred by chance. That is not the case when dealing with the two-sample t-test, as this particular test focuses on comparing results from two samples collected from different populations while using the same variable. The expectation in the two-sample t-test is that it will help in providing a clear analysis of the exact significance that can be seen from samples collected from two populations (McDonald, 2014).
As opposed to the one-sample t-test, the two-sample t-test does not have results from a known variable, which means that it would be much harder to determine the whether indeed the results from the samples can be considered as being accurate. Additionally, this also makes it hard to determine whether the occurrence of the effects, from the sample, can be deemed to have resulted from chance alone while considering the overall possibility of the results. Lastly, the paired-sample t-test seeks to focus on two samples that are collected from the specific population with the aim being towards using the same variable (McDonald, 2014). Although it may be similar to the two-sample t-test, it differs significantly with the two-sample t-test while considering the population in which the samples are collected or gathered.
Question 3
Based on the analysis of the different types of t-tests, it would be essential to examine the exact kinds of studies that would be appropriate for each with the focus being towards examining how they relate to the study results.
In the one-sample t-test, a type of study that would be considered relates to finding the mean height of female students in a local college greater than 5.5 feet. The focus of this study is getting the mean height for students with one of the local colleges while a sample of students that have a height that is greater than the required 5.5 feet. In this variable, the variable that is being considered is the height of the students with the specific focus being on students that are greater than 5.5 feet.
In the two-sample t-test, a type of study that would be appropriate towards understanding the exact statistical variations is examined the weight of middle-aged African American men before and after taking weight-loss pills and comparing the results to those of white American men. In this study, the central aspect of focus is that the populations of consideration are different, as the study seeks to compare results from African and white American men. However, the variable considered in this t-test is the same, which is weight before and after the men have taken weight-loss pills.
In the paired-sample t-test, a type of study that would be effective would be examining the rate of obesity among white American teenagers below the age of 17 years while comparing these results to the rate of obesity among a sample of white American adults between the ages of 24 and 35 years. The central aspect of focus is that the population is the same within both samples, which is white Americans, with the sample differing as a result of age. The variable of consideration as part of the t-test is the rate of obesity.
References
McDonald, J. H. (2014). Paired t-test. In Handbook of vital statistics (3rd ed.). Baltimore, Maryland: Sparky House Publishing.
McDonald, J. H. (2014). Student’s t-test for one sample. In Handbook of vital statistics (3rd ed.). Baltimore, Maryland: Sparky House Publishing.
McDonald, J. H. (2014). Student’s t-test for two samples. In Handbook of vital statistics (3rd ed.). Baltimore, Maryland: Sparky House Publishing.
