Reference no: EM132367336

Please comment on this post in a 150-200 words.

Comment should be statistically relevant with 1 APA reference.

The original question was:

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.

Answer:

The concept of T-test has been used for an extended period to facilitate the analysis of two populations. It relies on statistical analysis approaches. In most cases, T-tests are used or utilized with small population samples to enhance the ability of scholars in assess the differences between samples, particularly, when the variations of existing normal distributions are unknown (Derumigny & Fermanian, 2017).

There are several assumptions associated with the use of T-tests; one of the common assumptions that tend to emerge with regard to its application is based on the idea of scale of measurement. Individuals that rely on T-tests assume that the scale of measurement utilized on information collected usually follow an ordinal or continuous scale similar to the scores of an Intelligent Quotient assessment.

Also, T-tests are based on the assumption that reasonable substantial sizes of information or data are used by the respective researchers (Derumigny & Fermanian, 2017). The utilization of a relatively large sample size is considered an indication that the outcomes would approach a normal curve in the shape of a bell.

It is significant to take note of the fact that the use of larger sample sizes in any quantitative research has been associated with the prevention of skew, which could also generate larger margins of error. Besides, larger sample sizes are essential in the sense that they tend to facilitate the generation of mean credible and accurate values, including improving researchers' abilities to identify outliers.

The third assumption associated with the application of T-test is based on the concept of simple random sample. This assumption entails that information used in T-tests is usually gathered from a single representative, selected randomly from a particular population or target participants.

Statistically, simple random sample is considered a subset of a particular group or population; each member of such a population is assumed to have an equal possibility of being selected for purpose of a specific study. For example, when performing a research, a nongovernmental organization may decide to randomly select 100 people from a population of 600 individuals. In such a scenario, the sample used is random based on the fact that all the 600 individuals have an equal opportunity or chance to be selected or considered as participants in the research.

The assumption of based on the concept of simple random sample is not robust to violations. Scholars usually rely on critical and recommended sampling techniques that fundamentally reduce or prevent the possibility of violating this assumption (Delacre, Lakens & Leys, 2017). However, there are scenarios that the above assumption can be extremely violated by researchers. For example, researchers' bias, when selecting their samples may trigger the violation of the simple random sample assumption (Delacre et al. 2017).

In summation, the three common assumptions associated with the use of T-test include the idea that the scale of measurement utilized on information collected usually follows an ordinal or continuous scale similar to the scores of an Intelligent Quotient assessment.

Also, it is founded on the assumption that reasonable substantial sizes of information or data are used by the respective researchers. Consequently, T-tests are based on the assumption that in a particular research population, each participant has an equal probability to be selected to participate in an assessment.