# Hypothesis Testing for Single Population Essay

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Updated: Nov 20th, 2020

According to Davis and Mukamal (1078), hypothesis testing is the process of evaluating the strength of the relationship between various sections of the data. It involves the use of instrumental methods to determine the correlations evidenced by the sampled data. When modeling hypothesis tests, there is the preparation of specific hypotheses from the data sampled and the resultant findings are employed to conclude on data relationships. In the hypothesis modeling process, the given situation is in the form of a question, and to investigate it, the question is modified into alternate and null hypotheses. These two statements are comprehensive and jointly exclusive when covering the possible truth of the research question regarding the predictor and the outcome of the population. The null hypothesis clarifies the deficiency involved in the relationship between the forecaster and result whereas the alternate hypothesis illustrates the occurrence of the relationship (Davis and Mukamal 1079).

Moreover, Prins (1384) states that the statistical test determines how the facts displayed by the data can be beyond the question given to support one hypothesis statement as a way of deciding between the presented null and alternate hypothesis by employing the likelihood ratio test. The likelihood ratio test compares two models defined by some constraints statistically. Therefore, the likelihood test functions provide flexibility in testing a variety of questions. For instance, what is the difference statistically between the thresholds in conditions A and B? Nevertheless, these comparisons between models are only legitimate if the assumptions used in both models are accurate (Prins 1384)

However, all tests in statistics have assumptions, and violation of these assumptions makes the statistical test unreliable. For instance, when using a t-test to calculate the hypothesis test about a single population mean, there is a specification of the probability of the variable of the sample. In case there are assumptions violations, the allotment of test statistic t will no longer be t leading to the assessment of p determined to be contradictory. Besides, the assumptions in the parametric test are in theory. In practice, these assumption violations highly affect the model’s outcomes. This means the failure to observe the assumptions, the p-value, formulate the statistical test t invalidly (Quinn and Keuogh 44).

As a result, the following are the assumptions of the t-test and the various ways of inspecting them. Firstly, there is an assumption that samples are taken from a normally distributed population (Mordkoff 1). This assumption exceedingly affects the results of statistics t not unless the distribution, which has occurred, is exceptionally symmetrical. To check the distribution and symmetry of the sample data, there is the use of dotplots regulator, pplots, or boxplots. Moreover, doing variable alteration improves data normality. However, the formal significance normality test is not vastly used because the test is reliant on the size of the sample and may reject the hypothesis in some conditions that t statistical test is still consistent after doing other tests (Quinn and Keuogh 44).

Secondly, there is an assumption applied when deriving the samples from the population with equivalent variances. The level of its variances disturbing the t-test is elevated, and moderates when the extents of samples are the same. To fix the non-normality, the variance must be similar, and investigation occurs to the alike spreads in each boxplot for individual samples. However, it is recommended to accomplish the first-round test when the population variance is equivalent to the f ratio test. This is because the f ratio test is susceptible to non-normality than the cosseted t-test. Additionally, the F test is unsuccessful in sensing the dissimilarity in variance brought up by the coverage of the sample used and this could nullify the t-test or make the t-test results to asymmetrical variances, which will not demonstrate the unpleasant consequence of the failure to examine the assumption on values of t statistic (Quinn and Keuogh 44).

Thirdly, there is an assumption at the phase of creating the data, which involves taking an arbitrary sample from a definite population. If there is no likelihood of sampling haphazardly from the population, then, trying the broad dissimilarity hypothesis for the samples occurs through the randomization test. The used t-test has high sensitive normality assumptions and equal variance when the sizes of the sample are not equal. Consequently, there is a recommendation on the use of samples of equal sizes when designing studies (Quinn and Keuogh 44).

Lastly, there are incidences of outliers in many statistical tests. Outliers are the excessive values from a given sample. Moreover, they are dissimilar to other observational results. Hence, the outliers have tough implications on statistic test in consideration of errors type I and II. Outliers affect both the parametric and non-parametric t-tests even when the tests were undertaken are on their grading (Causineau and Chartier 59). However, ranking reduces the t-test’s vulnerability to outliers (Roberts and Tarassenko 272). Methods that are widely used to identify outliers include Dixons Q test, Grubbs test, Chauvenets criterion, Pierces Criterion, distance, and density-based (Weisstein).

In conclusion, unless for the t-tests that have the capability of making rectifications to violated assumptions, other tests are hard to make necessary corrections. This is because it is always hard to determine the extent of violation of assumption and the value of caused significance changes by the occurrence of the violation (Carpenter 6).

## Works Cited

Carpenter, Arthur L. n.d. PDF file. Web.

Causineau, Dennis and Sylvain Chartier. “Outliers Detection and Treatment: A Review.” International Journal of Psychology 3.1 (2010): 58-67. Print.

Davis, Roger B. and Kenneth J. Mukamal. “Hypothesis Testing Means: Statistical Primer for Cardiovascular Research”. Circulation. 114 (2006): 1078-1082. Print.

Mordkoff, Toby J. Assumptions of Normality. 2011. PDF file. Web.

Prins, Nicolaas. “Testing Hypothesis Regarding Psychometric functions: Robustness to Violation of Assumptions.” Journal of Vision 10.7 (2010): 1384. Print.

Quinn, Gerry P. and Michael J. Keuogh. Hypothesis Testing. 2001. PDF file. Web.

Roberts, Stephen and Lionel Tarassenko. “A Probabilistic Resource Allocating Network for Novelty Detection.” Neural Computation 6.2 (1995): 270–284. Print.

Weisstein, Eric W. 2013. MathWorld. Web.

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