Importance of Statistical Analysis
Performing statistical analysis is an essential procedure for making informed and data-driven decisions. Any choice, be it organizational, household, social, or business decisions, can be based on personal beliefs and vision of the environment alone; however, the practical value of such conclusions will be lower than if statistical analysis is used. The use of data helps to reduce bias in the results and to formulate decisions that will lead to success with greater accuracy.
Scenario Description
This assignment considers a scenario in which the subject of the study is consumer taste preferences based on a sample of 80 participants. The mechanics of the experiment consisted of each respondent trying four different flavors (A, B, C, and D) and then selecting the one they liked the most. Using a statistical test in this scenario aims to examine the significance of differences between groups and thus determine whether any of the flavors have the most extraordinary consumer liking.
Variable Identification
To select a statistical test as part of the analysis, the nature of the variables must be determined. Thus, there are only four flavors (A, B, C, and D) for which frequency distributions were collected. Category A was selected 12 times, category B 18 times, category C 28 times, and category D 22 times. At first glance, the differences are apparent: category C scored the most consumer liking and category A the least. However, such conclusions are not supported by statistical data, so a test is necessary.
Statistical Analysis
A suitable form of statistical analysis is the chi-square goodness of fit test because there is a de facto single variable, namely consumer preference (Turney, 2022). Since it was not specified what proportions should be expected, it can be assumed that the expected frequencies should be equal, that is, 20 for each of the flavors. We should also put the significance level of alpha equal to.05, as this reduces the probability of committing a Type I error to 5% and is a reasonably frequent value for statistical tests.
Then the procedure for this statistical test can be summarized in the table below:
The chi-square test level was found to be 6.8. With the chosen significance level of alpha and three degrees of freedom, the p-value of this result is p =.078553. This is higher than alpha, which means the null hypothesis is rejected, and inequality of proportions is postulated. In other words, it is now seen and is reasonable that flavor C has the most consumer preference points.
Reference
Turney, S. (2023). Chi-square (Χ²) tests | types, formula & examples. Scribbr. Web.