Statistics refers to the use of numerical information in everyday life to calculate facts and figures in limitless circumstances. In addition, statistics refers to the scientific collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical data. This week the class’s objectives were to apply the steps in testing a research hypothesis, to compare the means of two or more groups, and to calculate the correlation between two variables. Learning Team D’s members have reflected on each of these issues and share their insights on these objectives.
Testing a Research Hypothesis
The purpose of testing a research hypothesis is to prove or disprove the research question. The first step in testing a research hypothesis is to state the problem in the form of a question. The second step is to state the research question as it relates to the null hypothesis and alternative hypothesis. Then the parameters must be set to test the null hypothesis. The fourth step is to calculate the probability of the test statistics or rejection region. Finally, the findings from the tests must be stated. The hypothesis was familiar to one group member, so she felt comfortable with the topic. She did not struggle with any particular topic this week. This week’s topics directly relate to her field of study. As an accountant it is important to have a good understanding of mean, median, and mode, as well as statistical probability. These topics are all a part of learning to analyze information and make educated and well-thought business decisions.
Compare the Means of Two or More Groups
The experimental method of comparing the means of two or more groups is a pretty common occurrence in statistical research. The procedure for estimating and testing the hypothesis when using a single sample population will also apply in a case scenario with two or more groups or populations; however, modifications are required for accuracy. In other words, the 5-Step Hypothesis Testing procedure is used with multiple sample experiment, as well. Whenever the area of interest involves the differences, comparison, proportions or variability, then data can be collected on two or more groups—this would be considered the target parameter (Lind, Marchal, & Wathen, 2011). In a quantitative analysis the interest is more likely to compare means or variances; whereas, a qualitative experiment with two outcomes is more likely to focus on success or failure.
When comparing the means of two or more groups these populations can both or all be independent and the expectation is to determine the reason for a difference in the means—this would deliver a result where the means are other than zero. The typical assumption is that there will be a normal distribution and that a random sample is collected for each of the populations. Another characteristic of comparing means of two or more groups is that when standard deviation is known or unknown and the population sample is large, then a z distribution (z-test) is used and in the case where it is unknown and the sample size is small, then a t distribution (t-test) is used. However, in the case where the experiment calls for a test of two or more dependent samples for one group or population, then a paired t-test is used to draw results (Lind, Marchal, & Wathen, 2011).
Calculate the Correlation Between Two Variables
When calculating the correlation between two variables, the objective is to see how one variable is influenced by another variable. The bivariate relationship displays the connection between two variables (x and y) and correlation shows how to measure their relationship. The correlation is calculated using the coefficient of correlation. This measurement calculates the power between the two variables (x and y). (Coefficient correlation) The coefficient correlation will have limits between -1 and +1, and doesn’t rely on the initial values of x or y. The coefficient correlation would suggest the higher the number, the higher the correlation, and the lower the number, the lower the correlation (but this is a linear correlation). A value of zero will indicate no correlation.
In conclusion, the team learned that once a hypothesis has been formed the next step is to test it for acceptance or rejection. An experiment must then be created to determine if the predictions were correct or not. In many situations the interest lies in discovering relationships between the means of two or more groups. T-tests and analysis of variance are widely used statistical methods to compare group means. Moreover, the team learned how to calculate the correlation between two variables to determine the relationship or affect of one variable upon another. The correlation between two variables suggests that a change in one variable will cause a proportional change in the other variable.
Lind, D. A., Marchal, W. G., & Wathen, S. A. (2011). Basic statistics for business and economics (7th ed.). New York, NY: McGraw-Hill/Irwin.