Nonparametric Hypothesis Testing

Nonparametric Hypothesis Testing Paper

Throughout the Kansas City metropolitan area, it has been observed that the population purchases more Kansas University sportswear than Missouri University at Columbia sportswear. There will be observational studies, surveys, and other methods of testing to prove this hypothesis. After these methods of gathering data have been completed, the hypothesis can be either supported or rejected based on the research and data collected.

The data collected is qualitative and since the level of reliability for this research is at or near 95%, the critical value needed to either confirm or deny the null hypothesis is 55% since the possibility exists of a +/-5% error when the data is applied to the population from the sample group. This means that in order to confirm the null hypothesis greater than 55% of the subjects surveyed will prefer Kansas University sportswear versus Missouri University at Columbia sportswear. If the critical value is at or below 55% than the null hypothesis is denied and the alternate hypothesis is confirmed.

Nonparametric Testing

Chi-square is the probably the most useful and widely used nonparametric test (Apollo Group, 2007). Chi-square statistic is useful for analysis of nominal and ordinal level data, but it can be used for interval level data, if the quantitative data is broken into categories (Apollo Group, 2007). Chi Square tests are commonly used for categorical data, especially in the analysis of contingency tables, or cross-tabulations (Apollo Group, 2007). The two variables are identified as row or column variables, and their intersections in the table are referred to as cells (Apollo Group, 2007). Chi Square analysis involves calculating a test statistic that compares observed cell frequency to expected cell frequency (Apollo Group, 2007). This observed value is then compared to a critical value, found in either a Chi Square table or in statistical software output, and a decision is made on the null hypothesis (Apollo Group, 2007). As with all parametric statistics, a simple comparison of the observed probability with the significance level is used for decisions on the null hypothesis (Apollo Group, 2007). See Appendix F for results of Chi-square testing.

Hypothesis Testing

The first critical step for a given research project is hypothesis testing. To satisfy this requirement the following five-step process should take place: 1. State the null hypothesis, 2. Select a level of significance, 3. Indentify the test statistic, 4. State the decision rule and 5. Take a sample and arrive at a decision.

The null hypothesis or H0 for this research is more people from the Kansas City metropolitan area purchase Kansas University sportswear than Missouri University at Columbia sportswear. The alternate hypothesis or H1 is the inverse of H0, which is more people from the Kansas City metropolitan area purchase Missouri University at Columbia sportswear than Kansas University sportswear. With this stated the results of the research would either confirm or deny the null.

The level of significance or ? for selecting critical values will be 0.05 or 95% reliability. The ? directly relates to the weighting of variables in the analysis of the research data. The importance of stating this value during hypothesis testing is to set a standard for all data collected and analyzed for the research.

The test statistic for the research will be a t-test. T-test statistic testing is used when less than the required minimum n of 30 for each variable for a z-test is available. The data collected for this research produced a t-test value of 4.02 when compared in a proportion vs. hypothesized value statistical test.

The decision rule for this research is based upon the ? of the primary variable. The primary variable for this research is drawn from question number eight of the survey. The primary variable should meet or exceed 55% of the sampled data to accept the null.

Results of Testing

As stated previously the t-test value from the example data is 4.02 with a two-tailed p-value of 0.0015 thus denying the null. The calculated value of t-