Topic 7 DQ 1:2

Topic 7 DQ 1 Review the three "Non Parametric" test videos in the Calculations section of the "Statistics Visual Learner" media piece. How would you create a statistical analysis based on the scenario below? Explain. What level of significance would you test at and why? A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks a favorite. The distribution of preferences is as follows. Do these data indicate any significance preferences among the four flavors using the chi-square test? Ice Cream Flavor A B C D 12 18 28 22 To address this issue, we employ one of the three non-parametric tests designed for evaluating statistics using "nominal and interval" data, a departure from parametric tests that rely on "interval and ratio" data. Among the non-parametric tests, the Chi-Square test stands out, given that "it is utilized in three scenarios: (a) when dealing with nominal data, (b) when working with ordinal data, and/or (c) when the sample size is small, as it examines the independence between categorical variables." This aligns well with the characteristics of our provided data. Referring to the Chi-Square (X2) Distribution table, I identified the critical value of 7.815 at the intersection of a significance level of 0.05 and 3 degrees of freedom. Employing the formula X2=∑(O-E)2/E, where O represents the observed frequency of an outcome (given number), and E is the expected frequency of an outcome (average), I computed a Chi Squared statistic of 6.80. Consequently, I reached the conclusion that the available evidence does not substantiate the assertion of a significant difference in preference among the four ice cream flavors at a significance level of 0.05 and with 3 degrees of freedom. A. x 2 = ∑ ( 28 − 20 ) 2 20 = 8 2 20 = 64 20 = 3.2

B. x 2 = ∑ ( 22 − 20 ) 2 20 = 2 2 20 = 4 20 = 0.2 ∑ of A + B + C + D=3.2 + 0.2 + 3.2 + 0.2=6.8 x 2 = 6.80 x 2 ≤ 7.815 DQ 2 Parametric tests and nonparametric tests serve distinct roles in statistical analysis. Using assumptions like normal distribution, Parametric tests are suited for interval or ratio data. In contrast, nonparametric tests are versatile, making no assumptions about the underlying distribution, and applicable to nominal, ordinal, interval, or ratio data. The assumptions differ between these test types (Sedgwick, 2015). Parametric tests assume homogeneity of variance, normality, and linearity, while nonparametric tests, being distribution-free, do not impose specific population parameters. Regarding the parameters under scrutiny, parametric tests typically evaluate means, variances, and proportions, whereas nonparametric tests center on medians, ranks, and the distribution of scores. In terms of sensitivity, parametric tests demonstrate greater power when assumptions align, especially with larger sample sizes. Conversely, nonparametric tests exhibit less sensitivity but maintain robustness in the face of outliers or deviations from normality. Sample size considerations also play a role, with parametric tests often requiring larger samples for comparable power. In contrast, nonparametric tests can be practical with smaller sample sizes, particularly when assumptions are violated. Considering power