GEO Assignment 5

#1-a. Values f 0 f e f 0 − f e ( f 0 − f e )^2 ( f 0 − f e )^2 / f e Heads 0.6 0.5 0.1 0.01 0.02 Tails 0.4 0.5 -0.1 0.01 0.02 ∑ = 0 ∑ = 0.04 #1-b. df = 2 - 1 =1 in this case. #1-c. The null hypothesis for this example is that the coin is fair. An alternative hypothesis is that the coin is not fair and it is biased. #1-d. Since df = 1 and ɑ is 0.05, we can how that the Critical Value is 3.84 using the Chi- Square Critical Value table. #1-e. The chi-square is 0.04, and the Critical Value is 3.84. 0.04 < 3.84, and therefore, since the critical value is larger than the chi-square, you can not reject the null hypothesis, concluding the coin is fair.

#2-a. image 1. The image is showing the table for the result of 20 coin flips. #2-b. image 2. This image is showing the bar graph and the frequencies table for the 20 coin flip results.

#3-a. Party Affiliation Likes Oranges D N R Marginal Total No 6.5 13.43 6.07 26 Yes 8.5 17.57 7.93 34 Marginal Totals 15 31 14 60 #3-b. Valeus f 0 f e f 0 − f e ( f 0 − f e )^2 ( f 0 − f e )^2 / f e 1 6.5 10 -3.5 12.25 1.23 2 13.43 10 3.43 11.76 1.18 3 6.07 10 -3.93 15.44 1.54 4 8.5 10 -1.5 2.25 0.23 5 17.57 10 7.57 57.30 5.73 6 7.93 10 -2.07 4.28 0.43 ∑ = 0 ∑ = 10.34 #3-c. The null hypothesis for this case is that political affiliation has no association with the likings of oranges. An alternative hypothesis is that political affiliation has some association with the likings of oranges. #3-d. df = (3-1)(2-1) = 2. Therefore the degree of freedom for this example is 2. #3-e. With the df = 2 and ɑ of 0.05, the Critical Value is 7.81. Since ChiSquare is 10.34, the Critical Value is smaller than the ChiSquare, we can reject the null hypothesis and conclude that political affiliation and liking of orange have an association. #3-f. In this case, using Cramer’s V is better. Phi coefficient is useful for the table of 2x2. The table given in this example is 3x2, making Cramer’s V a better way to calculate effect size. #3-g. Cramer’s V = √ x 2 n ( df ) = √ 10.34 /( 60 × 2 ) = 0.29. Since 0.2 < 0.29 =< 0.6, we can know that the effect size is medium and the political affiliation and liking has linkage. #3-h. We use the Bonferroni method because it can be used in any type of statistical test and it is highly flexible and simple to compute. (ɑ for Bonferroni method) = ɑ / #. Therefore, in this example, ɑ = 0.05 and # = 6, and (ɑ for Bonferroni method) is 0.05 / 6 = 0.008.

#4-d. If the example is biased, the results will be biased. Even though it did not intend to be biased, since the examples contain only a limited number of samples, they oftentimes fail to reflect reality. Although the method used to get the result may be valid, we should be cautious in believing the result. In the case of the relationship between political affiliation impacting orange preferences, it can happen when the parties fight over a topic related to the orange. Still, it is significantly less likely to happen. Before accepting the result that there may be an impact, we should search for the possible cause behind it and verify whether this is the reflection of reality or the data being biased.