Three questions

1. 1hink of a variable from your everyday life that could be analyzed using a Chi-square goodness-of-t test. Answer the questions below using your chosen variable. (3 points) a. Discuss why the variable you have chosen would be appropriate to use for a Chi- square goodness-of-t analysis. (Hint. 111ink about how many variables you have, how many possible categories it has, and the measurement scale of that variable.) (2 points) Describe what the alternative hypothesis associated with the variable that you have chosen would be. You can state it in words or in statistical notation (Hint. Remember how the Chi~square is calculated - obsenred to expected frequencies.) (1 point) 2. Females (and increasingly males) are bombarded with 'idealized' images in the media and there is concern about how these images affect their perceptions of themselves. Daniels [2012) explored these perceptions in a study by showing young female participants (N: 200) images of successful female athktes (e.g., Anna Koumikova, Serena Williams) playing their respective sports (performance media images}. They then had the participants write down their thoughts about the athhtesm coded their responses for whether or not they would self-objectivity (i.e., comment on their own appearance/attractiveness in their description about the athletes). Thus, the outcome variable was whether the female participants made self-objectifying comments (yes) or not. Use the description of this research study to answer the questions below. (8 points) a. If the researcher does not know the eerrt to which females in the general population self-objectify after seeing images of idealized female athletes in the media, what should their expected frequencies be? Explain your answer in the context of the study. (Hint. You can state the expected frequencies as a raw number or as a proportion. In your explanation, think about how unsystematic variability is represented in dri- square andyses.) {2 points) b. The researcher's observed frequencies are below in the table. Use this information to calculate a goodnessrof-fit chi-square test statistic. Show your work. (2 points) Self-objectify Do not Self-objectify c. At an a-Ievel = .05, the researcher's xzmmmm = 3.84, and the pvalue associated with the researcher' s x2 test statistic = .000. Draw a Chi-square distribution and label the various parts. Include the x2 test statistic that you calculated above on the distribution. (Note. The Chi-square distribution with off: 1 loolrs almost identical to the distribution with df = 2 from the lecture.) {2 points). d. Now, imagine that the researcher decided to recruit 200 more females to participate in the study. These participants saw the female athletes in bathing suits (sexualized media images), rather than playing their respective sports. ('Ihis is actually what they did in the study!) Describe the type of analysis that the researcher should conduct and why, in the context of their study. (Hint. Describe the how many variables there are and their level of measurement.) (2 points} 3. Throughout the quarter we have discussed how every statistical equation is some form of systematic variability to unsystematic variability. Choose one of the equations that we have covered throughout the course, and describe how these two types of variability are represented in the equation. (Hint. Do not just give the equation but think about the statistics that are in the numerator and denominator.) (3 points)Correlation EZx * Zy Tx,y = n- 1 (X - M) 2 = 1-rz S ST (n - 2) Coefficient of determination = df = n -2 Regression Straight line equation and parameters P= a+b * X b = Txy * SX a = My - b *Mx Partitioning variance and the F-test SSTotal = [(x - MY) SS Residuals = > (P - 1)2 dfResidual = n - 2 [ (P - MY) d fRegression = 1 SSRegression or SS Regression = SSTotal - SSResiduals SS Regression MS Regression MSRegression = F = d fRegression MSResidual SS Residual R2 = SS Regression MSResidual dfResidual SSTotal F statistic to f statistic (? = F Chi-square Goodness-of-fit x2 = > Vo -fe)2 df = C-1 feIndependent-samples f-test (M] - M2) - (M1 - H2) df = n-2 S(M.-M2) $12 Sp S(M,-M2)= 721 S(MI-M.)= Sp 721 -+ nz nz Sp 2 = (n - 1)s, + (n2 - 1)$2 2 (n] - 1) + (n2 - 1) Effect size (Cohen's d) 95% Confidence Intervals d = M1 - Mz Lower bound: Mary - (critical * S(M, - M2)) Upper bound: Mairy + (tcritical * S(M, - M;)) Repeated-measures f-test XD = Xpost - Xare df = n-1 Mp = EXD E (XD - MD )2 n SD = (n - 1) MD - HD t= SEND = SEM Effect size (Cohen's d) 95% Confidence Intervals d = MD Lower bound: Mp - (teritical * SEMD) Upper bound: Mo + (tcritical * SEMp) Variance to SS SS = (n - 1)s? = $5 One-way between-subjects ANOVA GM - 2M k SSTotal = E(x - GM) dfrown = N - 1 SSBme = En,(M. - GM)? df Beren = k - 1 SS Washin = E(X X - MA )2 df mimi = N - k or E(SS) SSTotal = SSBetween + SSwin df foul = df Between + dfirithin MS Bendin SSaretween MS within SSwithin dfBetween df within MS Between F= MSwithin Two-way between-subjects ANOVA GM = EM SSTatl = E(x - GM) df foul = N - 1 SSheteen = En,(M. - GM)? df Between = k - 1 SS within = E(X K - M,)2 edf winkie = N - k or E(SS) SS Tatar = SSgaman + SSwithin dfrom = df Beoven + dfwithin MS within SSwithin df withinMain effect A SSA SSA = En (M. - GM)? MS.= dj A MSA do=k - 1 FA = MSwithin Main effect B SSP SSs = En (M. - GM) MSB = MSa dfo= k - 1 FB MSwithin Interaction A * B SSA-D dfan MSALE df * = di * dia FA-E MSwithin Effect Size (eta-squared) Tukey's HSD Test SSbetween/effect MSwithin HSD = q SStotal