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# For rescaled pain, examine the data, testing the normality of the distribution

INSTRUCTIONS TO CANDIDATES

1.[10] Both questions this week use the data set

Week04 Homework_2022.csv. In this study, Virtom, Soule & Kryjom (2022) studied adults over 18 years of age who live with arthritis and reside in Florida. They investigated the distribution of and associations among pain and self-reported weekly minutes in exercise. The researchers surveyed 180 adults; higher scores = higher levels of the named trait. Measures have been rescaled from their original metric, so don't worry about any odd looking values.

(a) For rescaled pain, examine the data, testing the normality of the distribution. Be sure to include measures of central tendency, measures of distribution, and measures/tests of normality. Say a word or two about what each of these mean in relation to the data set (i.e. is the data set normal?). What do statistical tests of normality tell you? Do the results conform to what you observe when you create a histogram, including the normal curve line? (b) What score corresponds to the 72nd percentile of the rescaled pain distribution? What does this percentile value mean, concretely? (e) At least one person has a pain score of 522. Based on YOUR OPERATIONAL DEFINITION OF "EXCEPTIONALITY", is this an "exceptionally high" or "exceptionally low" pain? Justify your response.

(d) Convert pain into a z-score distribution. Which rescaled pain score corresponds to a z-score of approximately -4.745358625? What does the value of this z-score tell you about this person's place in the distribution?

2./10] Turning to the weekly minutes in exercise variable, a. Recall that we have review in R various functions and packages that offer graphical tools for examining non-normality,

including histograms with superimposed normal curves, Q-Q plots and box-whisker plots. Obtain these and affirm the presence or absence of normality USING THESE GRAPHICAL TOOLS ONLY. Justify your response.

b. Now, add in quantitative tools for assessing normality. Looking at the weekly minutes in exercise variable, obtain quantitative estimates of non-normality, including coefficients (skewness and kurtosis), and statistical tests of normality. Also obtain the K-S and S-W tests. Do these affirm your visual conclusions in a. above? Explain your answer.

Rubric

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