invest_3ed.pdf

# C what about the probability of at least one type i

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(c) What about the probability of at least one Type I error among these 21 comparisons will that be larger or smaller than 0.05? Explain.

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Chance/Rossman, 2015 ISCAM III Investigation 5.1 327 Technology Detour Chi-Square Tests In R x If you have the counts for the two-way table, can pass the table using the matrix command: > spocktable = matrix(c(119, 235, 197, 533, 118, 287, 77, 149, 30, 81, 149, 403, 86, 511), ncol=7) > chisq.test(spocktable) x For the raw data (e.g., in spock ), create and pass in the frequency table, e.g., > chisq.test(table(spock)) In Minitab x If the two way table has been entered into I columns, choose Stat > Tables > Chi- Square Test for association . Use the pull down menu to select Summarized data… and the specify the columns containing the observed counts. x Click OK . x If the raw data for each categorical variable are contained in two different columns, choose Stat > Tables > Cross Tabulation and Chi-Square . Leave “Raw data” selected in the drop -down menu. x Specify the two variables rows and columns . Press the Chi-Square button and select “Chi - Square Analysis” to be displayed. Click OK twice. When checking the Chi-square test box, you can also ask Minitab to report the expected counts, and the cell contributions (the terms being summed together to determine the chi- square statistic). In Analyzing Two-way Tables applet x Paste either the raw data (press Use Data ) or the two-way table (press Use Table ) into the Sample data box, using one word category names. x Check the Show X 2 Output box. The applet reports the observed & 2 value, df, and cell contributions. (You can expand this window by dragging out the lower right corner. Check the Show table box to see the observed counts.)
Chance/Rossman, 2015 ISCAM III Investigation 5.2 328 Investigation 5.2: Nightlights and Near-sightedness (cont.) Recall from Investigation 3.2 we examined a simplified version of the study published by Quinn, Shin, Maguire and Stone (1999) that examined the relationship between the type of lighting children were exposed to and subsequent eye refraction. Now we are able to look at 3 categories for each variable. Below is the two way table and segmented bar graph from the study: Dark Night light Room light Total Far-sighted 40 39 12 91 Normal 114 115 22 251 Near-sighted 18 78 41 137 Total 172 232 75 479 (a) What proportion of subjects in this study were classified as being far-sighted? As having normal vision? As being near-sighted? [ Hint : Looking at the subjects all together now.] Far-sighted: Normal: Near-sighted: (b) If the children’s current eye conditions were not related to the level of lighting they were exposed to, what proportion of children in the darkness condition would be far-sighted? Have normal vision? Be near-sighted? (c) What would the proportional breakdown of eye conditions look like in the night-light group and in the room-light group if there was no association between eye condition and lighting level?

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