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Percentile Worksheet document sample
Test Selection Selecting a statistical test for the analysis of research data is a key step in the investigative process. In fact, experienced researchers are known to weigh that decision very carefully beforecollecting their data. Such prior planning assures that the statistical test under consideration is both appropriate for the data and capable of providing information that meets the goals of the study. Unfortunately, the sequential topic-by-topic coverage in an academic course provides limited opportunities to practice test selection. When confronted with the practice problems at the end of the t-test chapter, you knew to use a t test, and so forth for other problems in other chapters. The present workbook provides opportunities to practice test selection outside of such structure. As you encounter the research scenarios on the following worksheets, your task is to select and run the analysis that best meets the needs of the researcher. The solutions appear off to the right of each worksheet in an area initially out of view (column O and beyond). Do your analyses on the "my work" worksheets, then go back to the problem worksheets to compare your results to the solutions. he investigative very carefully est under mation that meets the provides limited roblems at the end of in other chapters. de of such structure. task is to select and appear off to the right o your analyses on are your results to the Data for Part I These are the data for the first group of problems. Excel will instantly forward any changes you enter on this worksheet to the data and solutions that follow. But for your first run through the workbook, it's fine to use the original data. Select the statistical analysis that is appropriate for the data and the research question, click a "my work" worksheet tab, and do the analysis. When done, go back to the problem worksheet and scroll right to see the solution. No peeking! Try the problems first on your own before looking at the solutions. 8 2 4 1 7 3 Any changes to the Part I 9 6 data must be made here, 13 10 NOT on the problem 14 16 worksheets. 19 18 17 15 20 5 12 11 d any changes you run through the is appropriate for the analysis. When done, eking! Try the the Part I de here, After inspecting complaints filed with the police, 210 dogs of ten different breeds were identified as excessive barkers. As part of a court-ordered attempt to address the problem, all the dogs were fitte with a special collar that administers an unpleasant shock each time it detects a vocalization above a specific decibel level. Was the success rate of the device relatively uniform across the 10 breeds (retain Ho), or did some breeds respond better to the collar device than others? First do your analysis. on the "my work 1-1" worksheet, then return here to compare your results to the solution. Barking Breed Stopped Continued A 8 2 B 4 1 Solution C 7 3 (Columns O to U) D 9 6 E 13 10 F 14 16 G 19 18 H 17 15 I 20 5 J 12 11 reeds were identified Solution for the chi-square test of i m, all the dogs were fitted degrees of vocalization above a freedom oss the 10 breeds c2(9)= First do your analysis. Barking Breed Stopped A 8 B 4 C 7 D 9 E 13 F 14 G 19 H 17 I 20 J 12 Totals 123 r the chi-square test of independence. See workbook 10-2. 11.486 p= 0.244 Barking Continued Totals Expected Frequencies 2 10 5.86 4.14 1 5 2.93 2.07 3 10 5.86 4.14 6 15 8.79 6.21 10 23 13.47 9.53 16 30 17.57 12.43 18 37 21.67 15.33 15 32 18.74 13.26 5 25 14.64 10.36 11 23 13.47 9.53 87 210 This worksheet is blank except for data set 1. Use it to carry out the statistical analyses for problem 1-1. Then compare your answers to the solution on the problem 1-1 worksheet. Data: 8 2 4 1 7 3 9 6 13 10 14 16 19 18 17 15 20 5 12 11 analyses for problem 1-1. The data below represent homes sold in 2005 by 20 agents of Blank & Best Real Estate, Inc. For the past five years, mean home sales for these 20 agents has been a fairly steady 6.75. Are the data for 2005 consistent with the historical mean sales performance of 6.75 (retain Ho), or was there a significant change in sales performance in 2005? Click the "my work 1 tab. Home Sales for 20 Agents 8 2 4 1 Solution 7 3 (columns O to S) 9 6 13 10 14 16 19 18 17 15 20 5 12 11 Solution for the single-sample t tes st Real Estate, Inc. airly steady 6.75. t= e of 6.75 (retain df = k the "my work 1-2" p= Home Sales for 20 Agents 8 2 4 1 7 3 9 6 13 10 14 16 19 18 17 15 20 5 12 11 r the single-sample t test. See workbook 6-2. 2.835 19 0.011 mean = 10.5 Use this sheet to carry out the statistical analyses for problem 1-2. Then compare your answers to the solution on the problem 1-2 worksheet. Data: 8 2 4 1 7 3 9 6 13 10 14 16 19 18 17 15 20 5 12 11 A researcher randomly divided 20 seedlings into two groups. One group was maintained using fertilizer A, and the other was maintained using fertilizer B. At maturity the researcher counted the number of blossoms on each plant. Was blossom count basically the same for the two fertilizers (retain Ho), or was there a difference in mean blossom count between the two groups of mature plants? Click the "my work 1-3" tab. Fertilizer A Fertilizer B 8 2 4 1 7 3 Solution 9 6 (Columns O to Y) 13 10 14 16 19 18 17 15 20 5 12 11 s maintained Solution for the independent-group y the researcher ly the same for nt between the Fertilizer A 8 4 7 9 13 14 19 17 20 12 Means: 12.3 r the independent-groups t test. Solution for the Mann-Whitney U. Note: The ranks of the original data contain no ties. t = 1.394 U = 32 z = 1.361 But, because of the way df = 18 With n 1 = n 2 = 10, U crit (a=.05) Excel resolves tied ranks, p = 0.180 equals 23 or 77. changes you make to the data set 1 worksheet that result in tied ranks will Fertilizer B Fertilizer A Ranks Fertilizer B Ranks cause the U value reported 2 8 8 2 2 here to be slightly different 1 4 4 1 1 from the output of other 3 7 7 3 3 statistical software. For the 6 9 9 6 6 more precise answer, type 10 13 13 10 10 over the "Ranks" values as 16 14 14 16 16 necessary to resolve the 18 19 19 18 18 ties. Review the "rank and percentile" worksheet in 15 17 17 15 15 workbook 1-2 for the 5 20 20 5 5 instructions on resolving 11 12 12 11 11 ties. 8.7 R1= 123 R2= 87 nks of the Not combined ranks contain no ties. intended 8 8 of the way for 4 4 s tied ranks, viewing 7 7 make to the 9 9 rksheet that 13 13 ranks will value reported 14 14 ghtly different 19 19 ut of other 17 17 tware. For the 20 20 answer, type 12 12 " values as 2 2 resolve the 1 1 the "rank and 3 3 orksheet in 6 6 n resolving 10 10 16 16 18 18 15 15 5 5 11 11 Use this worksheet to carry out the statistical analyses for problem 1-3. Then compare your answers to the solution on the problem 1-3 worksheet. Data: 8 2 4 1 7 3 9 6 13 10 14 16 19 18 17 15 20 5 12 11 Students took a test that assessed their knowledge of current events followed by another test that assessed reading comprehension. The two tests had the same number of questions. The numbers below represent the number of correct answers on each test. Do the data show a significant relationship between reading comprehension scores and knowledge of current events? If so, assemble the information you need to predict the variable "reading comprehension" from the variable "knowledge of current events." Click the "my work 1-4" tab. Current Reading Students: Events Comprehension Jim 8 2 Steve 4 1 Solution Matt 7 3 (Columns P to AA) Paul 9 6 Dave 13 10 Josh 14 16 Larry 19 18 Jerry 17 15 Ethan 20 5 Jacob 12 11 Solutions for the correlation and re ollowed by another test that r of questions. The numbers r XY = ata show a significant p= current events? If so, Here is the prehension" from the variable regression equation for Y on X. Students: Jim Steve Matt Paul Dave Josh Larry Jerry Ethan Jacob Solutions for the correlation and regression analyses (See workbooks 3-3, 3-6, and 6-4.) 0.700 Testing the r value for significance yields: 0.024 t = 2.775 p = 0.024 Here is the regression Y' = ay + by X To predict reading comprehension score equation for Y'= -1.29 + 0.812 X (Y) from knowledge of current events (X), substitute a current events score for Current Reading X in the regression equation -- or use Events (X) Comp. (Y) the FORECAST paste function. 8 2 4 1 7 3 9 6 r 2= 0.49 13 10 The r2 statistic reports the proportion of 14 16 the variability in the "reading 19 18 comprehension" variable Y that is 17 15 predictable from the "current events" 20 5 variable X. See workbook 3-6. 12 11 s 3-3, 3-6, and 6-4.) prehension score t events score for Use this worksheet to carry out the statistical analyses for problem 1-4. Then compare your answers to the solution on the problem 1-4 worksheet. Current Reading Data: Events Comprehension 8 2 4 1 7 3 9 6 13 10 14 16 19 18 17 15 20 5 12 11 Ten obese volunteers agreed to take part in a diet study for six months in which their food intake and exercise would be precisely managed. One expectation was that after a period of rapid weight loss in the first three months, pounds would come off more slowly during the second three months. Others disagreed, believing that weight loss need not slow during the second three months if food intake and exercise are precisely controlled. Which position do the data support? The data below are pounds lost by the 10 volunteers in each three-month period of the diet program. Click the "my work 1-5" tab. Jan.-Mar. April-June Jim 8 2 Steve 4 1 Solution Matt 7 3 (columns O to AG) Paul 9 6 Dave 13 10 Josh 14 16 Larry 19 18 Jerry 17 15 Ethan 20 5 Jacob 12 11 Solution of the paired-samples t te ch their food intake and (See workbook 7-3.) od of rapid weight loss nd three months. three months if food t= 2.515 port? The data below df = 9 rogram. Click the "my p= 0.033 Month 1 Jim 8 Steve 4 Matt 7 Paul 9 Dave 13 Josh 14 Larry 19 Jerry 17 Ethan 20 Jacob 12 MEANS: 12.3 the paired-samples t test. Solution of the Wilcoxon and Sign Tests (#DIV/0! error messages in cells W3 an following changes you make to "data set 1" indicate that an "illegal" tie is present in a row of data.) The Wilcoxon T is the smaller of these two values: 3 or To achieve statistical significance (n =10 pairs) T must be 8 (a=.05) or 3 (a=.01). The split is 1 negative and 9 positive values, so the sign-test output for these data is a p value = 0.021 rank of absolute value Month 2 differences Month 1 Month 2 differences of differences abs. value 2 6 Jim 8 2 6 6 9 1 3 Steve 4 1 3 3 5 3 4 Matt 7 3 4 4 8 6 3 Paul 9 6 3 3 5 10 3 Dave 13 10 3 3 5 16 -2 Josh 14 16 -2 2 3 18 1 Larry 19 18 1 1 1 15 2 Jerry 17 15 2 2 3 5 15 Ethan 20 5 15 15 10 11 1 Jacob 12 11 1 1 1 8.7 sums: 50 messages in cells W3 and Y3 Illustration based on the original "data set 1" values present in a row of data.) Because of the way Excel resolves tied 47 Excel's ranks, if some of the signed ranks are 05) or 3 (a=.01). ties, the value of T reported here may absolute value rank of differ slightly from the solution of other of differences absolute value positive values, so statistical software. For the more precise 6 9 answer, re-rank the "absolute value of 3 5 differences" (col. W) and enter the new signed ranks in column X (rank of absolute 4 8 ranks value). Try it yourself first, then see the 3 5 9 illustration (using the original data) in 3 5 columns AD to AG. 5 The "Rank and Percentile" worksheet in 2 3 8 workbook 1-2 explains the precise 1 1 5 method for resolving tied ranks. 2 3 5 15 10 -3 1 1 1 3 T now equals 3.5 rather than 3.0, 10 and p .05, but not .01. 1 44 n the original "data set 1" values Precise rank of signed absolute value ranks 9 9 6 5 8 8 6 5 6 5 3.5 -3.5 1.5 1 3.5 3 10 10 1.5 1 ather than 3.0, Use this worksheet to carry out the statistical analyses for problem 1-5. Then compare your answers to the solution on the problem 1-5 worksheet. Data: 8 2 4 1 7 3 9 6 13 10 14 16 19 18 17 15 20 5 12 11 Data for Part II In Part II, the data array expands from 2 columns to 4. As for Part I, select and run the correct statistical analysis, then scroll right to column O and beyond for the solution. To practice computational skills with new data, enter one or more new values below. (Make all changes to data here, not on the problem worksheets.) 53 44 40 52 54 59 61 63 42 47 55 59 Any changes to the Part II 47 41 48 57 data must be made here, 49 50 53 49 NOT on the problem 47 42 56 55 worksheets. 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 ct and run the e solution. To changes to the Part II must be made here, on the problem Ten fourth-grade children were evaluated by a team of psychologists with respect to four areas of development: reading skill, math skill, gross-motor development, and fine-motor development. Is there any association among these measures? For example, do students who read well also tend to do well in math? Determine the pattern of association among these behavioral measures, noting any relationships that are significant. Reading Math Gross Motor Fine Motor Jim 53 44 40 52 Steve 54 59 61 63 Solution Matt 42 47 55 59 (Columns O to S) Paul 47 41 48 57 Dave 49 50 53 49 Josh 47 42 56 55 Larry 57 50 43 53 Jerry 40 39 55 54 Ethan 42 39 45 40 Jacob 46 38 52 54 respect to four areas motor development. nts who read well also se behavioral Solution (Columns O to S) Solution for the intercorrelation matrix of the four variables. An example of using the correlation tool to generate an inter-correlation matrix is in workbook 7-1. Reading Math Gross Motor Fine Motor Reading 1.000 0.660 -0.269 0.253 Math 1.000 0.332 0.480 Gross Motor 1.000 0.573 Fine Motor 1.000 With n -2 = 8 degrees of freedom, r crit = 0.6319. To be significant, the absolute value of an r obt (above, in red) must equal or exceed the r crit value of .6319. Use this worksheet to carry out the statistical analyses for problem 2-1. Then compare your answers to the solution on the problem 2-1 worksheet. Data: 53 44 40 52 54 59 61 63 42 47 55 59 47 41 48 57 49 50 53 49 47 42 56 55 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 Forty male participants were randomly divided into 4 groups of 10 each. Each group had the same jigsaw puzzle to assemble, but under four different conditions. Group 1 participants worked on the puzzle while carrying on a hands-free cell-phone conversation, Group 2 worked while instant messaging on a hand-held device, Group 3 worked while listening to a talk-radio sports show, and Group 4 worked in silence. No participants completed the puzzle in the time allowed. The dependent variable is the number of puzzle pieces that the participant successfully joined to others. Do the data support the hypothesis that processing verbal information slows completion of a visual task? Group 1 Group 2 Group 3 Group 4 53 44 40 52 54 59 61 63 Solution 42 47 55 59 (Columns O to AB) 47 41 48 57 49 50 53 49 47 42 56 55 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 Each group had the oup 1 participants worked oup 2 worked while -radio sports zle in the time allowed. nt successfully joined to ation slows completion of Solution (Columns O to AB) Solution for the one-way ANOVA for independent groups. Group 1 Group 2 Group 3 Group 4 53 44 40 52 Using ESC file 8-3 as a guide, 54 59 61 63 the Tukey HSD was determined 42 47 55 59 to equal 7.57 47 41 48 57 49 50 53 49 So, to meet the criterion for 47 42 56 55 significance of an unplanned 57 50 43 53 comparison, means must be 40 39 55 54 7.57 units apart. 42 39 45 40 46 38 52 54 See chart Means: 47.7 44.9 50.8 53.6 Source of Variation SS df MS F F crit p value Between Groups 426.5 3 142.17 3.62 2.87 0.022 Within Groups (error) 1413 36 39.25 Total 1839.5 39 56 SC file 8-3 as a guide, y HSD was determined 54 Mean Pieces Assembled 52 50 eet the criterion for nce of an unplanned 48 son, means must be 46 units apart. 44 See chart 42 40 1 2 3 4 Group Use this worksheet to carry out the statistical analyses for problem 2-2. Then compare your answers to the solution on the problem 2-2 worksheet. Data: 53 44 40 52 54 59 61 63 42 47 55 59 47 41 48 57 49 50 53 49 47 42 56 55 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 A professor gave his 10 graduate students four examinations over the course of the semester, one on each quarter of the course content. Was overall student performance about the same on the four examinations, or did grades differ among the four tests? Students Exam 1 Exam 2 Exam 3 Exam 4 Jim 53 44 40 52 Steve 54 59 61 63 Matt 42 47 55 59 Solution Paul 47 41 48 57 (Columns O to AD) Dave 49 50 53 49 Josh 47 42 56 55 Larry 57 50 43 53 Jerry 40 39 55 54 Ethan 42 39 45 40 Jacob 46 38 52 54 urse of the semester, one about the same on the Solution (Columns O to AD) Solution for one-way repeated-measures ANOVA. (See workbook 8-2.) Students Exam 1 Exam 2 Exam 3 Exam 4 Row Means Jim 53 44 40 52 47.25 Steve 54 59 61 63 59.25 Matt 42 47 55 59 50.75 Paul 47 41 48 57 48.25 Dave 49 50 53 49 50.25 Josh 47 42 56 55 50.00 Larry 57 50 43 53 50.75 Jerry 40 39 55 54 47.00 Ethan 42 39 45 40 41.50 Jacob 46 38 52 54 47.50 Col. Means: 47.7 44.9 50.8 53.6 Source SS df MS F p value Between Subjects 717.00 9 79.67 3.09 0.011 Examinations 426.50 3 142.17 5.52 0.004 Error 696.00 27 25.78 Total 1839.50 39 Using ESC file 8-3 as a guide, 56 the Tukey HSD was determined 54 to equal 3.78 . 52 Exam Score 50 So, to meet the criterion for 48 significance of an unplanned comparison, means must be 46 must be 3.78 units apart. 44 42 See chart 40 1 2 3 4 Exam Use this worksheet to carry out the statistical analyses for problem 2-3. Then compare your answers to the solution on the problem 2-3 worksheet. Data: 53 44 40 52 54 59 61 63 42 47 55 59 47 41 48 57 49 50 53 49 47 42 56 55 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 SONY Corp. wanted to determine the age demographic of consumers who purchased plasma TV monitors in 2004. An inspection of 40 randomly selected post-purchase questionnaires (a form that consumers complete and return to the company to activate their warranty) revealed the 40 ages below. Based on these data, estimate the average age of consumers who purchased plasma TV monitors. Ages of 40 Buyers of Plasma TV Monitors 53 44 40 52 54 59 61 63 Solution 42 47 55 59 (Columns O to T) 47 41 48 57 49 50 53 49 47 42 56 55 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 o purchased plasma TV questionnaires (a form anty) revealed the 40 rs who purchased Solution (Columns O to T) Solution for an interval estimate of the mean age of the population of Plasma TV purchasers. Lower limit = 47.06 Upper limit = 51.44 Therefore, we are 95% confident that the mean age of plasma TV buyers is between 47.06 and 51.44 The topic of confidence intervals is covered in workbook 6-3. Use this worksheet to carry out the statistical analyses for problem 2-4. Then compare your answers to the solution on the problem 2-4 worksheet. Data: 53 44 40 52 54 59 61 63 42 47 55 59 47 41 48 57 49 50 53 49 47 42 56 55 57 50 43 53 40 39 55 54 42 39 45 40 46 38 52 54 Participants suffering from osteoarthritis of the hands were randomly assigned to one of four treatment conditions with an experimental drug (no drug, placebo, low dose, or high dose). The drug therapy was paired either with a cold compress or a hot compress. The eight treatment combinations (5 per cell) are evident from inspection of the table below. The data represent minutes (post treatment) needed to successfully master a finger flexibility task. What do the data tell you about the effectiveness of the two therapies working alone or in combination? no drug placebo low dose high dose cold compress 53 44 40 52 cold compress 54 59 61 63 Solution cold compress 42 47 55 59 (Columns O to Z) cold compress 47 41 48 57 cold compress 49 50 53 49 hot compress 47 42 56 55 hot compress 57 50 43 53 hot compress 40 39 55 54 hot compress 42 39 45 40 hot compress 46 38 52 54 Solution for the two-way d to one of four or high dose). The drug treatment data represent minutes o the data tell you A1 A2 Col. Means: Solution (Columns O to Z) Source Compress Drug Dose Interaction Error Total olution for the two-way ANOVA. (See workbooks 9-2 and 9-3.) 60 Cell Means Row 55 B1 B2 B3 B4 Means: 50 Flexibility Scores 49.00 48.20 51.40 56.00 51.15 46.40 41.60 50.20 51.20 47.35 45 47.70 44.90 50.80 53.60 40 Analysis of Variance Summary Table 35 SS df MS F p value 30 Cold Compress 144.40 1 144.40 3.77 0.061 25 426.50 3 142.17 3.71 0.021 Hot Compress 42.60 3 14.20 0.37 0.775 20 1226.00 32 38.31 No Drug Plscebo 1839.5 39 See chart Cold Compress Hot Compress Plscebo Low Dose High Dose Drug Treatment Use this worksheet to carry out the statistical analyses for problem 2-5. Then compare your answers to the solution on the problem 2-5worksheet. no drug placebo low dose high dose cold compress 53 44 40 52 cold compress 54 59 61 63 cold compress 42 47 55 59 cold compress 47 41 48 57 cold compress 49 50 53 49 hot compress 47 42 56 55 hot compress 57 50 43 53 hot compress 40 39 55 54 hot compress 42 39 45 40 hot compress 46 38 52 54 end of workbook