Creativity Scores in two Motivation Groups Intrinsic and Extrinsic | ST 511, Study notes of Statistics

Download Creativity Scores in two Motivation Groups Intrinsic and Extrinsic | ST 511 and more Study notes Statistics in PDF only on Docsity! Display 1.1 p. 2 Creativity scores in two motivation groups, and their summary statistics 5.0 5.4 6.1 10.9 11.8 12.0 12.3 14.8 15.0 16.8 17.2 17.2 17.4 17.5 18.5 18.7 18.7 19.2 19.5 20.7 21.2 22.1 24.0 12.0 12.0 12.9 13.6 16.6 17.2 17.5 18.2 19.1 19.3 19.8 20.3 20.5 20.6 21.3 21.6 22.1 22.2 22.6 23.1 24.0 24.3 26.7 29.7 ExtrinsicIntrinsic Motivation Group Sample Size: Average: Sample Standard Deviation: 24 19.88 4.44 23 15.74 5.25 Display 1.2 p. 3 Questionnaires given creative writers, to rank intrinsic and extrinsic reasons for writing INSTRUCTIONS: Please rank the following list of reasons for writing, in order of personal importance to you (1 = highest, 7 = lowest). You get a lot of pleasure out of reading something good that you have written. You enjoy the opportunity for self-expression. You achieve new insights through your writing. You derive satisfaction from expressing yourself clearly and eloquently. You feel relaxed when writing. You like to play with words. You enjoy becoming involved with ideas, characters, events, and images in your writing. You realize that, with the introduction of dozens of magazines every year, the market for free-lance writing is constantly expanding. You want your writing teachers to be favorably impressed with your writing talent. You have heard of cases where one bestselling novel or collection of poems has made the author financially secure. You enjoy public recognition of your work. You know that many of the best jobs available require good writing skills. You know that writing ability is one of the major criteria for acceptance into graduate school. Your teachers and parents have encouraged you to go into writing. INSTRUCTIONS: Please rank the following list of reasons for writing, in order of personal importance to you (1 = highest, 7 = lowest). List of extrinsic reasons for writing List of intrinsic reasons for writing Display 1.5 p. 9 Statistical inferences permitted by study designs ALLOCATION OF UNITS TO GROUPS S E L E C T IO N O F U N IT S A t R an do m N ot a t R an do m By Randomization Not by Randomization A random sample is selected from one population; units are then randomly assigned to different treatment groups. Random samples are selected from existing distinct populations. Collections of A group of study units is found; units are then randomly assigned to treatment groups. Causal inferences can be drawn Inferences to the populations can be drawn available units from distinct groups are examined. Display 1.6 p. 10 Illustration of a randomized experiment with two treatment groups Subjects Recruited Random Allocation to Group Apply Treatment 1 Apply Treatment 2 Data n = 23 n = 24 creativity Display 1.7 p. 12 Creating a different randomization for the creativity study 12.0 Intrinsic(2) 1 12.0 Intrinsic 2 12.9 Intrinsic 1 13.6 Intrinsic 2 16.6 Intrinsic 2 17.2 Intrinsic 1 17.5 Intrinsic 2 18.2 Intrinsic 2 19.1 Intrinsic 1 19.3 Intrinsic 2 19.8 Intrinsic 2 20.3 Intrinsic 2 20.5 Intrinsic 1 20.6 Intrinsic 2 21.3 Intrinsic 1 21.6 Intrinsic 2 22.1 Intrinsic 1 22.2 Intrinsic 2 22.6 Intrinsic 1 23.1 Intrinsic 1 24.0 Intrinsic 1 24.3 Intrinsic 1 26.7 Intrinsic 1 29.7 Intrinsic 1 Creativity Score Actual Grouping Another Average Intrinsic (2) Extrinsic (1) Averages from Another Grouping Group 1 Group 2 Group Averages from Actual Grouping Group Difference 19.88 15.74 18.87 16.80 4.14 2.07 Grouping 5.0 Extrinsic(1) 2 5.4 Extrinsic 2 6.1 Extrinsic 1 10.9 Extrinsic 2 11.8 Extrinsic 1 12.0 Extrinsic 1 12.3 Extrinsic 1 14.8 Extrinsic 2 15.0 Extrinsic 2 16.8 Extrinsic 2 17.2 Extrinsic 2 17.2 Extrinsic 1 17.4 Extrinsic 2 17.5 Extrinsic 2 18.5 Extrinsic 2 18.7 Extrinsic 1 18.7 Extrinsic 1 19.2 Extrinsic 1 19.5 Extrinsic 1 20.7 Extrinsic 1 21.2 Extrinsic 1 22.1 Extrinsic 2 24.0 Extrinsic 2 Creativity Score Actual Grouping Another Grouping Average Difference Display 1.10 p. 17 Back-to-back stem and leaf diagrams for the creativity study data Creativity Scores INTRINSIC GROUP n = 24 EXTRINSIC GROUP n = 23 Average = 15.74 SD = 5.25 Average = 19.88 SD = 4.44 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10 11 009 6 6 25 2 138 356 36 126 1 03 7 7 5 6 7 8 9 40 1 9 8 30 8 0 8 5422 775 52 7 2 1 0 Legend: 29 7 represents 29.7 The stem of 29.7 The leaf of 29.7 Leaves are ordered at each stem The median is 17.4, the The median is 20.4, halfway between the 12th12th smallest observation. and 13th smallest observations. Display 1.11 p. 18 Box plot of per-capita annual incomes for 105 countries, in 1974 U.S. dollars The values for these countries are more than 3 box-lengths away from the box. The values for these countries are more than 1.5 box-lengths away from the box. This is the largest income not more than 1.5 box- lengths from the box. This is the upper quartile. This is the median. This is the lower quartile. This is the smallest income not more than 1.5 box- lengths from the box. Sweden United States West Germany Denmark Canada $5,000 $4,000 $3,000 $2,000 $1,000 $0 P er -c ap it a A nn ua l I nc om e ($ U .S .) VERY EXTREME POINTS EXTREME POINTS Display 1.12 p. 19 Side-by-side box plots for the starting salary data $8,000 $7,000 $6,000 $5,000 $4,000 FEMALES MALES Starting Salary ($U.S.) Display 1.15 p. 24 Order from sun and distance from sun of the 9 planets and the asteroid belt (distance scaled so that earth’s distance is 10) Body Order from Sun Distance from Sun Mercury 1 3.87 Venus 2 7.23 earth 3 10.00 Mars 4 15.24 (asteroids) 5 29.00 Jupiter 6 52.03 Saturn 7 95.46 Uranus 8 192.00 Neptune 9 300.90 Pluto 10 395.00 Display 1.16 p. 25 Chromosome aberrations per 100 cells for 333 Hiroshima A-bomb survivors 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Number of Aberrations No Radiation (n = 263) 1-100 Rads (n = 70) Display 2.1 p. 29 Humerus lengths (inches) of adult male house sparrows, 24 that perished and 35 that survived in a winter storm Average: SD: n: .7380 .0198 35 65 66 67 68 69 70 71 72 73 74 75 76 77 78 9 9 932 3 96600 988761 543 422 5 7 39 5 13368889 0033569 111139 12256 679 0 0 68 7 represents 0.687 inchLegend: SURVIVEDPERISHED Average: SD: n: .7279 .0235 24 Display 2.4 p. 33 The relationship between the population distribution and the sampling distribution of the average in random sampling µ σ n SAMPLING DISTRIBUTION OF THE AVERAGE σ POPULATION DISTRIBUTION The sampling distribution is centered on the population mean CENTER SPREAD SHAPE Sample averages are closer to the mean than single values; the sampling distribution has SD(Y) = The shape of the sampling distribution will be more nearly normal than the shape of the population distribution. 1 2 3 µ Display 2.5 p. 36 Student’s t-distribution on 14 degrees of freedom -3 -2 -1 0 +1 +2 +3 -2.624 -2.145 -1.761 -1.345 0 +1.345 +1.761 +2.145 +2.624 1 2.5 5 10 50 90 95 97.5 99 5 percent of the t-ratios are smaller than -1.761 Percentages Percentiles A Percentage represents how frequently t-ratios are less than a certain value A percentile is a t-ratio having a specific percentage of the distribution below it Percentages are shown as areas under the curve Display 2.6 p. 37 Display 2.6 Calculations for the paired t-test and 95% confidence interval for the schizophrenia study Compute differences. 1 2 3 Obtain their average, Y, and standard deviation, s Yi is the volume for the unaffected twin minus the volume for the schizophrenic twin (i=1,...,15) Sample average: Y = .199 (cm3) Sample standard deviation: s = .238 (cm3); 14 d.f. Compute S.E.(Y) = s/ and d.f. = n-1 n S.E.(Y) = .238/ = .0615 (cm3)15 Paired t-test for the hypothesis that the population mean difference is zero t-statistic = .199/.0615 = 3.236 Find the p-value (2-sided here) as the propor- tion of values in a tn-1 distribution as far or farther from zero than the observed t-statistic two-sided p-value = .006 (from computer or Table A.2 and interpolation) 4 95% confidence interval for popu- lation mean difference Find the 97.5th percentile from the t-distribu- tion on n-1 degrees of freedom t14(.975) = 2.145 (from Table A.2) 95% confidence interval = Y ± t(n-1)(.975)×S.E.(Y) Compute the t-statistic for this hypothesis: (Y-0)/S.E.(Y) .199cm3 ± 2.145 × 0.615cm3 : 0.067cm3 to 0.331cm3 Display 2.9 p. 41 Construction of a 95% confidence interval for the difference between the mean humerus lengths of sparrows that died and that survived inches= 0.00567SE(Y2 - Y1) Group 1: Died 2: Survived Average (in.) SD (in.)n 24 35 .72792 .73800 .02354 .01984 t57(.975) = 2.002 Half-width = (2.002)(0.00567) = 0.01136 Y2 - Y1 = .73800 - .72792 = 0.01008 degrees of freedom = 24 + 35 - 2 = 57 Lower 95% confidence limit = 0.01008 - 0.01136 = -0.00128 inches Upper 95% confidence limit = 0.01008 + 0.01136 = 0.02144 inches from tables of the t-distribution with 57 degrees of freedom from Display 2.6 Display 2.10 p. 42 The t-test for the hypothesis that the mean humerus lengths of sparrows that died is the same as the mean for sparrows that survived inches= 0.00567SE( - Y1Y2 Group 1: Died 2: Survived Average (in.) SD (in.)n 24 35 .72792 .73800 .02354 .01984 ) - Y1Y2 = -.73800 .72792 = 0.01008 degrees of freedom = 24 + 35 - 2 = 57 from Display 2.8 t-statistic = 0.01008 - 0.0 0.00567 = 1.778 1-sided p-value = .040 2-sided p-value = 2(.040) = .080 Hypothesized Difference from tables of the t-distribution with 57 degrees of freedom: 1.778 = t57(.960) or P = .960 Display 2.11 p. 46 A histogram of t-ratios from 500 random regroupings of the creativity study data, with an approximating t-distribution density -3.0 -2.0 -1.0 0.0 +1.0 +2.0 +3.0 Value of the t-ratio Student’s t-distribution with 45 degrees of freedom Display 2.14 p. 51 Lifetimes of guinea pigs in two treatment groups 0 1 2 3 4 5 6 36,18 91,89,87,86,52,50 49,20,19,18,15,14,14,08,02 89,78,73,67,67,66,65,60 16,12,09 92,79,78,73 41 82,80,67,55 46,32,21,21 74,63,55 46,45,05 90,76,69 52,54,54,60,64,64,66,68,78,79,81,81,83,85,94,98 53,56,59,65,68,70,83,89,91 11,15,26,26 61,73,73,76,97,98 06 59,66 92,98 5 98 represents 598 daysLegend: Received bacilli Control 7 76,93,97 07,08,13,14,19,36,38,39 12,13,16,20,25,25,44 41,38,37,34,21,08,07,03 88,85,63,50 35,25 (n=64) (n = 58) Display 2.15 p. 53 Weights of male house sparrows that survived and perished; Bumpus Data Weights (g) of 35 males that survived 24.5 26.9 26.9 24.3 24.1 26.5 24.6 24.2 23.6 26.2 26.2 24.8 25.4 23.7 25.7 25.7 26.3 26.7 23.9 24.7 28.0 27.9 25.9 25.7 26.6 23.2 25.7 26.3 24.3 26.7 24.9 23.8 25.6 27.0 24.7 Weights (g) of 24 males that perished 26.5 26.1 25.6 25.9 25.5 27.6 25.8 24.9 26.0 26.5 26.0 27.1 25.1 26.0 25.6 25.0 24.6 25.0 26.0 28.3 24.6 27.5 31.1 28.3 Display 2.16 p. 51 Cholesterol levels in urban and rural guatemalans Serum total cholesterol (mg/l) levels among urban residents (n=45) 133 134 155 170 175 179 181 184 188 189 190 196 197 199 200 200 201 201 204 205 205 205 206 214 217 222 222 227 227 228 234 234 236 239 241 242 244 249 252 273 279 284 284 284 330 Serum total cholesterol (mg/l) levels among rural residents (n=49) 95 108 108 114 115 124 129 129 131 131 135 136 136 139 140 142 142 143 143 144 144 145 145 148 152 152 155 157 158 158 162 165 166 171 172 173 174 175 180 181 189 192 194 197 204 220 223 226 231 Display 3.2 p. 58 Box plots of rainfall amounts, in natural and transformed scales Unseeded Seeded 2,500 2,000 1,500 1,000 500 0 Rainfall (acre-feet) Unseeded Seeded Rainfall (acre-feet) 1,000 100 10 1 logarithm of Rainfall 8 7 6 5 4 3 2 1 0 (A) On the acre-feet scale (B) On the scale of the natural logarithm of acre-feet Both groups look skewed The group with the higher center also has larger spread No skewness on this scale Two groups have about the same spread Display 3.3 p. 59 Box-plots of 1987 dioxin concentrations in 646 Vietnam veterans and 97 veterans who did not serve in Vietnam D io xi n co nc en tr at io n pa rt s pe r tr ill io n 0 5 10 15 20 25 30 35 40 45 Vietnam Veterans Other Veterans (n = 646) (n = 97) Display 3.4 p. 61 Percentage of 95% confidence intervals that are successful when the two populations are non-normal (but same shape and SD, and equal sample sizes); each percentage is based on 1,000 computer simulations n1,n2 5 10 25 100 95.5 95.5 95.3 95.1 95.4 95.4 95.3 95.3 95.3 95.2 95.2 95.1 95.1 95.0 98.3 98.3 98.2 98.1 98.0 94.5 94.6 94.9 95.2 95.694.8 50 strongly skewed moderately skewed mildly skewed long- tailed short- tailed Display 3.7 p. 67 Outlier analysis for Agent Orange Data; effect of outliers on the p-value for equal population means 0 5 10 15 20 25 30 35 40 45 Obs #646 Obs #645 Since conclusion is not affected by the outliers, report analysis 3 p-value With all observations: .40 Without #646: .48 Without #645, 646: .54 Veteran # 645: reported 180 days of indirect military exposure to herbicides. Veteran # 646: reported no exposure (military or civilian) to herbicides. Compute relevant statistical measure, with and without outliers 2 but examine outliers carefully to see what else can be learned 4 Identify outliers (subjectively, by visual examination) 1 1-sided with full data set, Display 3.8 p. 69 The logarithmic transformation used to arrive at favorable conditions for the two-sample t-analysis Measurement Scale (Y) log(Y) +4 +3 +2 +1 0 10 20 30 40 50 60 70 80 90 1000 BEFORE TRANSFORMATION 1. Both histograms are skewed 2. The one with the larger center also has the larger spread AFTER Logarithm Curve 1. No skew; 2. Same spread. Display 3.9 p. 71 Two-sample t-analysis and statement of conclusions after logarithmic transformation — cloud seeding example 1202.6 830.1 372.4 345.5 321.2 244.3 163.0 147.8 95.0 87.0 81.2 68.5 47.3 41.1 36.6 29.0 28.6 26.3 26.1 24.4 21.7 17.3 11.5 4.9 4.9 1.0 7.092 6.722 5.920 5.845 5.772 5.498 5.094 4.996 4.554 4.466 4.397 4.227 3.857 3.716 3.600 3.367 3.353 3.270 3.262 3.195 3.077 2.851 2.446 1.589 1.589 0.000 2745.6 1697.8 1656.0 978.0 703.4 489.1 430.0 334.1 302.8 274.7 274.7 255.0 242.5 200.7 198.6 129.6 119.0 118.3 115.3 92.4 40.6 32.7 31.4 17.5 7.7 4.1 7.918 7.437 7.412 6.886 6.556 6.193 6.064 5.811 5.713 5.616 5.616 5.541 5.491 5.302 5.291 4.864 4.779 4.773 4.748 4.526 3.704 3.487 3.447 2.862 2.041 1.411 Y(acre-ft) log(Y) SEEDEDUNSEEDED Y(acre-ft) log(Y) 1 Transform the data 2 Use the two-sample t- Conclusion: There is convincing evidence that seeding increased rainfall tools on the log rainfall Difference in averages = 1.1436 (SE=0.4495)) 95% confidence interval for additive effect of cloud seeding on log rainfall: 0.2406 to 2.0467 Test of the hypothesis of no effect of cloud seeding on log rainfall: 1-sided p-value from two-sample t-test = .0070 (50 df) 3 Back transform estimate and confidence interval Estimate = e1.1436 = 3.1382 Lower confidence limit = e0.2406 = 1.2720 Upper confidence limit = e2.0467 = 7.7425 4 State the conclusions on the original scale (1-sided p-value = .0070). It is estimated that the volume of rainfall produced by a seeded cloud was 3.14 times as large as the volume that would have been produced in the absence of seeding. (95% confidence: 1.27 to 7.74 times). Display 3.12 p. 80 Life expectancy and per capita income in petroleum exporting countries and industrialized countries (NA = “not available”) Australia Austria Belgium Canada Denmark Finland France West Germany Ireland Italy Japan Netherlands New Zealand Norway Portugal South Africa Sweden Switzerland Britain United States 71.0 70.4 70.6 72.0 73.3 69.8 72.3 70.3 70.7 70.6 73.2 73.8 71.1 73.9 68.1 68.2 74.7 72.1 72.0 71.3 3426 3350 3346 4751 5029 3312 3403 5040 2009 2298 3292 4103 3723 4102 956 NA 5596 2963 2503 5523 Algeria Ecuador Indonesia Iran Iraq Libya Nigeria Saudi Arabia Venezuela 50.7 52.3 47.5 50.0 51.6 52.1 36.9 42.3 66.4 430 360 110 1280 560 3010 180 1530 1240 Life Expectance (years) Per Capita Income (1974 $U.S.) Life Expectance (years) Per Capita Income (1974 $U.S.) Industrialized Countries Petroleum Exporting Countries Display 3.13 p. 81 Proportions of pollen removed and visit durations by bumble bee queens and by honey bee workers Proportion of pollen removed Duration of visit (seconds) .07 .10 .11 .12 .15 .19 .28 .31 .30 .34 .35 .39 .38 .40 .41 .42 .48 .48 .47 .49 .50 .51 .53 .58 .59 .65 .60 .60 .69 .70 .70 .51 .70 2 5 7 11 12 11 9 9 16 17 12 14 23 35 21 10 9 7 11 13 14 16 14 17 22 13 13 12 19 23 21 27 28 58 15 .40 .42 .28 .37 .52 .65 .76 .89 .74 .70 .79 .78 .74 .77 3 12 10 17 24 33 44 46 48 51 64 78 Proportion of pollen removed Duration of visit (seconds) Bumble Bee Queens Honey Bee Workers (n = 35) (n = 12) Bumble Bee Queens Honey Bee Workers Proportion of pollen removed Duration of visit (seconds) Ave: SD: Ave: SD: .666 .183 .426 .182 35.8 23.2 16.2 10.0 Display 3.14 p. 82 Percentages of two forms of dietary iron retained by mice 0.71 1.66 2.01 2.16 2.42 2.42 2.56 2.60 3.31 3.64 3.74 3.74 4.39 4.50 5.07 5.26 8.15 8.24 2.20 2.69 3.54 3.75 3.83 4.08 4.27 4.53 5.32 6.18 6.22 6.33 6.97 6.97 7.52 8.36 11.65 12.45 Fe3+ Supplement Fe4+ Supplement Display 4.1 p. 86 Numbers of O-ring incidents on 24 space shuttle flights prior to the Challenger disaster 0 1 1 2 Launch Temperature Below 65° F Above 65° F Number of O-Ring Incidents 1 1 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Display 4.2 p. 87 Cognitive load experiment: conventional method of instruction (for finding the slope of the line that connects C to the midpoint between A and B) C(4,6) A(2,1) B(8,3) x y Solution: The coordinates of N are: N N 2+8 1+3 2 2= (5,2) The Slope of NC is: m 2-6 5-4 -4 1 or ,( ) = = = -4= In a conventional worked example, algebra and diagram are separated, giving students extraneous cognitive load of having to assimilate the two. Display 4.3 p. 88 Cognitive load experiment: modified method of instruction (for finding the slope of the line that connects C to the midpoint between A and B) C(4,6) A(2,1) B(8,3) x y N 2+8 1+3 2 2= ,( ) (5,2)=1 m 2-6 5-4 = -4 1 or= -4= 2 A modified worked example integrates algebra and picture, allowing the student to more easily acquire a schema for solving such problems. Display 4.6 p. 92 Facts about the randomization (or sampling) distribution of the rank-sum statistic—the sum of ranks in group 1—when there is no group difference PERMUTATION DISTRIBUTION OF THE RANK-SUM (T) CENTER SPREAD SHAPE The shape of the sampling distribution will be approximately normal if the sample sizes are large (and not too many ties) 1 2 3 Mean(T) Mean(T) = n1R SD(T) = s R n1n2 (n1+n2) where R and sR are the average and the sample standard deviation for the combined set of ranks (e.g. the 4th column of Display ) Display 4.7 p. 93 Finding the p-value with the normal approximation to the permutation distribution of the rank-sum statistic; calculations for the cognitive load data continued from . SD(T) = Determine the Z-statistic.3 Mean(T) = (14)(14.5) = 203; 14 (14 + 14 14) 8.202 = 21.70 Z = (137 - 203) 21.70 -3.04= 4 one-sided p-value = .00118 R = 14.5 1 sR = 8.202 Calculate the average and sample standard deviation of the ranks from the combined sample (column 4 of Display ) Compute the theoretical “null hypothesis” mean and standard deviation of T, using the formulas in 2 Find the p-value from a standard normal table × Display 4.8 p. 94 Using a rank-sum test to construct a confidence interval for an additive treatment effect; cognitive load study Confidence Hypothesized 2-sided Interval Effect (seconds) p-value Inclusion? -50 .0286 No -60 .0800 Yes -55 .0403 No -58 .0502 Yes -150 .1227 Yes -160 .0476 No -155 .0589 Yes -158 .0530 Yes -159 .0502 Yes Try several hypothesized values for δ to identify those that have 2-sided p- values ≥ .05 A 95% confidence interval is -159 sec- onds to -58 seconds. Display 4.11 p. 98 The conceptual difficulty with comparing population means when population spreads are not the same µB µA Lifetimes of Brand B Light Bulbs Lifetimes of Brand A Light Bulbs “On average” Brand A bulbs last longer; but there is also a greater chance of early burnout with A. The question of which brand is better may be more complex than simply “Which mean is larger?” Display 4.12 p. 100 Signed-rank test statistic computations; schizophrenia study Ordered Pair Unaffected Affected Difference Magnitude Order Rank +Ranks -Ranks 1 1.94 1.27 .67 .02 (+) 1 1 1 2 1.44 1.63 -.19 .03 (+) 2 2 2 3 1.56 1.47 .09 .04 (+) 3 3 3 4 1.58 1.39 .19 .07 (+) 4 4 4 5 2.06 1.93 .13 .09 (+) 5 5 5 6 1.66 1.26 .40 .10 (+) 6 6 6 7 1.75 1.71 .04 .11 (+) 7 7 7 8 1.77 1.67 .10 .13 (+) 8 8 8 9 1.78 1.28 .50 .19 (+) 9 9.5 9.5 10 1.92 1.85 .07 .19 (-) 10 9.5 9.5 11 1.25 1.02 .23 .23 (+) 11 11 11 12 1.93 1.34 .59 .40 (+) 12 12 12 13 2.04 2.02 .02 .50 (+) 13 13 13 14 1.62 1.59 .03 .59 (+) 14 14 14 15 2.08 1.97 .11 .67 (+) 15 15 15 1 Order the absolute differences and assign ranks to them 2 Signed rank statistics = sum of ranks for positive differences: = 110.5 Display 4.13 p. 106 Hypothetical O-ring data 0 1 1 3 Launch Temperature Below 65° F Above 65° F Number of O-Ring Incidents 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Display 4.16 p. 109 Tolerance to sunlight (minutes) for 13 patients prior to treatment and after treatment with a sunscreen Tolerance to sunlight (minutes) Patient Pre-treatment During treatment 1 30 120 2 45 240 3 180 480 4 15 150 5 200 480 6 20 270 7 15 300 8 10 180 9 20 300 10 20 240 11 60 480 12 60 300 13 120 480 Display 4.17 p. 110 Months of survival after beginning of study, for 58 breast cancer patients Control Patients (n = 24) 2, 6 ,8, 10, 12, 12, 14, 14, 14, 16, 16, 16, 18, 18, 18, 20, 22, 22, 26, 34, 36, 38, 40, 48 Patients Given Group Therapy for One Year (n=34) 2, 2, 4, 4, 4, 6, 6, 8, 10, 10, 12, 14, 16, 16, 16, 18, 20, 22, 32, 36, 46, 46, 48, 48, 58, 58, 66, 72, 72, 82, 122, 122*, 122*, 122* *These 3 patients were still alive at the end of the 122 month study period. Display 4.18 p. 110 Number of vomiting and retching episodes for 15 chemotherapy-receiving cancer patients, under placebo and marijuana treatments Total Number of Vomiting and Subject Retching Episodes Number Marijuana Placebo 1 15 23 2 25 50 3 0 0 4 0 99 5 4 31 6 2 21 7 1 79 8 4 113 9 9 53 10 0 0 11 22 61 12 11 18 13 0 12 14 0 6 15 0 5 Display 5.3 p. 116 Structure of planned comparisons for groups in the diet restriction study N/N85 (control) NP N/R50 N/R50 lopro R/R50 N/R40 (a) Does reducing from 85 to 50 kcal/wk increase life-span? (b) Is there an effect of pre-weaning diet restriction? (c) Does further reduction from 50 to 40 kcal/wk increase life-span more? (d) Does reduction in protein, with same calories, change lifetime distribution? (e) Do control mice have same lifetimes as the laboratory mice? Display 5.4 p. 117 Percents of women in 30-juror venires for Boston area U.S. District Court trials, grouped according to the judge presiding 0 1 2 3 4 64,87 33,36,50,52,77,86 31 68 08,36 05,89 70,89 20,27,55 56 10,34,75,75 05,19,25,38,38 43,97 77,97 15,79 48 02 65 07,35,64,67,95,98 19,62 Spock Trial Judge Other Boston Area U.S. District Court Judges A B C D E F Legend: 4 89 represents a venire with 48.9% women Display 5.5 p. 118 Percentages of women on venires of the 7 Boston judges Percentage of Women Judge Spock’s A B C D E F 50 40 30 20 10 Display 5.8 p. 124 Estimated means and residuals from two models for mean percentage of women (%W) in venires, from the Spock trial data 6.4 8.7 13.3 13.6 15.0 15.2 17.7 18.6 23.1 16.8 30.8 33.6 40.5 48.9 27.0 28.9 32.0 32.7 35.5 45.6 21.0 23.4 27.5 27.5 30.5 31.9 32.5 33.8 33.8 24.3 29.7 17.7 19.7 21.5 27.9 34.8 40.2 16.5 20.7 23.5 26.4 26.7 29.5 29.8 31.9 36.2 Spock Spock Spock Spock Spock Spock Spock Spock Spock A A A A A B B B B B B C C C C C C C C C D D E E E E E E F F F F F F F F F 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 26.6 -20.2 -17.9 -13.3 -13.0 -11.6 -11.4 -8.9 -8.0 -3.5 -9.8 4.2 7.0 13.9 22.3 0.4 2.3 5.4 6.1 8.9 19.0 -5.6 -3.2 0.9 0.9 3.9 5.3 5.9 7.2 7.2 -2.3 3.1 -8.9 -6.9 -5.1 1.3 8.2 13.6 -10.1 -5.9 -3.1 -0.2 0.1 2.9 3.2 5.3 9.6 14.6 14.6 14.6 14.6 14.6 14.6 14.6 14.6 14.6 34.1 34.1 34.1 34.1 34.1 33.6 33.6 33.6 33.6 33.6 33.6 29.1 29.1 29.1 29.1 29.1 29.1 29.1 29.1 29.1 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 26.8 26.8 26.8 26.8 26.8 26.8 26.8 26.8 26.8 -8.2 -5.9 -1.3 -1.0 0.4 0.6 3.1 4.0 8.5 -17.3 -3.3 -0.5 6.4 14.8 -6.6 -4.7 -1.6 -0.9 1.9 12.0 -8.1 -5.7 -1.6 -1.6 1.4 2.8 3.4 4.7 4.7 -2.7 2.7 -9.3 -7.3 -5.5 0.9 7.8 13.2 -10.3 -6.1 -3.3 -0.4 -0.1 2.7 3.0 5.1 9.4 est. res.judge EQUAL MEANS SEPARATE MEANS %W est. res. est. res.judge EQUAL MEANS SEPARATE MEANS %W est. res. Large residuals mean that the model fits poorly In the equal means model, estimated means are equal In the separate means model, estimated means are the group averages.to the grand average. Display 5.9 p. 126 Four F-distributions, having different degrees of freedom F-Statistic Values F2,2 F2,30 F30,2 F30,30 1.0 2.0 3.0 4.0 5.0 Display 5.10 p. 127 Analysis of variance table: a test for equal mean percents of women in venires of seven judges; Spock data Source of Variation dfSum of Squares Mean Square F-Statistic p-value Between Groups Within Groups Total 6 39 1,927.08 1,864.45 3,791.53 321.18 47.81 6.72 .000061 45 The F-statistic is the ratio of the Between MS to the Within MS A mean square is the ratio of a sum-of-squares to its degrees of freedom Sum of squared residuals from fitting the reduced (equal- means) model Subtract the “Within” from the “Total “ degrees of freedom Sum of squared residuals from fitting the full (separate- means) model 3 21 4 5 6 NOTE: This is sp 2 n-I n-1 The p-value comes from an F-distribution with 6 and 39 df 7 Display 5.13 p. 131 Success rates for 95% confidence intervals for µ1-µ2 from samples simulated from normal populations with possibly different SDs 10 20 10 10 10 10 20 10 10 10 10 20 95.4 95.5 94.1 95.6 98.9 98.7 98.7 99.6 99.9 99.8 99.9 99.9 91.9 84.8 97.0 90.4 96.8 91.7 98.8 97.5 99.6 98.9 99.8 99.9 n1 n2 n3 σ3=σ1 σ3=2σ1 σ3=4σ1 σ2=σ1 σ2=2σ1 σ3=σ1 σ3=2σ1 σ3=4σ1 Display 5.14 p. 132 Residual plot: lifetimes of mice fed six different diets 10 0 -10 -20 30 35 40 45 Estimated Mean Lifetime (months) Residual Lifetime (months) Display 5.15 p. 133 Some important patterns in residual plots R es id ua ls Estimated Means Estimated Means Time Order of Data Collection Estimated Means R es id ua ls R es id ua ls R es id ua ls (a) no problem (b) funnel-shaped: transform (c) non-constant variance (d) time trend Display 5.18 p. 136 Spock trial data, rank-transformed Judge Rank of venire from smallest (1) to largest (46) percent women Spock’s 1 2 3 4 5 6 9.5 11 16 A 8 31 37 44 46 B 22 26 34 36 41 45 C 14 17 23.5 23.5 30 32.5 35 38.5 38.5 D 19 28 E 9.5 12 15 25 40 43 F 7 13 18 20 21 27 29 32.5 42 Display 5.19 p. 139 Separate confidence intervals for two group means: are the means different? Estimate of Mean A Estimate of Mean B Case 2: Strong evidence Case 3: Inconclusive Case 4: No evidence Case 1: Convincing evidence Display 5.20 p. 142 Incomplete ANOVA table for Exercise 18 Source df Sum of Squares Mean Square F-statistic P-value Between Groups Within Groups Total 24 31 35,088 70,907 ? ? ? ? ? ? Display 5.23 p. 144 Summary statistics for areas of cavity entrances Cavity Area Summary Statistics - Logarithmic Scale Species n Mean Sample SD Mouse Pinyon Mouse Bewick’s Wren Mountain Bluebird Ash-Throated Flycatcher Plain Titmouse Northern Flicker Western Screech Owl American Kestrel 127 44 24 41 18 16 11 7 6 7.347 7.368 7.418 7.487 7.563 7.568 8.214 8.272 8.297 .4979 .4235 .3955 .3183 .3111 .4649 .2963 .3242 .5842 Display 5.24 p. 144 t-tests and 95% confidence intervals for group comparisons in the diet and lifetimes study Estimate SE 95% CI: t-stat p-valueLow High (a) N/R50 vs N/N85 (b) R/R50 vs N/R50 (c) N/R40 vs N/R50 (d) N/R50 lopro vs N/R50 (e) N/N85 vs NP 9.6 m 0.6 m 2.8 m -2.6 m 5.3 m 1.2 1.2 1.2 1.2 1.3 7.3 -1.7 0.5 -4.9 2.7 11.9 2.9 5.1 -0.3 7.9 8.08 0.50 2.39 2.18 4.07 < 0.0001 0.60 0.017 0.029 < 0.0001 2-sided Display 5.25 p. 145 Achievement test scores for LOW ability students who worked in different study group composition Highest Ability Level in the Study Group Low Low-Medium Medium-High High Average: St. Dev.: n: 0.26 0.14 17 0.37 0.21 24 0.36 0.17 25 0.47 0.21 14 Display 5.28 p. 147 Zinc levels (µg/g) in the hair of women 171 174 202 171 207 125 189 179 163 174 184 186 185 189 187 181 150 176 210 139 172 198 177 Pregnant Vegetarians Pregnant Non-Vegetarians Non-Pregnant Vegetarians Display 6.1 p. 150 Stem-and-leaf diagrams of applicant qualification scores given to applicants simulating five different handicap conditions 0 1 2 3 4 5 6 7 8 9 9 5 06 129 149 17 48 9 56 268 06 3589 1 2 7 033 18 0234 445 5 4 149 479 237 589 5 7 8 5 78 03 1124 246 None Amputee Crutches Hearing Wheelchair Legend: 7 4 represents a score of 7.4 on the Applicant Qualification Scale Applicant’s Handicap Display 6.2 p. 152 Experimental tank allowing female fish to choose between males Female moves to side compartments to engage in courtship activities with chosen male After one 10 minute observation period, the males switched ends to begin another 10 minute observation period. Female is placed in center compartment Male with yellow sword is in closed end compartment. (Control): Male with transparent sword is in closed compartment at opposite end.