Phase 8: Analysis of Variance (ANOVA) Between Subjects Overview The analysis of variance (ANOVA) is used to compare three or more populations (can also handle 2 populations, but the t-test is usually used instead), when all three population means are unknown. A Between Subjects ANOVA means that the observations are not paired. An Between Subjects ANOVA is similar to an independent t-test, but with more samples. An ANOVA test answers the question: Is there sufficient statistical evidence to conclude that at least one of the population means is different than the others? In T-tests (or z-tests), we usually subtract the means to get an indication of variability (spread) between the means. The difference can be thought of as a range of the means. When there are three or more means, we can no longer just simply subtract the means. Take for example the following population means: 1 = 10, 2 = 20, 3 = 30. If we subtract the means: [10 20 (30)], it would result in 0. A result of zero usually indicates that there is no difference, but that is not the case here. Clearly, the means are different from each other. Besides, subtracting three means does not really give you a range anymore. We need another form variability. Instead we use another form of variability between means, called Mean Squared Between (denoted; ). Mean squared between is the variance between the means (instead of the range of means). Basically, the Mean Squared Between is calculated by subtracting each sample mean from the grand mean, squaring the deviation from the grand mean, adding those squares up, and dividing by the degrees of freedom (more on this later; have to consider the sample sizes). This is similar to how you calculated variance in earlier phases, but we just do it with the means instead of individual values. The squaring gets rid of the problem of subtracting negative means. The denominator for any t-statistic (or z-statistic for hypothesis testing) is the standard error. The standard error is the standard deviation of the sample mean (for a one sample mean test or dependent t-test) or the standard deviation of the difference of the sample means. The standard error tells you how much sample means (or difference in sample means) are expected to vary by chance (due to sampling error). Please review the notes on the Central Limit Theorem for more information on standard error. The denominator in an ANOVA test is called Mean Square Within. The Mean Squared Within is the variance within the groups. The Mean Squared Within is the total of the Sum of Squares for each group divided by the total degrees of freedom. The Mean Squared Within is a weighted average variance within the groups. The Mean Squared Within is a measure of how much we would expect the sample means to vary by chance (due to sampling error). The Mean Squared Within is very similar to standard error. However, no square roots were used to get the standard deviation from the variance. In other words, it is a squared version of standard error. Depiction of Variability The F-Distribution The ANOVA test uses an F-statistic. The observed F is calculated with the following formula: = The F-statistic is always positive. The F-statistic is always positive, because both the mean square between and mean square within will always be positive (0 or greater), because variance is always positive. A sampling distribution of variances is skewed to the right and makes what is called a Chi-Squared distribution. When you divide two Chi-Squared distributions, you get a F-distribution, which is also skewed to the right. When the mean square between is equal to the mean square within, the F-statistic will equal one. When the F-statistic is one, the variance between the means is what is expected due to sampling error (by chance). The F-statistic has to be greater than one to be significant, how much greater depends of the degrees of freedom. A distribution has two types of degrees of freedom. Steps to ANOVA Hypothesis Test 1) 0 : 1 = 2 = 3 ... . 1 : . 2) Assumptions a. Random selection from all populations. b. All sampling distributions are normally distributed: One or both of the following are true: i. All population distributions are normally distributed. ii. The sample size for each group is at least 30. 3) Set Alpha Levels a. Alpha 4) Calculate the p-value: a. Find the sample mean for each group (1 , 2 , 3 ... ). b. Find the grand mean i. = ( ) i stands for each individual value. ii. OR = ( ) = 1 1 +2 2 + 3 3 ...+ J stands for each group. iii. OR if equal n's then = = 1 +2 + 3 ...+ c. Find : Sum of Squares between the sample means. 2 i. = ( ) = 1 (1 )2 + 2 (2 )2 + 3 (3 )2 ... + ( )2 d. Find the : Sum of Squares for within the sample means: It is the sum of squares for each group added up. 2 i. = ( ) = 1 + 2 + 3 ... + e. Find degrees of freedom: i. ( ) = 1 Subtracting off 1, because we estimated the grand mean. ii. ( ) = 1 + 2 + 3 ... . . f. OR = a. . b. ( ) i. Have to subtract off 1 for each sample mean we estimated. Find the : The Mean Square Between is the variance between the sample means. i. = g. Find the : The Mean Square Within is the variance within sample means. i. = h. Calculate the observed F statistic: = i. ANOVA Table Often times an ANOVA table is made. Below is a generic version of the table. The table can be used in number 4 to calculate the F-statistic. Sum of Squares Degrees of Mean Square F-statistic Freedom ( ) Between = = 2 = 1 = ( ) ( ) Within = 2 = = ( ) Total = 1 = ( )2 = + is the total sums of squares. It is the sum of the squares of the differences between the individual observations and the grand mean. The is the total amount of variability there is for the observations (not specifically variance, because it is not divided by the sample size or degrees of freedom, but is still a measure of variability). It also happens to equal to the sum of the and . Part of the total variability is due to the grouping ( ) and some is unexplained ( ). = ( )2 = + j. Calculate p-value with Excel: Use the function \"f.dist.rt.\" The f statistic is replaces the x, deg_freedom1 is the between degrees of freedom and the deg_feedom2 is the within degrees of freedom. 5) Conclusion Statement a. If p-value is less than alpha, then reject the null. i. There is statistical significant evidence to conclude that there is a difference in the population means (be more specific about what you are comparing). b. If p-value is greater than alpha, then fail to reject the null. i. There is not statistical significant evidence to conclude that there is a difference in the population means (be more specific about what you are comparing). 6) When the null is rejected, than follow t-tests should be done. Each of the groups should be compared to each other. There will be (1) 2 number of t-tests that should be conducted. For instance, if there are 3 groups, there will be three comparisons ( 32 2 = 3; 1 vs. 2, 1 vs. 3, and 2 vs. 3) For this class you will not be required to do the follow up tests, but you should know if they should be conducted or not. If you fail to reject the null, then it is not appropriate to do following up t-tests, because the omnibus (name for the overall test, in this case the ANOVA test) did not indicate there was a difference, so you should not look for differences with follow up tests. ANOVA Example A researcher is interested in comparing four diets. Below is sample data of pounds lost for 20 individuals (positive numbers indicate weight loss and negative numbers indicate weight gain) on various diets. Is there statistically significant evidence that the four population means differ? Conduct the steps of hypothesis testing using an alpha of .05. Low Calorie Low Fat Low Carbohydrate Control 8 2 3 2 9 4 5 2 6 3 4 -1 7 5 2 0 3 1 3 3 1) 0 : = = = 1 : . 2) Assumptions a. Random selection from all populations: ?. b. All sampling distributions are normally distributed: One or both of the following are true: ? i. All population distributions are normally distributed: ? ii. The sample size for each group is at least 30: X 3) Set alpha level: a. = .05 4) Calculate the observed F: a. Find the sample means: Low Calorie Low Fat Low Carbohydrate Control n1=5 n2=5 n3=5 n4=5 1 = 6.6 2 = 3.0 3 = 3.4 4 = 1.2 b. Find grand mean: i. = 71 20 ii. OR = = 3.55 (71 is the sum of all the observations). 6.65+35+3.45+1.25 20 = 71 20 = 3.55 iii. OR BECAUSE THERE ARE EQUAL N'S: = 6.6+3.0+3.4+1.2 4 = 14.2 4 = 3.55 c. Find Sum of Squares Between: i. = 5(6.6 3.6)2 + 5(3.0 3.6)2 + 5(3.4 3.6)2 + 5(1.2 3.6)2 = 45 + .02 + 28.8 + 1.8 = 75.8 d. Find the Sum of Squares Within: i. Find the SS for each group: Low Calorie (X - 6.6) (X - 6.6)2 8 1.4 2.0 9 2.4 5.8 6 -0.6 0.4 7 0.4 0.2 3 -3.6 13.0 0 21.4 Low Fat (X - 3.0) (X - 3.0)2 2 -1.0 1.0 4 1.0 1.0 3 0.0 0.0 5 2.0 4.0 1 -2.0 4.0 0 10.0 Low Carbohydrate (X - 3.4) (X - 3.4)2 3 -0.4 0.2 5 1.6 2.6 4 0.6 0.4 2 -1.4 2.0 3 -0.4 0.2 0 5.4 Control (X - 1.2) (X - 1.2)2 2 0.8 0.6 2 0.8 0.6 -1 -2.2 4.8 0 -1.2 1.4 3 1.8 3.2 0 10.6 2 ii. Add the SS's: = = ( ) = 21.4 + 10.0 + 5.4 + 10.6 = 47.4 e. : i. = = 4 1 = 3 ii. = = = 20 4 = 4 + 4 + 4 + 4 = 16 f. Source of Variation Make the ANOVA Table: Sums of Squares (SS) Degrees of freedom (df) Mean Squares (MS) F Between 75.8 4-1=3 75.8/3 = 25.3 25.3/3.0 = 8.43 Within 47.4 20-4=16 47.4/16 = 3.0 Total 123.2 20-1=19 g. Find the p-value: 0.001374 5) Conclusion statement: < : Reject the null a. There is statistically significant evidence to conclude that there is a difference between the four population means of weight lost for each of the weight loss groups. 0.01% = 8.43 6) In this instance, because we rejected the null, follow up t-tests would be appropriate. There would a. b. c. d. e. f. 43 2 = 6 follow up t-tests. Low Calorie vs. Low Fat Low Calorie vs. Low Carb Low Calorie vs. Control Low Fat vs. Low Carb Low Fat vs. Control Low Carb vs. Control ID Job Satisfaction 1997 Weight 1997 Income 1996 Gender 142 2 161 104 178 2 110 1000 200 2 142 2500 216 3 220 2500 225 1 130 200 266 2 125 500 278 4 160 4400 282 2 105 800 307 3 130 250 331 3 120 500 404 1 150 2000 480 3 128 2800 483 2 140 6000 511 3 150 1400 535 3 100 1000 621 3 155 4800 641 3 117 350 648 2 185 1000 654 1 135 998 672 1 160 300 720 2 190 360 731 2 160 1500 745 1 150 100 757 3 120 100 763 4 135 19 769 1 165 2800 775 1 200 2000 789 3 267 300 803 3 145 1000 819 1 145 624 837 2 160 2500 839 3 125 800 843 4 145 2000 856 3 175 500 893 3 125 150 962 2 160 3100 975 1 240 500 995 3 115 6000 997 3 205 900 1025 2 210 150 1065 3 165 2000 1094 1 180 420 1126 3 190 6000 1152 4 115 700 1167 2 160 3500 1182 2 130 1000 1186 2 135 3600 Race 2 2 1 2 1 2 1 1 2 2 1 2 1 1 2 1 2 1 2 2 1 1 1 2 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 Income 2010 4 35000 4 49500 4 5400 2 32000 4 48000 4 90000 4 40000 4 30000 4 70000 4 42800 4 49000 2 57000 2 50000 2 45000 4 146002 2 43000 4 34500 4 146002 4 46000 1 15000 4 28000 4 146002 4 61000 4 70000 4 20000 4 48000 4 48000 4 15000 4 40000 1 36000 4 55000 4 146002 4 15000 4 82000 2 26000 4 45000 4 55000 2 33000 4 16000 4 15000 1 27000 1 1000 1 76000 2 20000 4 146002 4 20000 4 146002 1228 1249 1265 1291 1320 1343 1362 1380 1410 1411 1429 1431 1441 1444 1454 1484 1488 1499 1503 1515 1521 1551 1604 1614 1618 1633 1644 1649 1654 1676 1687 1768 1771 1775 1776 1849 1854 1865 1873 1881 1884 1910 1980 1990 2037 2040 2059 2102 1 2 2 2 2 1 1 2 4 2 4 3 4 1 1 1 1 3 2 3 3 2 1 3 4 3 5 3 3 1 3 1 2 2 4 3 3 4 4 1 1 3 1 3 3 2 2 3 145 135 100 190 160 140 123 140 140 125 132 135 135 128 115 130 155 130 160 130 170 140 135 110 185 130 120 130 170 164 120 200 175 180 150 156 151 160 145 170 112 196 114 140 176 115 135 155 2300 100 1000 5500 3000 2500 450 1200 2000 1500 500 900 3200 900 750 650 5000 2000 1246 2000 50 2900 1200 500 3500 1400 3000 900 800 1500 500 1700 2000 4500 1600 3500 500 4600 1000 1000 150 3000 1680 2300 800 900 2000 400 1 2 2 1 1 1 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 2 2 2 1 2 2 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 2 1 1 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 1 4 4 4 3 4 4 2 2 2 4 4 1 40000 1500 40000 22000 32000 24000 35000 45000 146002 62000 0 75000 47000 33000 30000 46000 32000 52000 54000 50000 45000 79000 30000 8000 15600 36000 83000 60000 89000 146002 60000 30000 53000 45000 30000 34700 42000 24000 40000 20000 92000 28000 6000 37000 25000 24000 146002 10000 2110 2111 2139 2145 2147 2150 2163 2188 2189 2207 2208 2210 2249 2252 2254 2261 2275 2291 2318 2339 2349 2352 2378 2386 2392 2396 2397 2407 2414 2423 2426 2434 2447 2448 2498 2519 2529 2553 2558 2567 2579 2634 2638 2697 2701 2703 2704 2739 1 2 1 3 2 1 1 2 3 2 2 4 2 3 4 1 1 1 1 1 1 2 3 2 1 2 1 1 3 1 1 4 2 1 1 1 1 1 1 1 2 1 2 3 5 3 1 3 225 170 126 170 145 114 150 135 170 145 150 175 125 135 155 140 180 210 150 146 156 165 140 96 160 150 135 136 150 163 190 270 173 115 140 140 140 170 140 115 130 135 150 140 140 200 220 120 450 1500 1500 2000 1200 1200 2000 2000 100 1000 400 700 2000 1700 600 300 3000 250 200 5000 1000 3500 1100 1800 1000 1000 2000 200 150 1200 350 1500 2000 1638 2000 5000 800 2000 900 1500 1600 1980 210 800 2000 100 300 2000 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 2 2 2 2 1 1 1 1 2 1 1 2 1 1 2 2 1 2 2 2 2 1 1 1 1 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 47000 146002 67000 48000 7000 40000 53000 64000 71000 35000 46225 12000 44000 6750 35000 20000 40000 50000 35000 35000 65000 30000 20000 47000 41000 37000 26000 44000 27000 60000 25000 54500 45000 57000 47250 35000 42000 12000 146002 18000 41200 50000 52142 32000 60000 55000 41000 60000 2740 2762 2770 2784 2790 2795 2831 2843 2848 2850 2855 2866 2904 2907 2911 2915 2992 2997 3014 3023 3069 3089 3132 3148 3154 3161 3180 3186 3189 3200 3221 3254 3258 3274 3312 3319 3321 3326 3337 3345 3354 3367 3369 3400 3445 3474 3483 3510 3 4 1 1 1 1 2 1 1 3 1 1 2 3 5 4 3 2 5 2 1 3 2 3 4 2 1 1 1 2 1 4 1 1 2 1 3 5 2 5 1 2 2 1 3 3 2 1 130 145 115 220 208 135 185 115 109 170 210 150 140 155 140 245 155 120 109 125 210 185 140 140 135 140 126 130 140 150 147 107 145 210 108 170 190 125 175 125 150 205 245 110 125 205 155 98 400 650 1248 500 1200 100 3500 2000 1700 1992 2000 1 2200 530 2000 350 2500 150 1000 300 5000 2000 3000 1500 938 3000 700 1000 2000 1000 439 3000 300 400 900 67 1000 2880 840 320 2000 1500 3000 1000 400 1000 1500 1144 2 1 2 2 1 1 1 2 2 1 2 1 1 1 1 1 1 2 2 2 1 1 2 2 1 2 2 2 2 2 2 2 1 1 2 2 1 2 2 2 1 1 1 1 2 1 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 2 2 4 4 4 4 1 4 4 1 29000 12000 60000 37000 146002 25000 35000 22000 45000 49600 32000 25000 24000 25000 5000 17000 94000 23000 25000 75000 30000 80000 30000 55000 49800 55000 33000 7000 146002 19000 10000 38500 32000 50000 22000 6000 40000 28000 28000 12000 69000 28000 31000 44000 38800 26000 31000 18000 3526 3535 3548 3593 3719 3724 3742 3750 3763 3791 3836 3887 3952 3956 3957 3991 3992 4000 4003 4021 4052 4078 4080 4115 4179 4206 4210 4272 4353 4389 4410 4428 4445 4449 4459 4475 4477 4492 4555 4588 4617 4685 4692 4710 4730 4749 4758 4764 3 1 1 3 2 3 3 2 3 3 1 1 1 3 1 2 1 2 1 4 3 2 1 1 2 1 4 2 1 4 1 5 3 3 1 2 2 3 3 2 1 1 1 1 2 4 4 3 120 130 160 130 149 140 110 192 220 165 185 121 110 121 140 257 108 125 130 130 148 220 190 190 250 120 119 157 105 240 115 160 135 132 150 125 150 145 150 110 140 135 210 150 110 220 126 160 1500 1200 200 1000 500 5000 480 500 600 285 2400 1500 900 5175 0 1800 45 2000 175 300 637 500 1100 150 500 1500 746 600 500 0 4500 989 2000 700 400 500 2000 2000 2000 250 800 2000 3200 1700 150 0 600 200 2 2 2 2 1 1 2 1 1 2 1 2 2 1 1 1 2 2 1 1 2 2 1 2 1 2 2 2 2 1 2 2 1 2 2 1 1 1 1 2 1 2 1 1 2 1 2 1 4 4 4 4 2 4 4 1 4 1 1 1 4 1 1 4 4 4 4 4 4 4 2 2 1 4 1 4 2 2 4 1 4 2 4 4 4 2 2 4 4 4 4 4 4 4 1 2 15000 38000 41000 50000 21000 65000 20000 5000 30000 88000 31000 72000 30000 30000 70000 35000 19000 52000 50000 34000 18000 75000 27000 34000 30000 60000 50000 16500 22000 40000 90000 40000 146002 65000 26000 42000 16 85000 25000 25000 50000 42000 8000 60000 13200 28000 42000 45869 4769 4770 4785 4808 4817 4852 4860 4884 4915 4960 4972 4973 5009 5010 5038 5054 5082 5094 5103 5111 5166 5189 5215 5222 5235 5259 5281 5306 5311 5313 5314 5319 5338 5363 5389 5391 5396 5403 5417 5439 5441 5479 5481 5492 5509 5522 5528 5531 3 2 1 2 2 3 1 1 4 2 3 1 3 3 3 3 1 1 2 3 2 1 1 1 2 4 2 3 1 1 1 1 2 4 1 3 3 2 2 3 3 2 2 1 2 1 3 3 120 117 160 160 110 125 155 230 140 122 154 90 150 120 270 120 137 165 150 150 155 118 103 190 185 190 130 150 140 175 165 150 117 156 115 145 148 265 130 134 140 130 116 160 170 230 180 130 2800 1000 300 950 900 400 300 900 600 1000 120 300 1200 1500 0 1070 1500 5000 800 1500 3000 2000 1000 800 1500 1300 927 495 1000 500 2080 800 1400 700 2000 1600 5400 3000 7500 200 3000 850 2500 5200 500 1063 4000 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118 130 100 1700 600 150 2000 1999 1000 500 50 0 400 2500 4000 2500 2000 200 900 500 1600 2000 100 400 2820 600 200 1200 1000 4000 1100 1600 400 2000 1000 5000 3000 200 3000 384 5200 3 600 3000 700 650 650 2000 2600 3000 897 1 2 1 1 1 1 2 2 1 1 1 2 1 2 2 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 1 2 1 2 4 1 4 4 4 1 4 4 4 1 1 4 1 4 2 4 4 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 1 1 2 1 1 2 2 2 2 2 2 2 53000 24000 15000 50000 20000 30000 12000 23000 31000 52000 45000 30000 18000 22000 12000 15000 48000 63000 65000 400 30000 80000 146002 75000 40000 30000 146002 27000 45000 29000 90000 50000 78000 146002 42000 42000 53000 30310 18000 800 36000 54000 81000 41000 65000 19000 43000 36000 7182 7187 7196 7301 7354 7360 7385 7440 7506 7585 7590 7594 7603 7621 7641 7678 7680 7683 7839 7863 7875 7901 7931 8081 8116 8148 8178 8184 8194 8241 8303 8312 8313 8315 8325 8345 8481 8494 8500 8511 8540 8578 8618 8621 8625 8660 8692 8711 2 2 2 2 4 3 1 1 1 3 2 2 3 1 2 4 5 4 1 3 1 3 3 3 2 1 2 3 2 3 5 3 4 2 4 2 5 4 1 3 3 1 3 1 3 3 2 3 110 135 135 130 145 140 140 122 165 145 125 145 125 130 217 175 150 121 187 135 195 110 131 130 156 120 105 150 140 133 125 210 165 135 142 180 210 91 115 162 115 140 250 135 149 143 138 220 800 300 800 1300 0 300 900 3000 1200 160 1000 1496 500 1000 2000 600 4000 300 0 200 6500 650 500 914 3000 160 100 900 4500 1400 0 2000 0 1100 1131 3000 640 700 700 500 1000 200 350 3500 2000 500 1500 2000 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 1 2 1 2 1 2 2 2 2 1 2 2 1 1 2 1 1 2 2 2 1 2 1 1 2 2 1 1 1 1 1 2 1 2 2 1 2 2 1 2 2 2 2 2 2 2 1 1 2 2 1 1 1 1 1 1 2 1 2 2 2 2 1 1 1 1 1 1 1 2 2 1 2 2 2 2 2 1 1 1 55000 18000 21120 42960 24000 38000 21000 45000 85000 28000 9000 12006 50000 85000 52500 30000 45000 8000 40000 19000 93000 17000 80000 60000 40000 146002 17000 20000 32000 38000 18000 10000 30000 36300 16600 27000 18000 28500 34000 45000 52000 8000 5640 55000 18000 36000 17000 13000 8726 8750 8754 8766 8802 8824 8838 8851 8878 8885 8957 8977 9015 9020 9021 2 4 3 1 1 1 3 2 2 3 4 1 5 1 3 202 205 125 160 160 185 215 120 180 210 165 175 140 190 160 3000 900 2400 175 800 900 200 1000 700 1600 500 2000 3000 500 3000 2 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 4 4 4 4 4 1 4 4 1 4 4 1 4 4 38000 10000 32000 25000 50000 30000 35000 50000 22000 25000 146002 35000 56000 32000 35000 Job Satisfaction 2013 Weight 2013 1 150 1 165 4 178 3 304 1 320 2 113 5 200 2 135 2 130 2 150 4 185 1 145 2 160 2 220 4 120 3 160 4 111 1 248 1 140 1 240 2 265 2 215 3 160 1 125 3 155 1 210 2 260 2 218 3 200 3 172 4 240 2 125 2 188 3 210 3 225 1 285 2 300 2 110 1 255 1 255 3 280 1 250 1 225 2 125 1 200 1 180 2 150 2 2 2 3 1 2 1 2 1 2 3 1 1 2 1 1 2 3 3 3 1 1 2 2 1 2 2 2 4 1 1 1 1 2 3 3 1 3 2 1 1 3 3 2 1 2 1 2 207 132 110 215 210 190 165 210 166 136 164 168 200 140 125 150 155 145 165 185 156 125 150 115 350 129 180 150 225 240 175 280 200 285 242 208 170 240 230 200 130 235 150 180 225 120 190 185 1 1 2 3 1 2 2 1 2 2 2 3 1 1 2 1 1 2 3 2 2 1 1 2 1 2 1 1 3 1 1 1 4 1 2 1 4 1 1 1 3 1 2 1 2 1 3 2 182 225 175 260 155 187 210 165 180 180 175 260 148 140 160 178 225 195 220 185 263 230 167 117 140 220 210 140 215 250 200 415 205 114 205 220 168 250 170 112 165 185 265 195 150 260 250 140 1 2 3 1 2 1 5 1 2 2 3 2 1 1 1 3 1 2 2 2 1 3 2 2 2 2 1 2 3 4 1 1 1 3 2 1 2 1 3 1 1 3 4 1 2 3 2 2 123 167 200 170 265 140 280 150 200 215 288 260 180 210 150 350 260 135 165 250 265 205 137 165 170 155 150 135 160 155 160 117 170 270 128 185 200 162 180 140 203 235 280 125 174 180 225 173 1 2 1 3 2 2 1 2 3 1 1 2 2 4 2 3 1 2 2 1 4 1 2 1 3 2 2 1 1 3 1 1 1 1 2 3 3 1 3 1 2 2 1 3 1 2 5 2 135 196 190 190 220 180 150 289 213 257 220 163 145 155 180 250 148 138 175 165 185 245 265 250 230 140 161 185 125 410 137 220 155 160 230 160 175 210 190 140 180 195 74 170 118 220 115 210 2 1 1 1 1 2 2 2 3 3 3 5 4 4 4 2 1 1 1 1 4 1 1 3 2 1 2 1 4 1 3 2 1 2 2 1 1 1 3 3 3 1 3 1 3 1 2 3 155 125 200 265 145 175 180 260 170 120 200 115 175 182 250 160 158 195 210 170 216 140 130 235 225 260 160 182 200 220 230 220 135 218 155 175 185 265 172 178 185 175 165 182 230 245 195 140 2 3 1 2 1 2 2 3 1 1 1 1 2 2 3 2 1 1 1 1 2 1 1 2 2 2 1 2 1 2 3 5 1 1 1 2 4 2 3 3 2 2 1 3 1 3 1 2 195 160 185 260 325 160 250 135 170 255 245 125 260 178 150 250 180 275 175 250 140 200 210 180 169 175 230 135 210 180 275 150 180 225 183 350 350 170 176 175 250 153 175 200 69 180 164 117 1 2 1 2 1 2 1 1 1 2 2 2 4 1 1 1 1 3 2 4 3 1 2 1 1 1 5 1 2 3 1 2 1 3 3 1 3 1 1 1 1 2 1 1 1 1 3 3 148 160 200 175 150 180 240 195 210 180 145 217 123 170 230 220 285 140 280 134 245 277 156 185 195 184 126 220 200 165 140 280 268 201 173 160 260 152 145 200 150 148 325 192 190 170 165 240 2 3 3 1 3 3 2 2 3 1 2 3 1 1 3 283 200 170 150 180 175 260 132 185 290 270 200 140 245 185 R00001.00 [PUBID] 1997 PRIMARY VARIABLE Survey Year: PUBID, YOUTH CASE IDENTIFICATION CODE COMMENT: YOUTH CASE IDENTIFICATION CODE 0 998 999 997 996 998 996 994 994 989 23 ------8984 0 1 1000 2000 3000 4000 5000 6000 7000 8000 9000 Refusal(-1) Don't Know(-2) TOTAL =========> 0 Min: 4504.3 999 1999 2999 3999 4999 5999 6999 7999 8999 9999 0 0 8984 1 Hard Minimum: [0] TO TO TO TO TO TO TO TO TO TO VALID SKIP(-4) Max: 0 9022 NON-INTERVIEW(-5) Mean: Hard Maximum: [99999999] Lead In: R72976.00[Default] Default Next Question: R05363.00 ------------------------------------------------------------------------------R02447.00 [YEMP-101200.01] Survey Year: 1997 PRIMARY VARIABLE RS JOB SATISFACTION EMP 01 Which of the following best describes how you [feel/felt] about your job with [this employer]? UNIVERSE: R >= 14 has valid employer; not military; employer stopdate >= 16; job last 13+ weeks 353 295 1 Like it very much 2 Like it fairly well 321 89 47 ------1105 3 Think it is OK 4 Dislike it somewhat 5 Dislike it very much Refusal(-1) Don't Know(-2) TOTAL =========> 0 0 0 1105 VALID SKIP(-4) 7879 NON-INTERVIEW(-5) Lead In: R02440.00[Default] Default Next Question: R02454.00 ------------------------------------------------------------------------------R03227.00 [YHEA-2200] Survey Year: 1997 PRIMARY VARIABLE WEIGHT OF R - POUNDS Can you tell me approximately what your weight is? (INTERVIEWER: PRESS FOR "REFUSE", FOR "DON'T KNOW".) UNIVERSE: All 0 14 1077 5341 1865 349 57 5 1 0 0 0 ------8709 0 1 50 100 150 200 250 300 350 400 450 500 Refusal(-1) Don't Know(-2) Invalid Skip(-3) TOTAL =========> 0 Min: 132.26 Hard Minimum: [1] TO TO TO TO TO TO TO TO TO TO TO 49 99 149 199 249 299 349 399 449 499 999999: 500+ 54 205 16 8984 4 VALID SKIP(-4) Max: Hard Maximum: [999] 0 390 NON-INTERVIEW(-5) Mean: Lead In: R03226.00[Default] Default Next Question: R03228.00 ------------------------------------------------------------------------------R04902.00 [YINC-1700] Survey Year: 1997 PRIMARY VARIABLE TOTAL INCOME FROM WAGES AND SALARY IN PAST YEAR During 1996, how much income did you receive from wages, salary, commissions, or tips from all jobs, before deductions for taxes or anything else? UNIVERSE: R received income from job 64 2141 613 277 135 143 46 52 19 18 8 38 10 5 2 0 ------3571 0 1 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 7000 10000 20000 50000 Refusal(-1) Don't Know(-2) TOTAL =========> 0 Min: 681.63 Hard Minimum: [0] Soft Minimum: [0] TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO 499 999 1499 1999 2499 2999 3499 3999 4499 4999 6999 9999 19999 49999 999999: 50000+ 15 368 3954 0 (Go To R04903.00) (Go To R04903.00) VALID SKIP(-4) 5030 NON-INTERVIEW(-5) Max: Mean: 40000 Hard Maximum: [5000000] Soft Maximum: [200000] Lead In: R04899.00[Default] R04900.00[Default] Default Next Question: R04904.00 ------------------------------------------------------------------------------R05363.00 [KEY!SEX] Survey Year: 1997 PRIMARY VARIABLE KEY!SEX, RS GENDER (SYMBOL) COMMENT: Gender of Youth 4599 4385 0 ------8984 1 Male 2 Female 0 No Information Refusal(-1) Don't Know(-2) TOTAL =========> 0 0 0 8984 VALID SKIP(-4) 0 NON-INTERVIEW(-5) Lead In: R00001.00[Default] Default Next Question: R05364.00 ------------------------------------------------------------------------------R14826.00 [KEY!RACE_ETHNICITY] Survey Year: 1997 PRIMARY VARIABLE KEY!RACE_ETHNICITY, COMBINED RACE AND ETHNICITY (SYMBOL) COMMENT: Combined race - ethnicity variable 2335 1901 83 4665 ------8984 1 2 3 4 Refusal(-1) Don't Know(-2) TOTAL =========> 0 Black Hispanic Mixed Race (Non-Hispanic) Non-Black / Non-Hispanic 0 0 8984 VALID SKIP(-4) 0 NON-INTERVIEW(-5) Lead In: R05387.00[Default] Default Next Question: R05389.00 ------------------------------------------------------------------------------T75456.00 [YINC-1700] Survey Year: 2011 PRIMARY VARIABLE TOTAL INCOME FROM WAGES AND SALARY IN PAST YEAR During 2010, how much income did you receive from wages, salary, commissions, or tips from all jobs, before deductions for taxes or for anything else? UNIVERSE: R received income from job Truncated values are applied to the top 2 percent of respondents with valid non-missing responses. The lowest value for the top 2 percent of cases is used as the truncation level ($ 94,000 for this variable). Values for all cases at or over that level are averaged. That average is then assigned to each of the top 2 percent of the cases. 24 80 59 50 56 57 67 59 58 58 49 390 473 546 2226 1050 ------5302 0 1 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 15000 20000 25000 50000 Refusal(-1) Don't Know(-2) TOTAL =========> 1561 Min: 34163.66 Hard Minimum: [0] Soft Minimum: [0] TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO 999 1999 2999 3999 4999 5999 6999 7999 8999 9999 14999 19999 24999 49999 99999999: 50000+ 64 523 5889 0 (Go To T75457.00) (Go To T75457.00) VALID SKIP(-4) 1534 NON-INTERVIEW(-5) Max: Mean: 146002 Hard Maximum: [5000000] Soft Maximum: [200000] Lead In: T75454.00[Default] T75455.00[Default] Default Next Question: T75458.00 ------------------------------------------------------------------------------T87350.00 [YEMP-101200.01] Survey Year: 2013 PRIMARY VARIABLE RS JOB SATISFACTION EMP 01 Which of the following best describes how you [feel/felt] about your [{job_assignment}] [as/with] [employer name]([(loop)])? UNIVERSE: R >= 14 has valid employer; not military; employer stopdate >= 16; job last 13+ weeks; job last 2+ weeks since DLI 2093 1724 1241 213 146 ------5417 1 2 3 4 5 Like it very much Like it fairly well Think it is OK Dislike it somewhat Dislike it very much Refusal(-1) Don't Know(-2) TOTAL =========> 1843 5 1 5423 VALID SKIP(-4) 1718 NON-INTERVIEW(-5) Lead In: T87234.00[Default] T87329.00[Default] T87344.00[Default] T84717.00[Default] T86194.00[1:1] Default Next Question: T87359.00 ------------------------------------------------------------------------------T90393.00 [YSAQ-000B] Survey Year: 2013 PRIMARY VARIABLE R'S WEIGHT - POUNDS Approximately what is your weight? UNIVERSE: All 0 3 0 46 16 394 1164 1483 1405 1038 588 789 ------6926 0 1 25 50 75 100 125 150 175 200 225 250 TO TO TO TO TO TO TO TO TO TO TO 24 49 74 99 124 149 174 199 224 249 99999999: 250+ Refusal(-1) Don't Know(-2) TOTAL =========> 1843 Min: 185.53 93 117 7136 1 VALID SKIP(-4) Max: 5 474 Hard Minimum: [1] Hard Maximum: [999] Soft Minimum: [50] Soft Maximum: [400] Lead In: T90389.00[Default] T90392.00[Default] Default Next Question: T90394.00 NON-INTERVIEW(-5) Mean