Case StudyExampleVariablesSampling UnitsApplicationPlantation DataWhat you should knowData: The Heart of StatisticsBret HanlonDepartment of StatisticsUniversity of Wisconsin—MadisonFall 2011Data 1 / 13PurposeWe need to build our statistical vocabularlyFor example, to think about data and data analysis, we need tolearn how to classify variables.Data 2 / 13Cow ExampleExampleA study assigned 50 cows to various diets (based on the proportion ofan additive in the diet) and examined a number of outcomesassociated with characteristics of the produced milk, amount of drymatter consumed, and weight gain of the cow. Pre-treatment variablesinclude initial weight of the cow, number of lactations, and age of thecow. The primary purpose of the study was to examine the effect of thedifferent diets on the outcome variables, controlling for effects of othercovariates.Data Case Study Example 3 / 13Cow variablesThe variables in the data set are:treatment the diet, one of CONTROL, LOW, MEDIUM, and HIGH;level the proportion of the additive in the feed;lactation the number of lactations (pregnancies);age age of the cow at the beginning of the study in months;initial.weight initial weight in pounds;dry mean daily weight of dry matter consumed (pounds?);milk mean daily amount of milk produced (in pounds);fat percentage milk fat;solids percentage of solids in milk (by weight?)final.weight final weight of cow in pounds;protein percentage of protein in milk by (weight?)Data Case Study Example 4 / 13DataHere is a representative sample of the data:treatment level lactation age initial.weight dry milk fat solids final.weight proteincontrol 0 3 49 1360 15.429 45.552 3.88 8.96 1442 3.67control 0 3 47 1498 18.799 66.221 3.40 8.44 1565 3.03control 0 2 36 1265 17.948 63.032 3.44 8.70 1315 3.40control 0 2 33 1190 18.267 68.421 3.42 8.30 1285 3.37control 0 2 31 1145 17.253 59.671 3.01 9.04 1182 3.61control 0 1 22 1035 13.046 44.045 2.97 8.60 1043 3.03low 0.1 6 89 1369 14.754 57.053 4.60 8.60 1268 3.62low 0.1 4 74 1656 17.359 69.699 2.91 8.94 1593 3.12low 0.1 3 45 1466 16.422 71.337 3.55 8.93 1390 3.30low 0.1 2 34 1316 17.149 68.276 3.08 8.84 1315 3.40low 0.1 2 36 1164 16.217 74.573 3.45 8.66 1168 3.31low 0.1 2 41 1272 17.986 66.672 3.43 9.19 1188 3.59medium 0.2 3 45 1362 19.998 76.604 4.29 8.44 1273 3.41medium 0.2 3 49 1305 19.713 64.536 3.94 8.82 1305 3.21medium 0.2 3 48 1268 16.813 71.771 2.89 8.41 1248 3.06medium 0.2 3 44 1315 15.127 59.323 3.13 8.72 1270 3.26medium 0.2 2 40 1180 19.549 62.484 3.36 8.51 1285 3.21medium 0.2 2 35 1190 19.142 70.178 3.92 8.94 1168 3.28high 0.3 5 81 1458 20.458 71.558 3.69 8.48 1432 3.17high 0.3 3 49 1515 19.861 56.226 4.96 9.17 1413 3.72high 0.3 3 48 1310 18.379 49.543 3.78 8.41 1390 3.67high 0.3 3 46 1215 18.000 55.351 4.22 8.94 1212 3.80high 0.3 3 49 1346 19.636 64.509 4.16 8.74 1318 3.31high 0.3 3 46 1428 19.586 74.430 3.92 8.75 1333 3.37Data Case Study Example 5 / 13Categorization of variablesVariables are (usually) either numerical (quantitative) orcategorical (qualitative).numerical variables take on numerical values and are eitherdiscrete or continuous.categorical variables partition the observations into categories: ifthe categories have a natural order, the variable isordinal; if not, it is nominal.Variables are experimental or observational.experimental variables have values that are under control of theresearcher.observational variables have values that are observed and arenot set by the researcher.Variables may be response variables or explanatory variables.response variables are considered as outcomes;explanatory variables are thought potentially to affect outcomes.Data Case Study Variables 6 / 13Board WorkClassify each of the variables in the cow example.Data Case Study Variables 7 / 13Level of MeasurementData is often represented in a rectangular array where eachcolumn is a variable and each row is an observational unit orsampling unit.In the cow example, individual cows are sampling units and eachvariable measures something on the level of the cowIn other examples, there may be multiple levels of measurement.It is important to recognize different levels of measurementbecause it can affect the selection of an approriate method ofanalysis.Data Case Study Sampling Units 8 / 13Plantation DataExampleResearchers interested in forest restoration in Costa Rica conductedan experiment to examine which of several species of tree bestpromoted the growth of native woody plants in their understory inplantations that were being converted back to natural forest. Theapproach was to plant a fast-growing native tree in the plantation thatwould provide shade and a suitable environment for additional nativespecies to become established. At some point, the planted overstorytrees would be harvested, leaving a diverse natural forest behind.Data Application Plantation Data 9 / 13Plantation Data (continued)ExampleThe study included three sites, each a plantation that had beenpreviously cleared for agriculture. One site (La Selva) was a formerexperimental research station, while the other two sites (Paniagua andQuesada) had been private farms. The La Selva, Paniagua, andQuesada plantations were 100 m, 1.3 km, and 2.5 km from continuousforest, respectively. Each site was divided into six plots (of varioussizes) and each plot was planted with one of six species of tree,spaced in a regular array (of varying sizes). With minimalmanagement, the sites were allowed to grow for nearly a decade.Each plot included four subplots (4m by 4m) for which severalvariables were measured. The primary response variable is thenumber of woody stemmed plants in each subplot. Other variablesinclude the percentage of the subplot shaded by the canopy of theoverstory, whether or not the subplot was flat or sloped, and whether ornot the subplot had good drainage.Data Application Plantation Data 10 / 13Sample Datastems canopy site overstory spacing slope drainage distance250 14 LaSelva Cb 8 flat good 0.160 15 LaSelva Cb 8 flat good 0.146 13 LaSelva Ta 8 flat good 0.136 15 LaSelva Ta 8 flat good 0.1125 14 LaSelva Vg 8 flat good 0.1110 13 LaSelva Vg 8 flat good 0.145 12 LaSelva Ha 8 flat good 0.150 13 LaSelva Ha 8 flat good 0.110 15 Paiagua Cb 4 sloped good 1.30 11 Paiagua Cb 4 sloped good 1.326 14 Paiagua Ta 32 flat good 1.330 15 Paiagua Ta 32 flat good 1.322 10 Paiagua Vg 64 sloped good 1.315 10 Paiagua Vg 64 sloped good 1.34 8 Paiagua Ha 32 flat poor 1.325 8 Paiagua Ha 32 flat poor 1.322 11 Quesada Cb 16 flat poor
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