Whereas the previous section dealt with comparing

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Whereas the previous section dealt with comparing several groups on a categorical response variable, this one introduced you to comparing several groups on a quantitative response variable. You learned how to apply analysis of variance (ANOVA) to assess the significance of the differences among several sample/treatment means. The test procedure is based upon a probability distribution known as the F - distribution. You have seen that the same ANOVA procedure applies whether the data were gathered as independent random samples from several populations or from randomization of subjects to several treatment groups. (But like always, the scope of conclusions differs depending on how the data were collected.) You have also found that ANOVA results are affected by the variability in sample means, the variability within samples/groups, and the sample sizes. Like always, you have examined technical conditions that must be satisfied in order for this procedure to be valid; in addition to random sampling or random assignment, these conditions are that each group has a normal distribution and that the standard deviations are similar across groups. Example 5.2 presents an application of the ANOVA procedure.
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Chance/Rossman, 2015 ISCAM III Investigation 5.6 354 SECTION 3: RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In this section you will analyze data sets with two quantitative variables. The goal will be to describe the relationship between the variables. As always, you will start by learning some useful numerical and graphical techniques for summarizing the data. Then you will explore how to use a mathematical model of the relationship to make predictions of one variable from the other. In the next section you will then move on to inferential techniques based on simulated sampling and randomization distributions as well as a mathematical model. Investigation 5.6: Cat Jumping Evolutionary biologists are often interested in “form - function relationships” to help explain evolution history of say an animal species. Harris and Steudel (2002) investigated factors that are related to the jumping ability of domestic cats. Because jump ability and height are largely dependent on takeoff velocity, several traits were recorded for 18 healthy adult cats such as relative limb length, relative extensor muscle mass, body mass, fat mass relative to lean body mass, and the percentage of fast-twitch muscle fibers to see which might best explain maximum takeoff velocity (based on high-speed videos). In this investigation, you will examine the following data, also available in the file CatJumping.txt : ID Sex Body mass (g) Hind limb length (cm) Muscle mass (g) Percent body fat Takeoff velocity (cm/sec) A F 3640 29.1 51.15 29 334.5 B F 2670 28.55 46.05 17 387.3 C M 5600 31.74 95.9 31 410.8 D F 4130 26.9 55.65 39 318.6 E F 3020 26.11 57.2 15 368.7 F F 2660 26.69 48.67 11 358.8 G F 3240 26.74 64.55 21 344.6 H M 5140 27.71 78.8 35 324.6 I F 3690 25.47 54.6 33 301.4 J F 3620 28.18 55.5 15 331.8 K F 5310 28.45 68.8 42 312.6 L M 5560 28.65 79.8 37 316.8 M M 3970 29.82 69.4 20 375.6 N F 3770 26.66 60.25 26 372.4 O F 5100 27.84 60.7 41 314.3 P F 2950 27.89 55.65 25 367.5 Q M 7930 30.58 98.95 48 286.3 R F 3550 28.06 79.25 16 352.5 (a) Identify the observational units and the primary response variable of interest here. Also classify this variable as quantitative or categorical.
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