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Understanding the Index of Qualitative Variation

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Understanding the Index of Qualitative Variation Chapter 5: The Importance of Measuring Why is Variability important? Variability Simple Example: Suppose you wanted to • Measures of Central Tendency - know how satisfied CNAs are with their Numbers that describe what is typical or job and you found that the average average (central) in a distribution (e.g., mean, mode, median). score (on a five point scal)le) was “3”. • Measures of Variability - Numbers that describe diversity or variability in the How would knowing the variability help distribution (e.g., range, index of qualitative you to understand how satisfied CNAs variation, interquartile range, box plot, are with their job? variance, standard deviation). Answer: It would help you to see whether the average score of “3” means that the majority of CNAs are neutral about their jobs or that there is a split with CNAs either feeling very good (score of 5) or very bad (score of 1) about their job (average of 1’s and 5’s = 3). Another example. A measure of variability: Understanding the Index of Index of Qualitative Variation Qualitative Variation (IQV) • The IQV is a single number that expresses – A measure of variability for nominal variables. the diversity of a distribution. - A measure that shows how diverse a particular category •The IQV ranges from 0 to 1 of a variable is. • An IQV of 0 would indicate that the distribution has NO diversity at all. For example, when looking at ethnic diversity among •An IQV of 1 would indicate that the states, some states are very diverse with multiple ethnic distribution is maximally diverse. groups and lots of people in each group. Other states may have multiple ethnic groups but most of the state’s residents are in only one of the ethnic groups. IQV (NOTE: You will not be responsible for calculating would provide a measure for how diverse each state the IQV but you will be responsible for being able actually is. to interpret an IQV) Index of Qualitative Variation in Real Life: Diversity in the U.S. The Range (Numbers differ somewhat from text) State IQV State IQV State IQV Hawaii 0.82 North Carolina 0.56 Utah 0.30 California 0.72 Alabama 0.54 Indiana 0.30 New Mexico 0.68 Delaware 0.53 Wisconsin 0.28 New York 0.67 Oklahoma 0.48 Nebraska 0.28 • Range – A measure of variation in Texas 0.66 Colorado 0.46 South Dakota 0.26 interval-ratio variables. Maryland 0.65 Connecticut 0.46 Minnesota 0.26 Georgia 0.63 Arkansas 0.43 Idaho 0.25 Mississippi 0.62 Michigan 0.43 Kentucky 0.23 • It is the difference between the Louisiana 0.62 Tennessee 0.42 Wyoming 0.23 New Jersey 0.62 Washington 0.41 Montana 0.22 highest (maximum) and the lowest Florida 0.60 Massachusetts 0.38 North Dakota 0.18 South Carolina 0.59 Rhode Island 0.38 Iowa 0.17 (minimum) scores in the distribution. Illinois 0.58 Kansas 0.35 West Virginia 0.12 Nevada 0.58 Pennsylvania 0.35 New Hampshire 0.11 Arizona 0.58 Missouri 0.34 Vermont 0.07 Alaska 0.58 Ohio 0.34 Maine 0.07 Range = highest score - lowest score Virginia 0.56 Oregon 0.33 What is the range for these Index of Qualitative What is the range for these Index of Qualitative Variation (IQV) scores? Variation (IQV) scores? (higher number means more diversity) (higher number means more diversity) Steps to determine: subtract the lowest score ____from the Steps to determine: subtract the lowest score _.06___from highest _____to obtain the range of IQV scores_____. the highest _____to obtain the range of IQV scores_____. State IQV State IQV State IQV State IQV State IQV State IQV California 0.80 Alabama 0.51 Indiana 0.27 California 0.80 Alabama 0.51 Indiana 0.27 New Mexico 0.76 North Carolina 0.51 Utah 0.26 New Mexico 0.76 North Carolina 0.51 Utah 0.26 Texas 0.74 Delaware 0.49 Nebraska 0.24 Texas 0.74 Delaware 0.49 Nebraska 0.24 New York 0.66 Colorado 0.45 South Dakota 0.24 New York 0.66 Colorado 0.45 South Dakota 0.24 Hawaii 0.64 Oklahoma 0.44 Wisconsin 0.24 Hawaii 0.64 Oklahoma 0.44 Wisconsin 0.24 Maryland 0.62 Connecticut 0.42 Idaho 0.23 Maryland 0.62 Connecticut 0.42 Idaho 0.23 New Jersey 0.61 Arkansas 0.40 Wyoming 0.22 New Jersey 0.61 Arkansas 0.40 Wyoming 0.22 Louisiana 0.61 Michigan 0.40 Kentucky 0.20 Louisiana 0.61 Michigan 0.40 Kentucky 0.20 Arizona 0.61 Tennessee 0.39 Minnesota 0.20 Arizona 0.61 Tennessee 0.39 Minnesota 0.20 Florida 0.61 Washington 0.37 Montana 0.20 Florida 0.61 Washington 0.37 Montana 0.20 Mississippi 0.61 Massachusetts 0.34 North Dakota 0.17 Mississippi 0.61 Massachusetts 0.34 North Dakota 0.17 Georgia 0.59 Missouri 0.31 Iowa 0.13 Georgia 0.59 Missouri 0.31 Iowa 0.13 Nevada 0.57 Ohio 0.31 West Virginia 0.11 Nevada 0.57 Ohio 0.31 West Virginia 0.11 Illinois 0.57 Pennsylvania 0.31 New Hampshire 0.08 Illinois 0.57 Pennsylvania 0.31 New Hampshire 0.08 South Carolina 0.56 Kansas 0.30 Maine 0.06 South Carolina 0.56 Kansas 0.30 Maine 0.06 Alaska 0.56 Rhode Island 0.30 Vermont 0.06 Alaska 0.56 Rhode Island 0.30 Vermont 0.06 Virginia 0.53 Oregon 0.28 Virginia 0.53 Oregon 0.28 What is the range for these Index of Qualitative What is the range for these Index of Qualitative Variation (IQV) scores? Variation (IQV) scores? (higher number means more diversity) (higher number means more diversity)? Steps to determine: subtract the lowest score _.06___from Steps to determine: subtract the lowest score _.06___from the the highest __.80___to obtain the range of IQV scores_____. highest __.80___to obtain the range of IQV scores__.74___. State IQV State IQV State IQV State IQV State IQV State IQV California 0.80 Alabama 0.51 Indiana 0.27 California 0.80 Alabama 0.51 Indiana 0.27 New Mexico 0.76 North Carolina 0.51 Utah 0.26 New Mexico 0.76 North Carolina 0.51 Utah 0.26 Texas 0.74 Delaware 0.49 Nebraska 0.24 Texas 0.74 Delaware 0.49 Nebraska 0.24 New York 0.66 Colorado 0.45 South Dakota 0.24 New York 0.66 Colorado 0.45 South Dakota 0.24 Hawaii 0.64 Oklahoma 0.44 Wisconsin 0.24 Hawaii 0.64 Oklahoma 0.44 Wisconsin 0.24 Maryland 0.62 Connecticut 0.42 Idaho 0.23 Maryland 0.62 Connecticut 0.42 Idaho 0.23 New Jersey 0.61 Arkansas 0.40 Wyoming 0.22 New Jersey 0.61 Arkansas 0.40 Wyoming 0.22 Louisiana 0.61 Michigan 0.40 Kentucky 0.20 Louisiana 0.61 Michigan 0.40 Kentucky 0.20 Arizona 0.61 Tennessee 0.39 Minnesota 0.20 Arizona 0.61 Tennessee 0.39 Minnesota 0.20 Florida 0.61 Washington 0.37 Montana 0.20 Florida 0.61 Washington 0.37 Montana 0.20 Mississippi 0.61 Massachusetts 0.34 North Dakota 0.17 Mississippi 0.61 Massachusetts 0.34 North Dakota 0.17 Georgia 0.59 Missouri 0.31 Iowa 0.13 Georgia 0.59 Missouri 0.31 Iowa 0.13 Nevada 0.57 Ohio 0.31 West Virginia 0.11 Nevada 0.57 Ohio 0.31 West Virginia 0.11 Illinois 0.57 Pennsylvania 0.31 New Hampshire 0.08 Illinois 0.57 Pennsylvania 0.31 New Hampshire 0.08 South Carolina 0.56 Kansas 0.30 Maine 0.06 South Carolina 0.56 Kansas 0.30 Maine 0.06 Alaska 0.56 Rhode Island 0.30 Vermont 0.06 Alaska 0.56 Rhode Island 0.30 Vermont 0.06 Virginia 0.53 Oregon 0.28 Virginia 0.53 Oregon 0.28 Inter-quartile Range Inter-quartile Range • Inter-quartile range (IQR) – The width of the • Inter-quartile range (IQR) – The width of the middle 50 percent of the distribution. middle 50 percent of the distribution. • The IQR helps us to ggpet a better picture of • It is deffffined as the difference between the the variation in the data than the range. upper and lower quartiles. • The shortcoming of the range is that an • IQR = the larger quartile minus the smaller “outlying” case at the top or bottom can quartile or Q1 – Q3 increase the range substantially. What is the Inter-Quartile Range (IQR) for these Index of Qualitative Variation (IQV) Scores? What is the Inter-Quartile Range (IQR) for the State IQV State IQV State IQV California 0.80 Alabama 0.51 Indiana 0.27 Index of Qualitative Variation (IQV) Scores? New Mexico 0.76 North Carolina 0.51 Utah 0.26 Texas 0.74 Delaware 0.49 Nebraska 0.24 New York 0.66 Colorado 0.45 South Dakota 0.24 Steps to determine the IQR (Q1 – Q3): Hawaii 0.64 Oklahoma 0.44 Wisconsin 0.24 Maryland 0.62 Connecticut 0.42 Idaho 0.23 New Jersey 0.61 Arkansas 0.40 Wyoming 0.22 1. Order the categories from highest to lowest (or, if you order Louisiana 0.61 Michigan 0.40 Kentucky 0.20 the case s from lowe st to hig he st then you would su btrac t Q1 Arizona 0.61 Tennessee 0.39 Minnesota 0.20 from Q3) Florida 0.61 Washington 0.37 Montana 0.20 2.
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