Wk 4 Discussion 2 - Measures of Variation due Sat

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Wk 4 Discussion 2 - Measures of Variation [due Sat] Due Saturday Measures of variation provide us with information about how a set of scores are distributed. Refer to the data you collected in Week 1 or other dataset practice, running measures of variability for each of your variables. Write a 250- to 300-word response to the following:  What specific considerations did you use to determine which test to run? o See week 1 for type of measurement for the test  Why are measures of variability important when interpreting your data? Measures of variability are numbers that variability in a distribution of data. There are five measures of variability: the index of qualitative variation, the range, the interquartile range, standard deviation, and the variance. Researchers will often use measures of variability along with measures of central tendency to describe the data in a study (Frankfort-Nachmias et al, 2019). The mock research topic in this course is to determine if there is a relationship between an individual’s socioeconomic status, the sex of the individual, and whether they earned a bachelor’s degree or higher. The two independent variables are socioeconomic index and sex of the participant. The dependent variable is bachelor’s degree or higher completed. The independent variable socioeconomic index is an ordinal level of measurement; therefore, I chose range and the interquartile range (IQR) as the measure of variability because this level of measurement’s research objective will determine variability by measuring range of this rank ordered category. The range is the difference between the maximum score and the minimum score in a distribution and the interquartile range (IQR) remedies limitations of the range and is the width of the middle 50% of a distribution and is calculated by taking the difference between lower and upper quartiles. Both measure the ordinal and interval-ratio variables. The independent variable Sex of the Respondent is a nominal level of measurement; therefore, I chose the index of qualitative variation (IQV) as the measure of variability because with nominal variables your choice is restricted to the IQV and the IQV measures variability for variables such as race and ethnicity. The dependent variable bachelor’s degree or higher is a nominal level of measurement, therefore chose the index of qualitative variation (IQV) as the measure of variability because with nominal variables your choice is restricted to the IQV and the IQV measures variability for variables such as race and ethnicity. This variable only answers the question yes or no (Frankfort-Nachmias et al, 2019). Tokunaga (2018) defines measures of variability as a descriptive statistic of the amount of differences in a set of data or a variable. The purpose of these measures is to represent numerically a set of data based on how the scores differ (vary) from each other. Researchers will use measures of central tendency with measures of variability to describe data. The amount of variability helps researchers generalize results from a sample to a population and this can help predict information on a population based on the sample. In addition, the presence of outliers or anomalies in the data can be indicated by determining variability. This helps researchers identify patters or trends in the data for a population. In conclusion, understanding variability can help

researchers make better decisions as well as predictions based on the data (Salkind & Frey, 2019). Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2019). Social statistics for a diverse society (9th ed.). SAGE Publications. Salkind, N. J., & Frey, B. B. (2019). Statistics for people who (think they) hate statistics (7th ed.). SAGE Publications. Tokunaga, H. T. . (2018). Fundamental statistics for the social and behavioral sciences (2nd ed.). SAGE. https://uk.sagepub.com/sites/default/files/upm-assets/ 95832_book_item_95832.pdf Include your own experience as well as 2 citations that align with or contradict your comments as sourced from peer-reviewed academic journals, industry publications, books, and/or other sources. Cite your sources using APA formatting. If you found information that contradicts your experience, explain why you agree or disagree with the information. Another way of summarizing a distribution of data is by selecting a single number that describes how much variation and diversity there are in the distribution. Numbers that describe diversity or variation are called measures of variability. e concept of variability has implications not only for describing the diversity of social groups such as Asian American women but also for issues that are important in your everyday life. In Chapter 2, you learned about different types of averages, what they mean, how they are computed, and when to use them. But when it comes to descriptive statistics and describing the characteristics of a distribution, averages are only half the story. The other half is measures of variability.In the simplest of terms, variability reflects how much scores differ from one another. Together, these two (average and variability) can be used to describe the characteristics of a distribution and show how distributions differ from one another. Variability (also called spread or dispersion) can be thought of as a measure of how different scores are from one another. It’s even more accurate (and maybe even easier) to think of variability as how different scores are from one particular score. And what “score” do you think that might be? Well, instead of comparing each score to every other score in a distribution, the one score that could be used

as a comparison is—that’s right—the average. So, variability becomes a measure of how much each score in a group of scores differs from the average, usually the mean. Three measures of variability are commonly used to reflect the degree of variability, spread, or dispersion in a group of scores. These are the range, the standard deviation, and the variance. The range tells you how different the highest and lowest values in a data set are from one another—that is, the range shows how much spread there is from the lowest to the highest point in a distribution. So, although the range is fine as a general indicator of variability, it should not be used to reach any conclusions regarding how individual scores differ from one another. And you will usually never see it reported as the only measure of variability but as one of several—which brings us to…. the standard deviation (sometimes abbreviated as SD, sometimes s) represents the average amount of variability in a set of scores. In practical terms, it’s the average distance of each score from the mean. The larger the standard deviation, the larger the average distance each data point is from the mean of the distribution and the more variable the set of scores is. the standard deviation is an average deviation from the mean. he standard deviation can be used to help us compare scores from different distributions, even when the means and standard deviations are different. Amazing!The standard deviation is computed as the average distance from the mean. So, you will need to first compute the mean as a measure of central tendency. Don’t fool around with the median or the mode in trying to compute the standard deviation.The larger the standard deviation, the more spread out the values are, and the more different they are from one another.Just like the mean, the standard deviation is sensitive to extreme scores. When you are computing the standard deviation of a sample and you have extreme scores, note that fact somewhere in your written report and in your interpretation of what the data mean.If s = 0, there is absolutely no variability in the set of scores, and the scores are essentially identical in value. This will rarely happen and actually makes it hard to compute statistics about the relationship between scores. Without variability, we can’t see connections between variables. And, when you think about it, a variable is only a variable when it varies. This third measure of variability, the variance, is simply the standard deviation squared.In other words, it’s the same formula you saw earlier but without the square root bracket, like the one shown in Formula 3.3: the variance is important because it is used both as a concept and as a practical measure of variability in many statistical formulas and techniques. Well, they are both measures of variability, dispersion, or spread. The formulas used to compute them are very similar. You see them (but mostly the standard deviation) reported all over the place in the “Results” sections of journals.They are also quite different.First, and most important, the standard deviation (because we take the square root of the average summed squared deviation) is stated in the

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original units from which it was derived. The variance is stated in units that are squared (the square root of the final value is never taken).What does this mean? Let’s say that we need to know the variability of a group of production workers assembling circuit boards. Let’s say that they average 8.6 boards per hour and the standard deviation is 1.59. The value 1.59 means that the difference in the average number of boards assembled per hour by each worker is about 1 1/2 circuit boards. This kind of information is quite valuable when trying to understand the overall performance of groups. Salkind, N. J., & Frey, B. B. (2019). Statistics for people who (think they) hate statistics (7th ed.). SAGE Publications. A measure of variability is a descriptive statistics of the amount of differences in a set of data for a variable. The purpose of measures of variability is to numerically represent a set of data based on how the scores differ or vary from each other. https://uk.sagepub.com/sites/default/files/upm-assets/95832_book_item_95832.pdf variability refers to how spread out data points are from the center of the distribution. Measures of variability in statistics is a summary explaining the proportions of fluctuation in the dataset. While a measure of tendency reflects the typical value, the measure of variability shows how far away data points tend to fall. If the data points fall far from the center of the distribution, we call it a high dispersion, and if the data points cluster tightly around the center, it is low dispersion.

Wk 4 Discussion 2 - Measures of Variation due Sat

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