Looking For Assistance With Statistic Assignment.

Averages don't always reveal the most telling realities. You know, Shaquille O'Neal and I have an average height of 6 feet. ~ U.S. Labor Secretary Robert Reich (He is 4' 10" tall whereas US basketball star Shaquille O’Neal is 7’1” tall!)

Introduction

You have completed five weeks of applied statistics. HURRAH! This is quite an accomplishment via DL. Some of you have done so with ease, while others have worked hard with persistence and sweat. Still others have had a mix of these two reactions—ease with some topics, while having to work on other topics to grasp the concepts and computations (not to worry, I am always in the latter group).

You now should be well familiar with descriptive, bivariate and multivariate statistics—what they are (and their names) and how to calculate them with the help of Salkind’s chapters, my modules and/or statistical software. Most of all, you should have a firm understanding of hypothesis testing using statistics. Simply put, you should know when to reject or fail to reject the null hypothesis that there is no relationship between variables by using p values.

During this week, we will go over applications of some of the statistics you just learned over the last five weeks. We will see how specific statisics are used in published journal articles. In this module, we will discuss some examples of how to interpret descriptive, bivariate and multivariate statistical results. Hopefully you will appreciate both the application and interpretation of statistics, especially when you read the assigned materials for your other DL classes.

Learning Objectives in Modules 6 and 7:

· Applying descriptve statistics to examples published in journal articles

· Evaluting bivariate statisics to examples published in journal articles

Interpreting Descriptive Statistics: Measures of Central Tendency and Dispersion

Measures of central tendency (mean, mode, and median) and dispersion (range, variance and standard deviation) are routinely used by researchers in journal articles and reports to describe the distribution of a variable, that is, to summarize a large number of cases/records in a dataset into one point estimate. That estimate is a summary of the values of all the cases/records in the dataset. Telling the reader that the range of the age of the sample (18 - 65 years old), average age of the sample (30.5 years), and its standard deviation (18.9) is illustrative of this point. These pieces of information merely help you to see what the distribution of the variable would look like if you were to plot each value of the variable. So, instead of a graph of the frequency of each value of the variable (in this case, age), descriptive statistics are used to summarize these values and tell you in a single value the one score that best describes the centrality of and variation in the data.

Measures of central tendency and dispersion—descriptive statistics—are commonly used to describe the demographic characteristics of a sample, or the respective distributions of the independent and dependent variables. Such information is needed so that readers can ‘see’ and understand what the variable looks like summarized in a single value rather than to look at each value of the variable for each case/record (e.g., individual) or across all the variables (e.g., all the socio-demographic variables).

Example from a Journal Article

So, let’s look at an example taken from following published article:

Fisher Bonnie S., John J. Sloan III, Francis T. Cullen, and Chunmeng Lu. (1998). “Crime in the Ivory Tower: The Level and Sources of Student Victimization.” Criminology. 36(3), 671 – 710.

From this table, we can see lots of means and standard deviations (S.D.) being reported. Knowing that a mean is an appropriate statistic used for ratio and interval-level data, we can see that the average amount of money that college students spend per week on non-essential items is $35.12 (keep in mind this was the mid 1990s). The S.D. is 30.14, so we can see that that there is some variability in the dispersion. We also see that students, on average, spent less than one night (0.75 nights) partying on campus and slightly more nights (0.85) partying off campus. On average, the college students were not very likely to take recreational drugs (average = 1.7, or ~ 2). They were, on average, more likely to regularly drink three or more alcoholic beverages during the year (average = 4.3). Notice that the last two interpretations are made within the context of the scale or metric in which the variable was measured (1 = definitely not likely to 10 = definitely likely).

Okay, so, on average, what percent of students live on campus? The answer is: 36% with a S.D. of 27.30 and ranging from 3 to 95; given the S.D., there is some variation in this measure. This is quite a straightforward interpretation.

What is the average rate per 1,000 students of registered national social frats and sororities? On average about 2.4 per 1,000 students. Given the range of 0 to about 8, is this a lot or not? So for every 1,000 students on average there are 2 social frats and sororities…start thinking about a campus of 5,000. Remember that this is the number of social frats and sororities NOT the number or count of their members (one frat or sorority could have 75 plus members)! Again, knowing what is being measured (and hence, what was not measured) and its metric are good starts to proper interpretation.

Now you may be asking yourself, how can a nominal-level variable, such as sex or race, have a “meaningful” mean (no pun intended)? You are asking this question because you know that it does not make sense to calculate the mean for a nominal-level variable and that a percent (e.g., percent male, percent Black, percent Asian) is a more appropriate descriptive statistic. Good question!

If and only if a variable is a dichotomous variable, that is, it is coded 0 = some value and 1 = another value (e.g., 0 = female, 1 = male), then the mean of that variable is the percentage of cases that are coded as 1. Looking at the table, we can see that 44% of the college students in the sample were males (mean = 0.44), 31% were between 17-20 years old, 13% were Black, 8% were Asians, and 15% were married.

Let’s see if you got the hang of interpreting a dichotomous variable coded 0 or 1. What percentage of the sample of students experienced a violent victimization? What percentage experienced a theft? Three percent and 11%, respectively. Do you see how we arrived at these percentages? Take a look at the respective mean of each of these two variables. Now do you see how we arrived at 3% and 11%?

Keep in mind to always KNOW what is being measured (e.g., age, number of nights out partying), in what units (e.g., years, night out), and the values of what is being measured (e.g., 0 = what, 1 = what, 2 = what, etc. or if a continuous measure…any value on the number line in the case, of say, income). Then, looking at the descriptive statistic, you merely interpret the single value (e.g. mean, mode, mean) within what is being measured (e.g., years of age, money, number of victimizations) with respect to its scale or metric (e.g., dollars 0 – infinite, Likert scale).

Another way to use and interpret descriptive statistics is to compare them. No, this is not hypothesis testing, but we can get a relative sense of comparison. For example, we can see that the samples are comprised of a larger percentage of Black students (13%) compared to Asians (8%). By comparing just the magnitude of these two percentages, we can get some idea, a picture if you will, that there will slightly more Blacks in the sample compared to Asians. We cannot tell how many more in terms of actual counts but we can compare the percentage of the sample that is Black to Asians. This also means that what percentage of students were NonBlack or NonAsian? 100% - (13% + 8%) = ??? I will let you do the math here!

Ready to try an assignment in applying and interpreting descriptive statistics? If yes, then get started on the descriptive statistics assignment. You have from Monday – Saturday night at 11:59 pm to turn in this assignment on Blackboard. Enjoy using your new skills!