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Descriptive Statistics

Descriptive Statistics Program Transcript

MATT JONES: Some of the most basic, yet most frequently used in useful sets of statistics, are measures of central tendency and variability. Let's go to SPSS.

To perform a descriptive statistics analysis, let's first click on Analyze. And from the drop down menu hit Descriptive Statistics. You'll see that there are a number of options to the right. But let's first start by exploring frequencies.

Let's say I want to perform a descriptive statistics analysis of the variable age of respondent. That is I'd like to know some summary statistics about my sample. I know this is a metric or interval ratio level variable because I can see the scale ruler indicates as such.

If I click on it, I can click on the arrow to move it over to the Variables box. I have to click on Statistics to tell SPSS what statistics I would like from the analysis. For measures of central tendency, I'm going to select Mean, Median, and Mode. For measures of dispersion, I'm going to select Standard Deviation, Range, Minimum, and Maximum. And you can certainly select other options as well.

For distribution, I'm provided with two statistics. I can request the skew or skewness, and also kurtosis. Select Continue. I'm also given the option of selecting some charts or a figure. So I will select Charts.

Since this is a metric global variable, I think that a histogram is the most appropriate graphical presentation. Once I hit OK, I will receive my output. The first box give us all of our summary statistics.

From these, I can see my variable, age of respondent, and that I have 1,483 valid cases with 17 of them missing. The mean age of my sample is 49.21 years with the median a 49 years. The most frequently occurring or the mode is 29 years of age.

The standard deviation or the measure of spread how far my data are dispersed in the sample is 17.55. Using the empirical rule, I know that approximately 68% of my data will fall within this range. That is 49.2 years of age plus or minus 17.5 years.

I have a skewness statistic of 0.273. A statistic of 0 indicates no skewness at all. That is a perfect, normal distribution. The further I get away from 0, the further I deviate from a normal distribution. 0.273 is rather close to 0. And a half slightly positive skew.

Descriptive Statistics

For all intents and purposes, as far skewness is concerned, I can consider this data non-skewed. I have a kurtosis statistic of negative 0.801. Again, the further I get away from 0, the further I deviate from a normal distribution.

Positive kurtosis indicates a pointy and tail heavy distribution. Negative kurtosis indicates a rather flat distribution. I have a range of 71 years of age, which is the difference of my minimum and maximum. As denoted here, with the minimum age of the sample, with the respondent being 18, and the maximum being 89 years of age.

The next piece of output I'm provided with is the age of respondents. Frequency tables for metric level variables, that is interval or ratio level variables, can be somewhat overwhelming. Therefore, it's often recommended that you only select frequency tables for categorical variables.

But for the purposes of demonstration, you can see that in my sample I have 4 respondents who are 18 years of age, 5 respondents who are 19 years of age, going on up to 22 respondents who are 89 or older. I know from my maximum statistic that the oldest person or persons in the sample are 89.

Below I'm provided with a histogram. Again, a histogram is a good visual depiction of the data. And I can see from the distribution of the data that this rather closely resembles a normal distribution.

The analysis of age of respondent is appropriate because it's a metric level variable. But there are plenty of categorical variables that we would like to request descriptive statistics on. Let's look at an example.

Analyze, Descriptive Statistics, and remain within the frequency dialog box. I would like to request descriptive statistics on the respondents highest degree. You see highlighted here, with the three circles off to the left, indicating this is a categorical variable. Move this over to my variables box. If I click on Statistics, I'm not going to request central tendency, measures of central tendency, or measures of dispersion for this particular variable because of its categorical nature.

I can however, still request a chart type. I will request a bar chart. Continue.

Once I click OK, I obtain my output. I can see here that I have 1,500 valid cases. I requested only a frequency table, again, due to the categorical nature of this variable.

I see that 207 people in the sample have less than a high school degree. 742 have a high school degree. 112, a junior college. 277, bachelor. And 162, a graduate degree. SPSS then breaks down the percentage of these respective categories for the sample.

Descriptive Statistics

If I scroll down, I'm able to see my chart. Again, another visual description of the data. Clearly I can see that for the majority of the sample, the highest level of education attained is a high school degree.

We've just gone through a couple of different ways to request some basic summary statistics from SPSS, both for interval ratio level variables and also categorical variables. How you obtain summary statistics from SPSS or by which procedure you do it, will often depend upon the context, what you would like to know, and how your variables are measured.