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03 Descriptive Statistics and z Scores in SPSS – SPSS for Beginners

Research By Design · 955 words · 5 min read

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0:08Welcome to the third video in SPSS for Beginners from the RStats Institute

0:15at Missouri State University. So far, we've learned how to create variables in

0:20SPSS, enter data, do a frequency count, and calculate measures of central tendency,

0:26and measures of variability. Collectively, these are called

0:30"Descriptive Statistics," because they describe what the set of numbers looks

0:34like. The mean tells us what is the average height, and the standard

0:39deviation tells us how spread out the heights are around that average. We are

0:45now going to learn a little bit more about descriptive statistics and how to

0:49convert them to z-scores.

0:58Continuing with the data set that we created in the first video, we're going

1:02to get some more descriptive statistics. Go to Analyze -> Descriptive Statistics and

1:08choose Descriptives. When this window pops up, move over all of the variables

1:16except for the random ID number. Now click on Options. Here we are presented

1:25with all kinds of options for descriptive statistics. Some - like mean

1:30and standard deviation - are already checked by default.

1:34Others - like Range or Sum - are available to check, if we want them.

1:40I think that the default settings are good, so let's just continue and click OK.

1:48Here in the output, we see some useful information. For instance, we see the

1:53number of valid scores for each variable. We also see the Valid N (listwise), which

1:59is the number of complete cases with no missing data. For gender, we see that the

2:05minimum is 1; the maximum is 2. That is kind-of-useful, at least for

2:10checking that we do not have any data entry errors, but the mean and standard

2:14deviation for gender is pointless. The average of 1.58 for male and female

2:21does not really tell us anything; it just hints that there were a few more females

2:25than males. On the other hand, the mean and standard deviation for height and

2:30weight can be very useful. For example, the average weight was 133 pounds. The

2:40standard deviation was 13.4 pounds, which tells us that about

2:45two-thirds of our participants are going to be between 13.4 pounds

2:50heavier and 13.4 pounds lighter, than the mean of 133 pounds.

2:59Let me show you one more way to get descriptive statistics. This is going to

3:03give you even more detail about each variable, and more options for plotting

3:08and statistics. Let me show you how. Go to Analyze -> Descriptive Statistics -> Explore.

3:18I'm going to do this twice; the first time we're going to focus just on the scale

3:23variables. Move height and weight into the dependent list box. Now click on

3:30Statistics. Let's really push it this time: click on Outliers and Percentiles,

3:39and then Continue. Now click on Plots and choose Histogram.

3:47We are really going all out, so click Continue and OK. Look at all of this

3:55data! We have every kind of descriptive statistic that you could dream of. We

4:00even have a special box for Percentiles. We have another one that would identify

4:04if we have any outliers or extreme values. And there's our old friend the

4:10histogram. Plus, a small stem-and-leaf plot.

4:14Plus a new graph called a box plot. And those are for height only. We have a

4:21second set of graphs for weight. So, you can see that we get a lot of information

4:26here. But wait...there's more! Let's split all of this by gender.

4:33Go to Analyze -> Descriptive Statistics -> Explore. We're going to keep the same

4:40settings that we had previously. Simply move gender into the factor list,

4:45and then click OK. Now we see the same descriptive statistics have now been

4:54calculated separately for males and females. Remember this splitting

5:00would work similarly if we had three groups, or four, or more. Notice that we

5:05have separate histograms for males and females, separate stem-and-leaf plots, and

5:12the box plots are now side-by-side, so that we can do comparisons. Knowing about

5:19these options for descriptive statistics can help us to visualize our data,

5:24depending upon the level of information that we need. If you need only the basics,

5:31use the Descriptives command. If you want flexibility to choose exactly what

5:38output you get, use Frequencies. And if you want to know the exquisite details

5:44or to split the analysis by a categorical variable, use Explore.

5:51But there is something else that I want to show you about these variables. Let's run

5:56one more analysis and I will show you how

6:00standardized values. Go to Analyze -> Descriptive Statistics -> Descriptives

6:09First, I want to move gender out. We don't need that. Notice that there's a

6:14little box down here that says "Save standardized values as variables." I'm

6:20going to check that, and then click OK. In the output window, we see exactly the

6:27same table that we had last time. But if you go back to your spreadsheet, you'll

6:32notice two new variables. They are called "Z height" and "Z weight." You know what

6:41those are? Those are the z-scores. SPSS converts each height measurement into a

6:47standardized score that tells us how many standard deviation units this score

6:53is away from the mean. Negative z-scores mean that a raw score is below average.

7:01A positive z-score means that it is above average. So, that is a quick and easy way

7:06to get z-scores in SPSS. This was just a quick introduction to z-scores. When

7:14you are ready to learn more, check out these other videos from RStats

7:17Institute and learn how to calculate z-scores by hand or how to do a z-test

7:23using SPSS. Next, we are going to explore correlation and learn how to

7:31measure the relationship between two scale variables.

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