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Find z-Scores in SPSS; How to Standardize a Variable; Find z Scores
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This video shows how to standardize a variable using SPSS. Standardizing a variable puts them in z score form, where the mean is equal to zero and the standard deviation is equal to one.
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Video Transcript: Now to calculate Z scores on this variable, what we want to do is go to Analyze on the Menu bar, select Descriptive Statistics, and then select our option Descriptives here. Move the variable, scores, over to the variable box and then right here, Save standardized values as variables, we want to click on this box and when we do that this is what is going to produce the z-scores in SPSS. Let's go ahead and go to Options as well. And under Options, notice we have the Mean and Standard Deviation selected by default, as well as Minimum and Maximum. Let's go ahead and deselect Minimum and Maximum for now. Click Continue and then click OK. The SPSS output window opens and here we have just one table of output or we have the mean and standard deviation for the variable, scores. OK so you may ask yourself, what happened, where the z-scores? Well the z-scores are actually provided in the Data Editor window. So if we click here we'll go back to our Data Editor, and notice this column now, Zscores. So we have a z score for each of the original scores, a z score is calculated and provided in SPSS. If we go to our output here by clicking on Window and select Output, then you'll see here in our output we have a mean, if we round to a whole number place, the mean is equal to 47, rounding once again to a whole number. OK so a mean of 47, keep that in mind. Let's go back to our data. Let's take a few of these as an example. Here we have a score of 32, recall that the mean was 47 when we rounded, 32 is below 47 and notice how our z score is negative. 39 is also less than 47 and notice how z score is once again negative. Moving down here to observation 7, 54, that's greater than our mean of 47, and notice now that our z score is positive. Taking one more example, 76, that's also greater than the mean of 47, and once again z score is positive. This illustrates a property of z scores, and that is, values that are less than the mean of 47, would produce negative Z scores. Whereas values that are greater than the mean of 47, would produce positive Z scores. OK that's a basic property of the z score distribution. Something else that's interesting and you may have learned in your introductory statistics course, is what the mean and standard deviation of a z score distribution is equal to. Let's take a look at that on our own. Go to Analyze, Descriptive Statistics, and then go to Descriptives once again. And then now let's move our new variable, notice this variable here, z score, this is new, we produced it by checking on this box before. Let's move it over and then let's deselect this this time, because we already have our z score variable. Click OK, and now notice what we get here in our output, in this second table here. We have the same mean and standard deviation for scores, as we did before, which shouldn't be surprising since it's the same variable. But this is where it's interesting. Notice the mean and standard deviation for the z score variable. Now this here is scientific notation, 0E-7, and what that means is, it's point six zeros and then a number. So .000000 and then some number. In other words it's very, very small, and what that really means is it's just rounding error, this value is really zero for all intents and purposes. It's just a rounding error. So the mean is equal to 0, and the standard deviation is equal to 1, which is another property of a z score distribution. If you take any variable in SPSS, no matter what the values are, and you calculate z scores on that variable, and you obtain a mean and standard deviation of the new z score variable, the z-score variable always have a mean of zero and a standard deviation of one, just as we see right here. Just keep in mind there may be a little bit of rounding error. This concludes the tutorial on obtaining z scores in SPSS.
YouTube Channel: Quantitative Specialists
Channel Description: For step by step help with statistics, with a focus on SPSS. Subscribe today!
(Remember to click on "Subscribe")
Video Transcript: Now to calculate Z scores on this variable, what we want to do is go to Analyze on the Menu bar, select Descriptive Statistics, and then select our option Descriptives here. Move the variable, scores, over to the variable box and then right here, Save standardized values as variables, we want to click on this box and when we do that this is what is going to produce the z-scores in SPSS. Let's go ahead and go to Options as well. And under Options, notice we have the Mean and Standard Deviation selected by default, as well as Minimum and Maximum. Let's go ahead and deselect Minimum and Maximum for now. Click Continue and then click OK. The SPSS output window opens and here we have just one table of output or we have the mean and standard deviation for the variable, scores. OK so you may ask yourself, what happened, where the z-scores? Well the z-scores are actually provided in the Data Editor window. So if we click here we'll go back to our Data Editor, and notice this column now, Zscores. So we have a z score for each of the original scores, a z score is calculated and provided in SPSS. If we go to our output here by clicking on Window and select Output, then you'll see here in our output we have a mean, if we round to a whole number place, the mean is equal to 47, rounding once again to a whole number. OK so a mean of 47, keep that in mind. Let's go back to our data. Let's take a few of these as an example. Here we have a score of 32, recall that the mean was 47 when we rounded, 32 is below 47 and notice how our z score is negative. 39 is also less than 47 and notice how z score is once again negative. Moving down here to observation 7, 54, that's greater than our mean of 47, and notice now that our z score is positive. Taking one more example, 76, that's also greater than the mean of 47, and once again z score is positive. This illustrates a property of z scores, and that is, values that are less than the mean of 47, would produce negative Z scores. Whereas values that are greater than the mean of 47, would produce positive Z scores. OK that's a basic property of the z score distribution. Something else that's interesting and you may have learned in your introductory statistics course, is what the mean and standard deviation of a z score distribution is equal to. Let's take a look at that on our own. Go to Analyze, Descriptive Statistics, and then go to Descriptives once again. And then now let's move our new variable, notice this variable here, z score, this is new, we produced it by checking on this box before. Let's move it over and then let's deselect this this time, because we already have our z score variable. Click OK, and now notice what we get here in our output, in this second table here. We have the same mean and standard deviation for scores, as we did before, which shouldn't be surprising since it's the same variable. But this is where it's interesting. Notice the mean and standard deviation for the z score variable. Now this here is scientific notation, 0E-7, and what that means is, it's point six zeros and then a number. So .000000 and then some number. In other words it's very, very small, and what that really means is it's just rounding error, this value is really zero for all intents and purposes. It's just a rounding error. So the mean is equal to 0, and the standard deviation is equal to 1, which is another property of a z score distribution. If you take any variable in SPSS, no matter what the values are, and you calculate z scores on that variable, and you obtain a mean and standard deviation of the new z score variable, the z-score variable always have a mean of zero and a standard deviation of one, just as we see right here. Just keep in mind there may be a little bit of rounding error. This concludes the tutorial on obtaining z scores in SPSS.
YouTube Channel: Quantitative Specialists
Channel Description: For step by step help with statistics, with a focus on SPSS. Subscribe today!
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