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Convergent and discriminant validity are both considered subcategories or subtypes of construct validity. The important thing to recognize is that they work together -- if you can demonstrate that you have evidence for both convergent and discriminant validity, then you've by definition demonstrated that you have evidence for construct validity. But, neither one alone is sufficient for establishing construct validity.

I find it easiest to think about convergent and discriminant validity as two inter-locking propositions. In simple words I would describe what they are doing as follows:

 measures of constructs that theoretically should be related to each other are, in fact, observed to be related to each other (that is, you should be able to show a correspondence or convergence between similar constructs) and measures of constructs that theoretically should not be related to each other are, in fact, observed to not be related to each other (that is, you should be able to discriminate between dissimilar constructs)

To estimate the degree to which any two measures are related to each other we typically use the correlation coefficient. That is, we look at the patterns of intercorrelations among our measures. Correlations between theoretically similar measures should be "high" while correlations between theoretically dissimilar measures should be "low".

The main problem that I have with this convergent-discrimination idea has to do with my use of the quotations around the terms "high" and "low" in the sentence above. The question is simple -- how "high" do correlations need to be to provide evidence for convergence and how "low" do they need to be to provide evidence for discrimination? And the answer is -- we don't know! In general we want convergent correlations to be as high as possible and discriminant ones to be as low as possible, but there is no hard and fast rule. Well, let's not let that stop us. One thing that we can say is that the convergent correlations should always be higher than the discriminant ones. At least that helps a bit.

Before we get too deep into the idea of convergence and discrimination, let's take a look at each one using a simple example.

Convergent Validity

To establish convergent validity, you need to show that measures that should be related are in reality related. In the figure below, we see four measures (each is an item on a scale) that all purport to reflect the construct of self esteem. For instance, Item 1 might be the statement "I feel good about myself" rated using a 1-to-5 Likert-type response format. We theorize that all four items reflect the idea of self esteem (this is why I labeled the top part of the figure Theory). On the bottom part of the figure (Observation) we see the intercorrelations of the four scale items. This might be based on giving our scale out to a sample of respondents. You should readily see that the item intercorrelations for all item pairings are very high (remember that correlations range from -1.00 to +1.00). This provides evidence that our theory that all four items are related to the same construct is supported. Notice, however, that while the high intercorrelations demonstrate the the four items are probably related to the same construct, that doesn't automatically mean that the construct is self esteem. Maybe there's some other construct that all four items are related to (more about this later). But, at the very least, we can assume from the pattern of correlations that the four items are converging on the same thing, whatever we might call it.

Discriminant Validity

To establish discriminant validity, you need to show that measures that should not be related are in reality not related. In the figure below, we again see four measures (each is an item on a scale). Here, however, two of the items are thought to reflect the construct of self esteem while the other two are thought to reflect locus of control. The top part of the figure shows our theoretically expected relationships among the four items. If we have discriminant validity, the relationship between measures from different constructs should be very low (again, we don't know how low "low" should be, but we'll deal with that later). There are four correlations between measures that reflect different constructs, and these are shown on the bottom of the figure (Observation). You should see immediately that these four cross-construct correlations are very low (i.e., near zero) and certainly much lower than the convergent correlations in the previous figure. As above, just because we've provided evidence that the two sets of two measures each seem to be related to different constructs (because their intercorrelations are so low) doesn't mean that the constructs they're related to are self esteem and locus of control. But the correlations do provide evidence that the two sets of measures are discriminated from each other.

Putting It All Together

OK, so where does this leave us? I've shown how we go about providing evidence for convergent and discriminant validity separately. But as I said at the outset, in order to argue for construct validity we really need to be able to show that both of these types of validity are supported. Given the above, you should be able to see that we could put both principles together into a single analysis to examine both at the same time. This is illustrated in the figure below.

The figure shows six measures, three that are theoretically related to the construct of self esteem and three that are thought to be related to locus of control. The top part of the figure shows this theoretical arrangement. The bottom of the figure shows what a correlation matrix based on a pilot sample might show. To understand this table, you need to first be able to identify the convergent correlations and the discriminant ones. There are two sets or blocks of convergent coefficients (in green), one 3x3 block for the self esteem intercorrelations and one 3x3 block for the locus of control correlations. There are also two 3x3 blocks of discriminant coefficients (shown in red), although if you're really sharp you'll recognize that they are the same values in mirror image (Do you know why? You might want to read up on correlations to refresh your memory).

How do we make sense of the patterns of correlations? Remember that I said above that we don't have any firm rules for how high or low the correlations need to be to provide evidence for either type of validity. But we do know that the convergent correlations should always be higher than the discriminant ones. take a good look at the table and you will see that in this example the convergent correlations are always higher than the discriminant ones. I would conclude from this that the correlation matrix provides evidence for both convergent and discriminant validity, all in one analysis! But while the pattern supports discriminant and convergent validity, does it show that the three self esteem measures actually measure self esteem or that the three locus of control measures actually measure locus of control. Of course not. That would be much too easy.

So, what good is this analysis? It does show that, as you predicted, the three self esteem measures seem to reflect the same construct (whatever that might be), the three locus of control measures also seem to reflect the same construct (again, whatever that is) and that the two sets of measures seem to be reflecting two different constructs (whatever they are). That's not bad for one simple analysis.

OK, so how do we get to the really interesting question? How do we show that our measures are actually measuring self esteem or locus of control? I hate to disappoint you, but there is no simple answer to that (I bet you knew that was coming). There's a number of things we can do to address that question. First, we can use other ways to address construct validity to help provide further evidence that we're measuring what we say we're measuring. For instance, we might use a face validity or content validity approach to demonstrate that the measures reflect the constructs we say they are (see the discussion on types of construct validity for more information).

One of the most powerful approaches is to include even more constructs and measures. The more complex our theoretical model (if we find confirmation of the correct pattern in the correlations), the more we are providing evidence that we know what we're talking about (theoretically speaking). Of course, it's also harder to get all the correlations to give you the exact right pattern as you add lots more measures. And, in many studies we simply don't have the luxury to go adding more and more measures because it's too costly or demanding. Despite the impracticality, if we can afford to do it, adding more constructs and measures will enhance our ability to assess construct validity using approaches like the multitrait-multimethod matrix and the nomological network.

Perhaps the most interesting approach to getting at construct validity involves the idea of pattern matching. Instead of viewing convergent and discriminant validity as differences of kind, pattern matching views them as differences in degree. This seems a more reasonable idea, and helps us avoid the problem of how high or low correlations need to be to say that we've established convergence or discrimination.

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