Divergent validity helps to establish construct validity by demonstrating that the construct you are interested in (e.g., anger) is different from other constructs that might be present in your study (e.g., depression). To assess construct validity in your dissertation, you should first establish convergent validity, before testing for divergent validity.
Divergent validity is important because it is common to come up with an operational definition for a construct that actually measures more than one construct. Unfortunately, we are typically not aware that this has happened; after all, if we had, we wouldn't have made the mistake in the first place; that is, we would have come up with a more reliable operational definition. For example, we think that the questions we ask in a survey about the construct, anger, only measure anger, when in fact they also measure another construct, depression. In order to establish that the scores we obtained when collecting data reflect anger and not depression, we need to test for the divergent validity of the measurement procedures we used to capture anger and depression. To do this, we will have two different measurement procedures and research methods to measure both constructs we are examining. This could mean that we have a total of four measurement procedures, but often you will have used the same research method to collect data for both constructs (e.g., you used participant observation to measure both anger and depression amongst your sample, following this up with a survey, which included questions also measuring both anger and depression).
The extent to which divergent validity has been demonstrated is establish by the strength of the relationship between the scores that are obtained from the two different measurement procedures and research methods that you have used to collect data about the two constructs you are interested in. Unlike convergent validity, where we are interested in the extent to which the scores converge (i.e., we want to see a strong relationship between the two scores on the same construct), with divergent validity, we are interested in the extent to which the scores diverge (i.e., we want to see little or no relationship between the two scores from the two constructs). This is a two-step process:
Establish convergent validity: A strong relationship should be established between the two scores for each of the two constructs (e.g., a strong relationship for anger and a strong relationship for depression).
Establish divergent validity: Little or no relationship should be found between the two scores between the two constructs (e.g., little or no relationship between anger and depression) when comparing the same methods used to collect the data (e.g., comparing anger and depression from the observational scores, and comparing anger and depression from the survey scores).
Let's look at an example:
Construct #1 = Sleep quality
Construct #2 = Sleep quantity
Note: Quality vs. Quantity of Sleep
Let's imagine that in Study #1 we were able to establish a strong relationship between the two sets of scores from the two different measurement procedures under the two research methods (i.e., the scores from the survey and the scores from the participant observation); in other words, we started to establish convergent validity for the construct, sleep quality. However, now that we look back at Study #1, we are concerned that we included sleep quantity within the same set of measures (e.g., the questions in the survey) that we used when measuring sleep quality. We say that we are concerned about including these measures within the same measurement procedure because we are unsure whether sleep quality and sleep quantity are part of the same construct or are two different constructs (i.e., let's imagine that no previous studies are able to answer this question for us). Now if sleep quality and sleep quantity are two different constructs, but we measured them as if they were the same construct, we have introduced a confounding variable that will inevitably reduce the internal validity of our study [see the articles: Extraneous and confounding variables and Internal validity]. Therefore, we decided to examine whether sleep quality and sleep quantity are different constructs.
To achieve this, we use the same research methods as in Study #1; that is, we ask participants to complete a survey, as well as observing participants whilst sleeping. However, the survey contains (a) questions that measure sleep quality and (b) questions that measure sleep quantity. Similarly, when we observe participants, we record scores separately for (a) sleep quality and (b) sleep quantity. In order to assess whether the two constructs (i.e., sleep quality and sleep quantity) are different, we first need to find that both constructs have convergent validity. Therefore, there should be a strong relationship between the survey scores and observational scores for (a) sleep quality and (b) sleep quantity. Next, we need to find that these two constructs are distinct; that is, that we have divergent validity. Therefore, there should be little or no relationship between (a) the survey scores for sleep quality and the survey scores for sleep quantity and (b) the observational scores for sleep quality and the observational scores for sleep quantity. If this is the case, we can be more confident that sleep quality and sleep quantity are, in fact, two separate constructs. Since we had to establish convergent validity before we could establish divergent validity, we can also be satisfied that we have created two valid measurement procedures for sleep quality and sleep quantity (i.e., a survey and observational measurement procedure for sleep quality, and a survey and observational measurement procedure for sleep quantity).
Construct validity can start to be established when you:
Find that the scores that are obtained from the measurement procedures you used from two different methods to assess the construct you are interested in are strongly related; that is, the scores converge, suggesting that both measurement procedures reflect the construct you are interested in, establishing convergent validity.
Find that the scores obtained for the two constructs you are interested in diverge (i.e., are unrelated); that is, there is little or no relationship between the scores for the two constructs when comparing these scores using the same methods. This establishes divergent validity.
We say that construct validity can start to be established when both convergent and divergent validity are established because construct validity is something that is built over time. No single study can establish construct validity [see the article: Construct validity].