Lab 5 Question 2b

[asukajames]

Hello, Could you please clarify "what is the decision rule?" ? If you could explain what this question exactly means, I would appreciated it!

[danafuller]

@asukajames I interpreted that as if the slope was significant then that would be the "decision rule" to indicate that there was secular trend.

[lecy]

For example, in lab 2 where you are trying to establish group equivalency the decision rule would be calculate all of the contrasts, adjust alpha=0.05 by the bonferroni rule, then compare the adjusted alpha to the lowest p-value.

If adjusted alpha > lowest p-value --> do not reject the NULL --> the NULL is that the groups are equivalent

And if the p-value is smaller we conclude the groups are NOT equivalent.

That is an example of a decision rule. Basically state what you conclude if you have a significant result and what you conclude if you have a non-significant result.

I interpreted that as if the slope was significant then that would be the "decision rule" to indicate that there was secular trend.

Specifically regression tables always report p-values and significance. But do you understand which hypothesis is tested by each slope?

In this case with the pre-post data from the comparison group the level of significance associated with b1 corresponds to the trend hypothesis:

b0 = C1
b0 + b1 = C2

# default test in a regression: 
b1 = 0  

# null trend hypothesis: 
C1 = C2
C1 - C2 = 0

# with substitution 
b0 - (b0+b1) = 0
b1 + b0 - b0 = 0
b1 = 0 

So we can see that the test of whether b1=0 is the same as testing for the absence of trend (C1=C2). If we reject the null that means we observe some non-zero level of trend in the data.

Make sense?

[lecy]

Note that this corresponds with the zero trend assumption necessary for reflexive models to be valid.

If you are testing for group equivalency, the null hypothesis would be C1=T1.

You can follow the same logic above to set up a model that tests that assumption if you want to use the post-test only estimator.

The diff-in-diff model is convenient because you get everything in one model. One coefficient represents the trend test, one coefficient represents the pre-treatment equivalency test, and one gives you the program effect.

[asukajames]

@danafuller Thanks for jumping in and for helping me out with my question :)

@lecy Thank you for the explanation!