# What is difference between Student's t test and Chow test?

#### paweljamiolkowski

##### New Member
In the wikipedia thread Student's t-test: Slope of a regression line is used Student' t test for checking a slope of regression. So this seems to be the same as the Chow test. Assumptions aside (normality etc.), why not use the t-test to check for parameter changes? Or is the Chow test just a generalization of the t-test?

#### Miner

##### TS Contributor
The t-test shown in the article focuses solely on detecting differences in the slopes. The Chow test looks at changes in the slope AND the y-intercept.

#### paweljamiolkowski

##### New Member
But after all, you can do a Student's test for two means also to check intercept... The only difference from Chow test would be that you perform the t-test twice: for intercept and slope.

#### noetsi

##### No cake for spunky
There are multiple uses and types of t test that make different assumptions. So you have to be careful when you talk about a t test. Some test single populations, some test if two populations are essentially the same, some pool data and some do not.

#### paweljamiolkowski

##### New Member
The t-test shown in the article focuses solely on detecting differences in the slopes. The Chow test looks at changes in the slope AND the y-intercept
There are multiple uses and types of t test that make different assumptions. So you have to be careful when you talk about a t test. Some test single populations, some test if two populations are essentially the same, some pool data and some do not.
I'm talking about time series. And I also added that assumptions about the distribution are irrelevant. If I want to see if two samples have the same mean, I can either use Student's test, but I can also combine the two samples into one, create a linear regression: y = a , where a is a constant. That is, I do not include the slope at all. On this regression I perform the Chow test. Logically, the test doesn't check for slope, because I removed that condition. It follows that what Miner wrote is not true. Is any difference between the two tests?

#### paweljamiolkowski

##### New Member
I checked my hypothesis in R and I see that I'm right: the t-test and Chow give the same results in terms of p-values. What's interesting is that in gretl they are not the same - the program counts p differently.

#### paweljamiolkowski

##### New Member
One correction - the p-values are the same, but only when the lengths of the two samples are the same (i.e., the parameter changes exactly halfway through the period for the Chow test). If the samples are different, then the p-values are already different. I'm still talking about the algorithm used in R (more specifically, the strucchange package). Interestingly, with a split of say 30:70, sometimes the Chow test correctly rejects the hypothesis, and sometimes the t-test (i.e., after repeatedly generating random data from a normal distribution). It follows that both should be used to reduce the risk of error.

Or to put it another way, if you want to test the difference in means between two samples with a Gaussian distribution (without autocorrelation), you should use the Student's t test with Chow test together by imposing the condition slope = 0.

#### noetsi

##### No cake for spunky
The chow test in time series is used to test if there is a structural break I believe.