Lecture 7 - Type 1 & Type 2 Errors. More on reporting t-statistics. Flashcards
What is an experimental hypothesis?
A statement about what is believed to be true or what could be true.
What are statistical hypotheses?
The null hypothesis and the alternative hypothesis.
Do we report statistical hypotheses in our write ups?
No. It is assumed when you run a t-test that you have postulated a null hypothesis and if the null hypothesis is rejected there must be an alternative hypothesis, an alternative explanation for the results.
What are the 3 steps of the inferential process of NHST?
Step 1: Model - define the statistical hypotheses
Step 2: Data - Run a t-test to find a p-value
Step 3: Decision - decide whether or not to reject the null hypothesis based on the 0.05 threshold
If a p-value is less than 0.05 then we _____________.
Reject the null hypothesis in favour of an alternative hypothesis.
If we reject the null hypothesis this means that our t-value is likely to _______________________.
Come from a different distribution.
Note here that we use the word ‘likely’, this is not a certainty.
What is a Type 1 Error?
A False Positive
When we find a p=value of less than 5% and reject the null hypothesis based on our sample data, but in fact, in the population, the null hypothesis is true.
So when our data shows that there IS a difference, but in reality, there IS NOT a difference.
What is a Type 2 Error?
A False Negative
When we find a p=value of more than 5% and fail to reject the null hypothesis based on our sample data, but in fact, in the population, an alternative hypothesis is true.
So when our data shows that there IS NOT a difference, but in reality, there IS a difference.
The area under the distribution curve where a Type 1 Error could occur is known as _____.
α - alpha
The area under the distribution curve where a Type 2 Error could occur is known as _____.
β - beta
What is the Rejection Level or Significance Level?
The probability with which we are willing to reject the null hypothesis when it is actually correct. Usually 5%. 0.05
What is the Rejection Region?
The set of outcomes that will lead to rejection of the null hypothesis.
The area under the curve on either end of the distribution that is more extreme than the rejection level.
If the rejection level is 5% then the rejection region is the uppermost and lowermost 2.5%
What is the Critical Value of T?
The value of t that we need to exceed in order to obtain a significant difference.
What is a Critical Value?
The value of a test statistic at or beyond which we reject the null hypothesis.
If p is less than .001 how do you report that?
p < .001
