Module 3 Flashcards
What is a Hypothesis test?
A hypothesis test is a statistical procedure aiming
to decide if a statement, called the null hypothesis is plausible according to the data of a sample, or if it must be rejected.
What are the 5 test procedures to test a hypothesis?
- Formulate the hypotheses
- Calculate the p-value
- Make a decision
- Ensure the test validity
- Appropriately interpret the result
How is the hypothesis formulated?
There are two opposite statements
called H0 and H1, between which we will have to decide.
H0 is often called the null hypothesis, and H1, the alternative hypothesis.
Hypotheses are always statements regarding
the population studied.
Why is the p-value important?
The p-value is important because it is the measure which the decision rule is based on, whether we decide in favor of H0 or H1.
how to assess the importance of the difference between H0 and H1?
We compute the ratio of the observed difference between the sample data and what is expected under H0 over the estimated standard
deviation of this measured difference in the numerator.
Define a test statistic?
It is the standardized measure, which allows us to judge the difference between the data and H0.
The test statistic is a measure that distinguishes between H0 and H1 that is corrected for the estimation error
The value of the test statistic is usually calculated using software.
What does a large test statistic or distance suggest?
If the test statistic or distance is large, meaning that what is observed in the sample is far from what is expected under H0, it is a sign that H0 is probably false.
This suggests we conclude in favor of H1.
What does a small test statistic or distance suggest?
If the distance is small, the data is compatible with H0 and it makes sense to keep the assumption.
How can the values of a test statistic be described?
The values of the test statistic can be described by a probability distribution.
When will the deviation of the data from H0 will be judged.
It is on the basis of the probability distribution of the sample distance
under H0, that the deviation of the data from H0 will be judged.
What does it likely mean If the distance, or test statistic, calculated from the data we observed, is situated in the tail ends of the distribution?
This means our data are unlikely under H0.
This justifies the conclusion in favor of H1.
What does it mean if the test statistic is in the center of the curve?
If the test statistic that we calculate is in the center of the curve,
this means our data are compatible with H0.
Therefore, there is no reason to reject the hypothesis.
How do we universally interpret the test statistic?
The distribution varies between each test statistic.
There are no universal markers to interpret the test statistic.
Fortunately, it is possible to convert to another measure which is universal, the p-value.
What is the P-Value?
The P value is a measure of the compatibility between the observed data and H0. It is a probability.
Unlike the test statistic, the P value is interpreted exactly
the same for all statistical tests.
The P value is usually calculated by a software.
How is the P-Value calculated?
The P value is usually calculated by a software.
To calculate, we assume H0 is true for the population.
The P value is defined as the probability of observing data that is equivalent to or either further from what is expected for H0, than what we actually observed, should the data collection be repeated and the same test procedure applied.
Hence, it is the probability that new data collected would be further away from H0 than the measured distance -2.31 (In the bank example) .
