Stats - null hypothesis and p value
If you are assessing the safety of a vehicle or an airplane, what type of alpha level will you want?
-a very low alpha level
In order to perform a statistical test of the hypothesis, the null must be a statement about what?
-about the value of a parameter for a model
In terms of the person and the disease, what does this mean?
-an infected person is diagnosed disease free
When must you select the alpha level, before or after you look at the data?
-before you look at the data
How can we reduce β for all alternative parameter values?
-by increasing the alpha level
What is one second type of test help you to confirm the results of a hypothesis test?
-confidence intervals
What can be used as a shortcut for hypothesis tests?
-critical values (z*)
What impact does increasing the sample size have on both Type I and Type II error?
-decreases both
Does this make it easier or harder to make Type I errors?
-easier to make Type I errors
As alpha level increases, does it become easier or harder to reject the null?
-easier to reject the null
If we observe a statistic whose P-value based on the null hypothesis is greater than the alpha level, what do we do?
-fail to reject the null hypothesis
True or false: the P-value is the probability that the null hypothesis is true.
-false
What is it tell us the probability of?
-getting results at least as unusual as the observed statistic, given that the null hypothesis is true
What is the value of β?
-harder to assess than the alpha level
Does this make it easier or harder to make Type II errors?
-harder to make Type II errors
As β increases, does the probability of a Type II error increase or decrease?
-increases
What impact does this have on the power of the test?
-increases power
Which type of error is more serious?
-it depends on the situation
What is one disadvantage to using this method?
-it gives us less information about the hypothesis because we don't have the P-value to think about
Reducing the alpha to lower the chance of committing a Type I error will have what impact on a critical value?
-it will move it
When the power is high, we can be confident that we...?
-looked hard enough
Does statistical significance carry with it any sense of practical importance or impact?
-no
Is the test then statistically significant?
-no, it is not
When the P-value falls below the alpha level, we say that the test is...?
-statistically significant
As the probability of a Type II error increase, what happens to the power of the test?
-test will decrease (per the relationship power = 1 - β)
In medical disease testing, what is typically the null hypothesis?
-that a person is healthy
What is the alternative then?
-that he or see has the disease we're testing for
What value corresponds to the likelihood of making a Type I error?
-the alpha level
How do we choose the null hypothesis?
-the appropriate null hypothesis arises directly from the context of the problem; it is dictated by the situation
What value corresponds to the likelihood of making a Type II error?
-the beta level
What is a type II error?
-the null hypothesis is false, but we fail to reject it
What is a type I error?
-the null hypothesis is true, but we mistakenly reject it
Since we know that beta is the probability that a test fails to reject a null hypothesis, what is the power of a test equal to?
-the probability that a test rejects a null hypothesis: 1 - beta
What is the power of a test?
-the probability that it correctly rejects a false null hypothesis
What is the alpha level also known as?
-the significance level
Whenever a study fails to reject its null hypothesis, what comes into question?
-the test's power
If we observe a statistic whose P-value based on the null hypothesis is less than the alpha level, what do we do?
-we reject the null hypothesis
In a jury trial, when does a Type I error occur?
-when a jury convicts an innocent person
In a jury trial, when does a Type II error occur?
-when a jury fails to convict a guilty person
The movement of this critical value will have what impact on β?
-β will increase
In general, a confidence interval with a confidence level of C% corresponds to a two-sided hypothesis test with an alpha level of ____?
In general, a confidence interval with a confidence level of C% corresponds to a two-sided hypothesis test with an alpha level of 100 - C%?
What should you say when you have not found sufficient evidence to reject the null according to the standard that you have established?
-"The data have failed to provide sufficient evidence to reject the null hypothesis." -->don't ever say that you "accept the null hypothesis."
What are four common alpha levels?
-0.10 -0.05 -0.01 -0.001
Medically speaking, what is a Type II error know as?
-a "false negative"
Medically speaking, what is a Type I error known as?
-a "false positive"
In terms of the person and the disease, what does this mean?
-a healthy person is diagnosed with a disease
If you are wondering whether folks prefer their pizza with or without pepperoni, what type of alpha level might you choose?
-a higher alpha level
What is an alpha level?
-the threshold P-value that determines when we reject a null hypothesis
What is one good way to identify both the null and the alternative hypothesis?
-think about the "why" of the situation
What is the only way to reduce both types of error?
-to collect more evidencce
What is one way to keep the names straight?
-to remember that we start by assuming that the null hypothesis is true, so a Type I error is the first kind of error that we could make
Since confidence intervals are naturally two-sided, what type of z-test do they correspond to?
-two-sided z-tests
When we conduct a hypothesis test, what are we really trying to do in terms of the null hypothesis?
-we are trying to detect a false null hypothesis
Since it can be hard to justify the selection of a given alpha level, what value do we often arbitrarily choose?
0.05
When we perform a hypothesis test, what two types of errors can we make?
1. Type I error 2. Type II error
A P-value is actually a ______________ probability.
A P-value is actually a CONDITIONAL probability.
A confidence interval with a confidence level of C% corresponds to a one-sided hypothesis with an alpha level of _____?
A confidence interval with a confidence level of C% corresponds to a one-sided hypothesis with an alpha level of 1/2*(100-C)%?