Z tests Flashcards
Null hypothesis
- Designated by: HO or HN Pronounced as “H oh” or “H-null”
- The null hypothesis represents a theory that has been put forward, either
because it is believed to be true or because it is to be used as a basis for
argument, but has not been proved.
Alternative hypothesis
- Designated by: H1 or HA
- The alternative hypothesis is a statement of what a hypothesis test is set up to
establish. - Opposite of Null Hypothesis.
- Only reached if HO is rejected.
- Frequently “alternative” is actual desired conclusion of the researcher!
Which hypothesis do we accept/ reject?
The final conclusion, once the test has been carried out, is always given in terms of the null hypothesis. We either ‘reject H0 (in favour of H1)’ or ‘do not reject H0’; we never conclude ‘reject H1’, or even ‘accept H1’.
How can we determine which
hypotheses is more likely to be true?
- Null Hypothesis Significance Tests
Significance tests are quantitative techniques to evaluate the probability of observing the data, given that the null hypothesis is true.
This information is used to make a binary (yes/no) decision about whether the null hypothesis is a viable explanation for the study results.
What does it mean if the null hypothesis is true?
If null hypothesis is true, then sample mean is likely to be close to the known population mean (due to
randomness).
The two sections in which the distributions of sample means are divided into
- Sample means that are likely to be obtained if H0 is true; that is, sample means that are close to the null hypothesis (i.e., population mean μ)
- Sample means that are very unlikely to be obtained if H0 is true (those in the critical region: shaded
region); that is, sample means that are very different from the null hypothesis (i.e., population mean μ).
- Sample means that are very unlikely to be obtained if H0 is true (those in the critical region: shaded
When can the z test be used
whenever mean and standard
deviation for the variable of interest is known for the entire population.
What is Error I
The hypothesis is rejected when it should be accepted
What is Error II
The hypothesis is accepted when it should be rejected
What is Error III
Answering the wrong question
What is Error IV
Answering the right question from the wrong paradigm
What is a directional (alternative) hypothesis (e.g., greater than …, higher than …, shorter than …) examined using
a one tailed test
What is a non-directional hypothesis
(e.g., different from …) examined using
A two tailed test
Steps to perform statistical tests
- State the hypothesis
- Select statistical test and significance level
- Collection of sample data
- Finding the region of rejection
- Calculate the test statistic
- Make statistical decision
What is the alpha level?
The upper limit of p-value, that should be acceptable to make a statistical decision has to be decided
before testing the hypothesis
What risk does the alpha level represent?
As the alpha level of 0.05 represents the risk that the results could be obtained by chance and not
due to the experiment.
What is type I error
Your test is
significant (p < .05), so you reject
the null hypothesis, but the null
hypothesis is actually true.W
What is Type II error
Your test is not
significant (p > .05), you don’t
reject the null hypothesis, but you
should have because it is false.
What is alpha in terms of error
is the probability of making a Type I error when the null
hypothesis is true, The alpha level thus indicates about how much
probability of making a Type I error researchers will tolerate.
What is beta in terms of error
on the other hand, represents the probability of making a
Type II error if the alternative hypothesis is true. The probability of
not making a Type II error is therefore 1 – β, which refers to the
power of the statistical test of hypothesis.
