PSYC*1010 Chapter 8: Intro to Hypothesis Testing Flashcards
What is a hypothesis test?
A statistical procedure that uses sample data to evaluate a hypothesis about a population
What is the basic assumption about the effect of a treatment?
If the treatment has an effect, a constant amount will be added or subtracted from each score
What is assumed about the shape and standard deviation of a population after treatment?
The shape and standard deviation for the population after treatment is the same as the original population
What is the unknown population?
The population after treatment
What are the four steps of a hypothesis test?
- State the hypothesis and alpha level
- Set the criteria for a decision
- Collect data and compute sample statistics
- Make a decision
How are hypotheses stated in a hypothesis test?
Stated as two opposing hypotheses in terms of population parameters about the unknown population
What does the null hypothesis state?
That there is no change, difference, or relationship for the general population (the IV has no effect on the DV)
What does the alternative hypothesis state?
That there is a change, difference, or relationship for the general population (the IV has an effect on the DV)
T or F: The null hypothesis and alternate hypothesis are mutually exclusive and exhaustive
True
Which hypothesis is used to predict what type of sample should be obtained?
The null hypothesis
What is the notation used to state hypotheses for two-tailed tests?
H0: μ with treatment = μ without treatment
H1: μ with treatment ≠ μ without treatment
What is the alpha level?
The probability value used to define the concept of “very likely” in a hypothesis test
What is the critical region?
The extreme sample values that are very unlikely (as defined by the alpha level)
What is the conclusion of a hypothesis test if sample data fall in the critical region?
The null hypothesis is rejected
What is used to define the exact location for the boundaries that define the critical region?
The alpha level probability and unit normal table
In a hypothesis test, how is the sample data compared to the hypothesis?
By computing a z-score that describes where the sample mean is located relative to the hypothesized population mean from H0
What is the formula for calculating z-score of a sample mean?
z= (M-μ)/σM
Which statistic is used to make a decision about the null hypothesis?
The z-score
What are the two possible outcomes of a hypothesis test?
- The null hypothesis is rejected
- The null hypothesis fails to be rejected
What conclusion is made about the hypothesis if the data are located in the critical region?
The null hypothesis is rejected
What conclusion is made about the hypothesis if the data are not located in the critical region?
The null hypothesis fails to be rejected
What is a test statistic?
A statistic that summarizes the sample data in a hypothesis test and is used to determine if the data is in the critical region (ex. z-score)
How can the z-score be stated as a ratio?
z= the actual difference between the sample (M) and the hypothesis (μ) / the standard difference between M and μ with no treatment
What does a large value for a test statistic indicate?
That the sample data are very unlikely to have occurred by chance alone
What is a type I error?
- Occurs when a null hypothesis is rejected that is actually true
- The conclusion that a treatment did have an effect when it actually had no effect
What is a type II error?
- Occurs when a null hypothesis fails to be rejected but was actually false
- The conclusion that a treatment did not have an effect when it actually did
Which type of error has the most severe consequences?
Type I
What is the probability of a type I error?
The alpha level
Is it possible to determine a single, exact probability for a type II error?
No
How is the probability of a type II error represented?
Represented by the symbol β
What is the primary concern when selecting an alpha level?
To minimize the risk of a type I error
By convention, what is the largest permissible value for alpha?
0.05
How does the size of an alpha level effect the demands of a hypothesis test?
The lower the alpha level, the more evidence the hypothesis test demands to reject the null hypothesis
What are the two functions of the alpha level?
- Determine the boundaries for the critical region
- Determine the probability of a type I error
In a statistical test, what does a significant result mean?
That the null hypothesis has been rejected
What five things must be included when reporting a rejected null hypothesis in APA?
- The word significant
- The z-score (z= )
- The alpha level (p<.05)
- The type of test (ex. one or two tailed)
- Cohen’s d value (d= )
What four things must be included when reporting a null hypothesis that failed to be rejected in APA?
- The z-score (z= )
- The alpha level (p>.05)
- The type of test (ex. one or two tailed)
- Cohen’s d value (d= )
Do sample means that fall into the critical region have a probability less than or greater than alpha?
Less than alpha (p<α)
Do sample means that fall outside the critical region have a probability less than or greater than alpha?
Greater than alpha (p>α)
In a hypothesis test, what is the conclusion if p<α?
Null hypothesis should be rejected
In a hypothesis test, what is the conclusion if p>α?
Null hypothesis should fail to be rejected
What is the most obvious factor influencing z-scores?
The difference between the sample mean and the hypothesized mean from H0
How does increasing the variability of scores affect the standard error and z-score?
Increasing variability of scores increases standard error and decreases the z-score (value closer to 0)
How does increasing the sample size affect the standard error and z-score?
Increasing sample size decreases standard error and increases the z-score (value farther from 0)
In hypothesis tests with z-scores, what is assumed about sampling?
That participants in the study were selected randomly
In hypothesis tests with z-scores, what is assumed about observations?
That the values in the sample consist of independent observations
In hypothesis tests with z-scores, how is the assumption that observations are independent satisfied?
By using a random sample
In hypothesis tests with z-scores, what is assumed about the standard deviation before and after treatment?
That the standard deviation for the unknown population (after treatment) is the same as the population before treatment
In hypothesis tests with z-scores, what is assumed about the sampling distribution?
That it’s normal
What is a directional/one-tailed test?
- The statistical hypotheses (H0 and H1) make a statement about the direction of the effect
- The critical region is only in one end of the distribution
What is the notation used to state hypotheses for one-tailed tests?
H0: μ with treatment = μ without treatment
H1: μ with treatment </> μ without treatment
For a one-tailed/directional test, do the two hypotheses concern the general population or the individuals in the sample?
The general population
If the prediction in a one-tailed test is a decrease, in which end of the distribution is the critical region?
The left-hand tail of the distribution
If the prediction in a one-tailed test is an increase, in which end of the distribution is the critical region?
The right-hand tail of the distribution
How do the four main steps of a hypothesis test change when using a one-tailed test rather than a two-tailed test?
- Directional prediction is incorporated into the statement of H0 and H1
- Criteria for decision changes… Critical region is located entirely in one end of the distribution, rather than split between two
- Calculate z-score (same as two-tailed)
- Make a decision (same as two-tailed)
What is the major distinction between one- and two- tailed tests?
- The criteria used to reject H0
- One-tailed: allow H0 to be rejected when the distance between the sample and population is relatively small
- Two-tailed: require a relatively large distance between the sample and population to reject H0
Which type of hypothesis test is more sensitive?
One-tailed
Which type of hypothesis test is more precise?
One-tailed
Which type of hypothesis test is more rigorous/requires more evidence to reject H0?
Two-tailed
Generally, when are one-tailed tests used?
When there is a strong justification for making a directional prediction
What are the two serious limitations when using a hypothesis test to establish the significance of a treatment?
- That the focus is on the data rather than the hypothesis
- That a significant treatment doesn’t necessarily indicate a substantial treatment
What does effect size provide a measurement of?
The absolute magnitude of a treatment effect, independent of the size of sample(s) being used and the decision rule (alpha)
What is cohen’s d?
A standard measure of effect size
What does cohen’s d measure?
The size of the treatment effect in terms of standard deviation
What is the formula for cohen’s d?
d= (μ with treatment - μ with no treatment)/σ
T or F: Cohen’s d is an estimation value.
True
Why is cohen’s d an estimated value?
Because the population mean after treatment is unknown, so the treated sample must be used in its place as an estimate of what it would actually be
What range of values for cohen’s d indicate a small effect size?
0.2 ≤ d < 0.5
What range of values for cohen’s d indicate a medium effect size?
0.5 ≤ d < 0.8
What range of values for cohen’s d indicate a large effect size?
0.8 ≤ d
When referencing overlapping distributions, what does cohen’s d help identify?
The degree of separation between two overlapping distributions
What is the power of a statistical test?
The probability that the test will correctly reject a false null hypothesis
As effect size increases, what happens to the power?
As effect size increases, so does the power of the test
How does sample size affect power?
In general, a larger sample produces a greater power for a hypothesis test
How does alpha level affect power?
Reducing the alpha level will reduce the power of the test
What do confidence intervals measure?
Confidence intervals estimate the possible range of values for the potential mean of the unknown population that would correspond with the sample mean
What is the formula for confidence intervals?
CI= M ± (critical z for that level of confidence) σM
