28 Questions
What does it mean if the Shapiro-Wilk test of normality is significant?
The data are not normally distributed
How can one remember the significance of the Shapiro-Wilk test?
It's a test of normality
What does Levene's Test for Equality of Variances assess?
Equality of sample variances
What does a p-value greater than .05 in the Shapiro-Wilk test suggest?
Data are normally distributed
In the context provided, what is the purpose of testing two group's variances using Levene's Test?
To check for homogeneity of variances
What is another name for the Paired-Samples t-test?
Repeated Measures t-test
What type of variable should the dependent variable be in a paired-samples t-test?
Continuous
In a paired-samples t-test, how many categorical, related groups should the independent variable consist of?
Two
What does the paired-samples t-test compare the mean difference between?
Matched pairs
What type of distribution should the differences in the dependent variable between related groups have for the dependent t-test?
Normal distribution
What does a statistically significant correlation coefficient indicate?
The value of one variable follows the value of another closely enough to not likely be a coincidence.
What is the key point to remember about correlation and causation?
Correlation never implies causation.
What is a spurious correlation?
An illegitimate presumption that two variables are correlated when they are not.
What can be the result of spurious correlation?
A false appearance of correlation due to chance or unapparent factors.
What are the assumptions made with respect to Pearson's correlation?
The variables must be either interval or ratio - i.e., continuous.
Which statement best describes the relationship between a rise in 'Variable A' and a rise in 'Variable B' according to the text?
'Variable A' and 'Variable B' can be influenced by other unknown factors causing them to rise together.
What is the purpose of assumption #5 when conducting an independent t-test?
To ensure the dependent variable is normally distributed in each group
Why is the independent t-test considered 'robust' to violations of normality?
Because it can still provide valid results even with slight deviations from normality
What does an unbalanced design in an independent t-test refer to?
Unequal sample sizes across the groups
How does having unequal sample sizes affect the validity of an independent t-test?
Negatively impacts the validity of the test
Why is it preferable to have a balanced design in an independent t-test?
It reduces the impact of violating assumptions on test validity
In an independent-samples t-test, what is subtracted from what according to the formula?
Mean of Group 1 from Group 2
What is one of the assumptions described in the text regarding correlation coefficients?
A linear relationship between two variables is necessary.
In what scenario will a correlation coefficient like the Pearson product-moment correlation coefficient 'r' under-estimate the relationship between two variables?
When there is a curvilinear relationship between the variables.
What type of relationship does a correlation coefficient like 'r' assume between two variables?
Positive linear relationship.
Why does a correlation coefficient under-estimate the strength of the relationship between anxiety and performance on a complex task?
Because the relationship is non-linear.
What should be done with outliers according to one of the assumptions mentioned in the text?
Outliers should be kept to a minimum or removed entirely.
Which statement best describes how a correlation coefficient like 'r' handles relationships between two variables?
'r' is limited to measuring linear relationships only.
Study Notes
Independent T-Test
- Assumption #5: Dependent variable should be approximately normally distributed for each group of the independent variable.
- The independent t-test is "robust" to violations of normality, meaning that this assumption can be slightly violated and still provide valid results.
- Assumption #6: The two groups' (within group) variances are equal in the population.
- The independent t-test assumes the variances of the two groups being measured to be about the same.
Sample Size and Unequal Ns
- A study should have at least six participants in each group to proceed with an independent-samples t-test.
- Ideally, you would have more participants in each group.
- An independent-samples t-test will run with less than six participants, but the ability to infer/generalize to a larger population will be more difficult.
- A balanced design (same number of participants in each group) is ideal, although it can be hard to achieve in practice.
- An unbalanced design (unequal sample sizes) can negatively affect the validity of the test.
Independent T-Test Formula
- The formula subtracts the mean of Group 1 from the mean of Group 2.
- The order of the subtraction does not affect the statistical significance of the t.
Dependent T-Test (Paired-Samples T-Test)
- The dependent t-test is used to determine whether the mean difference between paired observations is statistically significantly different from zero.
- Participants are either the same individuals tested at two time points or under two different conditions on the same dependent variable.
- Alternatively, two groups of participants that have been matched (paired) on one or more characteristics can be tested on one dependent variable.
Dependent T-Test Assumptions
- Assumption #1: One dependent variable measured at the continuous (i.e., ratio or interval) scale.
- Assumption #2: One independent variable with two categorical, related groups or matched pairs.
- Assumption #3: No significant outliers in the differences between the two related groups.
- Assumption #4: The distribution of the differences in the dependent variable between the two related groups should be approximately normally distributed.
Correlation
- A statistically significant correlation coefficient indicates that the value of one variable follows the value of another closely enough that it's not likely to be a coincidence.
- Correlation does not imply causation, but it does not rule it out.
- A statistically significant correlation can be a reflection of causation.
Spurious Correlations
- A false presumption that two variables are correlated when, in reality, they are not.
- Spurious correlation can be the result of a third factor that is not apparent at the time of examination or pure chance.
Correlation Assumptions
- Assumption #1: Variables must be either interval or ratio – i.e., continuous.
- Assumption #2: Two continuous variables should be paired (i.e., each case has two values – one for each variable).
- Assumption #3: Linear relationship between the two variables.
- Assumption #4: Outliers are either kept to a minimum or removed entirely.
- Assumption #5: The two groups' variances are equal in the population.
Shapiro-Wilk Test
- Used to test for normality of data.
- A significant Shapiro-Wilk test indicates that the data are not normally distributed.
- A non-significant Shapiro-Wilk test indicates that the data are normally distributed.
Levene's Test
- Used to test whether the variances of two groups are equal in the population.
- Levene's test is used to formally test whether the variances are different in the population.
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