W6 - Short Answer Questions Flashcards
What is the main characteristic in data being assessed by an independent samples two group design?
What is the assumption on this comparison?
Independent samples: Main features
- Individual scores
- Means of the two groups
- (because the test is predicated on there being an expected difference between the two groups)
This comparison assumes that the variances of the two groups are the same (i.e., that the variances are homogenous)
What are different estimators for a standardized mean difference in two-group designs and what does each one assume? Where can they be used?
Two estimators for a standardized mean difference are:
- Hedges’ g
- Normality of observed scores
- Homogeneity of variance
- Bonnet’s d
- Normality of observed scores
- Both estimators assume independence of observations.
- Both estimators can be used in either an independent or a dependent design
What do we always know for sure about the sample size in each group in a dependent two-group design? Why? How many paired scores are there? What happens if the design is unbalanced?
- Must be the same
- Because the basis of the test is the difference score formed from each pairing of scores.
- There will be as many paired scores as there are people in the sample.
- If there are more people one group than the other (e.g., people drop out between time 1 and time 2, and therefore time 2 has a smaller sample than time 1), then any person who does not have a paired score at each time point is dropped from the analysis.
What are the key assumptions of a dependent two-group design? Explain why one of them is not an assumption
- Independence of observations.
- Normality of difference scores.
- No homogeneity of variance assumption
- Inferences made on set of difference scores calculated between the two groups and only one set of difference scores can be obtained when there are only two groups.
What are two different ways that two dependent groups can be formed for undertaking research?
- Each person measured on two separate occasions
- Two occasions are designated as being two groups and the scores in each group indicate the score of each person at each time point
- Each person in one group being matched on a pairwise basis with the score of a different individual person in a second group
- e.g., sister and brother from the same family
What are the key statistical assumptions of an independent two-group design?
- Independence of observations
- Normality of observed scores.
- Homogeneity of variances in each group
What are the main features in the data being assessed in a dependent samples t test? How are they typically formed? And what is the variance used for?
The main feature of the data being assessed in a dependent samples t test:
-
Mean of the difference scores
- (Typically) formed by subtracting the paired score at time 2 (i.e., in the second group) from the paired score at time 1 (i.e., in the first group).
- Variances of the difference scores are used as the basis for forming standard error
What are probability distributions used for?
Probability distributions are used in calculating:
- Confidence intervals on sample statistics
- Undertaking null hypothesis significance testing.
What is the underlying rationale behind probability distributions?
Any sample statistic has a corresponding sampling distribution, which can be obtained from calculating the value of that statistics over a very large number of samples drawn from a population of scores.
Under
- Certain assumptions
- Suitable standardizing transformation using SE of sample statistic
- Sampling distribution can be shown mathematically to be equal to a probability distribution
Therefore, the probability distribution can be used to undertake statistical inferences.
What are the names of commonly employed probability distributions? And what are their parameters?
- Normal distribution (most commonly, the standard normal distribution)
- Defined by two parameters for the mean and the standard deviation
- Chi-squared distribution
- Defined by a degrees of freedom parameter
- Student’s t distribution
- Defined by a degrees of freedom parameter.
-
F distribution
- Defined by degrees of freedom parameters for both numerator and denominator;
What is meant by a robust confidence interval?
- Coverage rate remains unaffected by violation of the statistical assumptions underlying its construction
- Captures unknown population parameter value in repeated samplings by the same percentage of times as defined by the size of the interval when one or more assumptions are being violated
- i.e., if the interval is set as 95%, the proportion of times the interval will contain the actual population parameter value will be 95% of the time over repeated constructions of the interval using a large number of independent samples drawn from the population
In what circumstances will inferences in a independent two-group design not be robust to violation of assumptions?
Inferences in an independent two-group design will not be robust to violation of assumptions when:
- (a) the sample size in each group differs; and
- (b) the homogeneity of variance assumption for the two groups is not being met.
If group sample sizes are the same, then the design is reasonably robust to violation of the homogeneity of variance assumption (unless the scores are very non-normal).
What are three different ways that two groups can be formed for undertaking research
How do these three ways differ fundamentally?
(1) Mutually-exclusive/ Independent
- Each person belonging to only one of the two groups
(ii) Mutually-dependent/Dependent/ Repeated-Samples
- Each person being measured on two separate occasions, whereby the two occasions are designated as being the two groups
(iii) Mutually-dependent/Dependent/Matched-Samples
- Pair-wise matching
- Each person in one group being matched on a pairwise basis with a different individual person in a second group.
