t-test etc. Flashcards
Advantages of the repeated measures design?
- Number of subjects – requires fewer subjects because the same subjects are measured in both of the treatment conditions (important when there are relatively few subjects available)
- Study changes over time – well suited fro studying learning, development or other changes that take place over time
- Individual differences – the primary advantage, because it reduces or eliminates differences such as age, IQ, gender, and personality
Disadvantages of the repeated-measures design
- Order effects
- Fatigue
- Practise
- Carry-over
- Solution: counterbalancing
z score formula for distribution of sample means?
z = (𝑀−μ)/σ𝑀
Standard Error of the Mean formula?
σ𝑀 = σ/√n
What is the central limit theorem?
For any population with mean μ and standard deviation σ, the distribution will…
1) Always have a mean μ
2) Always have a standard deviation of σ𝑀 = σ/√n
3) Will approach a normal distribution as n->∞
The shape of the distribution of sample means will be almost perfectly normal if…
1) n>30, or
2) Population from which samples are selected is a normal distribution
What is the mean of the distribution of sample means?
The mean of sample scores equals the mean of the population.
Why do we have to use a different table for t-test?
Because the value of the estimated standard error is only an estimate. Instead of the variance of the distribution of sample means (σ^2) in the denominator, it is the variance of the sample. The variance of the sample is unlikely to be smaller than the variance of the distribution of means. Hence, the denominator is likely to be larger giving the overall t-score a smaller value.
- Hence a lot more scores can fall outside of this range
As a result it would not really be fair to treat the answer as a z score and use the table of z. To do so would give us too many “significant” results, that is, we would make more than 5% Type I errors when testing the null hypothesis at significance level alpha = .05.
Brief summary of independent-measures design
Allows researchers to evaluate the mean difference between two populations using data from two separate samples
Used to test for mean differences between two distinct populations (such as men vs. women; children vs. adults; dancers vs. scuba-divers; etc.)
Also used to test for two difference treatment conditions (such as drug vs. no- drug)
What are parametric tests designed to do? What are some examples?
Designed to test hypotheses about specific population parameters
What are non-parametric tests; how do they differ from parametric tests?
Do not state hypotheses in terms of a specific parameter and they make a few (if any) assumptions about the population distribution
What are some examples of non-parametric tests?
- Distribution-free tests
- Categorical variables
- Measurements on nominal or ordinal scales
- Mode (for example, academic major for each student)
- The data are frequencies (i.e. the number of individuals that fall into a particular category)
What are the steps to hypothesis testing?
Step 1: State the hypothesis
Step 2: set the criteria for a decision
Step 3: Compute the test statistics
Step 4: Make a decision
What is the z value range at which alpha (type 1 error probability) = .05?
z+1.96
What is the alpha level, or the level of significance?
The α level establishes a criterion, or “cut-off”, for making a decision about the null hypothesis. The alpha level also determines the risk of a Type 1 error.
