Test 3 Flashcards
Null Hypothesis (Ho)
no true effect on pop; the apparent effect could be a matter of sampling error
Alternative Hypothesis (H1)
true effect in population (often called research hypothesis)
What do we estimate with hypothesis testing?
We estimate the probability that the null hypothesis is true
- If prob is very low (.05 or less) then reject Ho and decide that the apparent effect is probably a true effect
- If prob is greater than .05, then fail to reject Ho and conclude that any apparent effect may be a matter of sampling error
Z formula for hypothesis testing
z = m - μ / σm
remember that σm = σ / square root of N
Nondirectional (two-tailed) test
The alternative hypothesis is that the treatment has an effect, without specifying the direction:
H1: μT ≠ μu
ALWAYS use this in class
Directional (one-tailed)
If there is an empirical and or theoretical basis for believing that the effect can only occur in one direction, then a directional test may be used:
H1: μT > μu
or H1: μT < μu
Significance level α
α = probability of rejecting the null hypothesis when it is in fact true
Set at .05 or .01
Try to minimize claims that a treatment has an effect when it does not
Type I Error
When you reject null but the null is true
p = α
Type II Error
When you fail to reject null but the null is false
p = β
Correct decision p = 1 - β
when you reject null when null is false
- power
Correct decision p = 1 - α
when you fail to reject null when null is true
Power
probability of rejecting the null hypothesis when it is in fact false (p= 1 - β)
How do you increase power?
by:
- Increasing sample size
- Increasing alpha, but cannot go higher than .05
- Using a one-tailed test (if the effect is in the predicted direction)
Underlying assumptions (hypothesis testing)
- At least an interval level of measurement
- Random sample
- The sampling dist. of the mean is normally distributed, which is likely when:
- —-The sample is selected from a population that is normally distributed
- —-N is very large (central limit theorem)
Robustness
probability of a type I error (rejecting Ho when it is true) is close to α even when the assumptions underlying the use of an inferential statistic are violated
Cohen’s d for hypothesis testing
effect size d = m - μ / σ small: d < .2 med: d is .2 - .8 large: d > .8
t statistic
t = m - μ / sm
What is the difference between t and z distributions?
t distributions change with the sample size (or technically the df, which is n-1)
- as sample size (df) decreases, t becomes flatter and more heavy (higher probabilities) in the tails
When a re T-tests are most commonly used to make statistical inferences about the effect of an IV on a DV?
when: The IV has only 2 levels Often experimental conditions - Treatment and control The DV is measured on an interval scale
Types of Two-Independent Samples
Between-subjects (independent groups)
Within-subjects (related samples, repeated measures)
Between-subjects (independent groups)
Comparisons are made between separate (independent) groups (samples) of participants
Each group is assigned to a different level of the IV
To get comparable groups, use RA
Within-subjects (related samples, repeated measures)
Participants are either not separated into independent groups (repeated measures) or are related to one another
Most often, each individual participates at all levels of the IV- thus, the same individuals are compared over different levels of the IV
Two kinds of Two-sample t-tests
Independent Samples
Related samples
Independent Samples
Use with independent-groups designs
Compare separate groups of individuals
Related samples
Use primarily with within-subjects designs
Compare between experimental conditions, not between groups
Non-independent- either:
-Repeated measures: same individuals measured more than once
-Matched pairs: matched on common characteristics
Conditions for independent samples
Comparing 2 independent groups (samples)
Both groups measured on the same interval measure
Assumptions for independent samples
- Random selection
- Homogeneity of pop. variances
- The sampling distribution for the difference between the means is normally distributed- will be true when:
- —-The population distributions for both conditions are normal
- —–n is large (>30)
df for two-independent sample t tests
df = n1 + n2 - 2
Conditions for related samples
Comparing the same (or related) participants in 2 conditions
Interval level
Assumptions for related samples
- Random selection
- The sampling distribution for the difference between means is normally distributed- true when:
- —The populations for both conditions are normally distributed
- —n is large
df for related samples t tests
df = nD - 1
Why is there reduced error variance with a within-subjects design?
Rationale for using difference scores:
- Between conditions overall individual differences on the DV are controlled because the same (or related) individuals are in both conditions
- Each participant serves as their own control
- By using difference scores we:
- –Take away overall individual differences on the DV
- –Yet maintain the apparent size of the effect on the IV for each participant
Goal for confidence interval estimation
be 95% confident that our interval contains μ
Why use standard normal distribution as a model for sampling distribution?
- Areas (proportions of scores) under it are known
- Good fit – the sampling distribution is likely to be normal in form if either one of the following holds:
- —the scores are randomly selected from a population that is normally distributed
- —n is sufficiently large (Central Limit Theorem)
Why use a t distribution as a model for the sampling distribution?
- Areas under them are known
- Good fit – t distributions have symmetrical bell-shapes
- When σ is unknown a t-distribution provides a more accurate model than does the standard normal distribution
2 goals for estimating in inferential statistics
Two goals:
- Make unbiased estimates
- Assess error made when making estimates
- A sampling distribution helps accomplish these goals
Sampling distributions and why its useful
A distribution of a statistic derived from all possible samples of a given size
Useful for:
- establishing the rationale for estimation of population parameters from statistics
- assessing the amount of error we are likely to make when using a statistic to estimate a parameter
When to use z-test
when we know population SD
When to use t-test
when we do not know population SD
