PSY1022 WEEK 12 DISC 6 Flashcards
PROBABILITY VS INFERENTIAL STATISTICS
Probability is used to predict what kind of samples are likely to be obtained from a population.
Inferential statistics used to make generalizations about a population from a sample.
SAMPLING DISTRIBUTION OF MEANS
A frequency distribution showing all possible sample means that occur when samples of a particular size are drawn from a population.
A sampling distribution is approximately a normal distribution.
CENTRAL LIMIT THEOREM
A statistical principle that defines the mean, standard deviation, and shape of a theoretical sampling distribution.
STANDARD ERROR OF THE MEAN
The standard deviation of the sampling of the means.
SAMPLING ERROR
The difference, due to chance, between a sample statistic and the population parameter it represents.
MEAN OF A SAMPLING DISTRIBUTION
The mean of the sampling distribution equals the mean of the underlying raw score population from which we create the sampling distribution.
Population mean so use µ.
STANDARD DEVIATION OF THE SAMPLING DISTRIBUTION
Is mathematically related to the standard deviation of the raw score population.
REGION OF REJECTION
That portion of a sampling distribution containing values considered too unlikely to occur by chance, found in the tail or tails of the distribution.
CRITERION
The probability that defines whether a sample is unlikely to have occurred by chance and thus is unrepresentative of a particular population.
Determines the size of the region of rejection.
Usually 0.5 (5%)
But if doing +ve and -ve then 2.5 each end.
Represented by alpha α.
CRITICAL VALUE
The score that marks the inner edge of the region of rejection in a sampling distribution; values that fall beyond it lie in the region of rejection.
INFERENTIAL STATISTICS
Procedures for determining whether sample data represent a particular relationship in the population.
PARAMETRIC STATISTICS
Inferential procedures that require certain assumptions about the raw score population represented by the sample; used to compute the mean of the scores.
NON PARAMETRIC STATISTICS
Inferential procedures that do not require stringent assumptions about raw score population represented by the sample data.
EXPERIMENTAL HYPOTHESES
Two statements made before a study is begun, describing the predicted relationship that may or may not be demonstrated by the study.
TWO-TAILED TEST
The test used to evaluate a statistical hypothesis that predicts a relationship but not whether the scores will increase or decrease.
ONE-TAILED TEST
The test used to evaluate a statistical hypothesis that predicts that scores will only increase or only decrease.
STATISTICAL HYPOTHESES
Two statements that describe the population parameters the sample statistics will represent if the predicted relationship exists or does not exist.
- alternative hypothesis
- null hypothesis
ALTERNATIVE HYPOTHESIS
The hypothesis describing the population parameters that the sample data represent if the predicted relationship does exist.
- It says the changing the independent variable produces the predicted difference in populations.
NULL HYPOTHESIS
The hypothesis describing the population parameters that the sample data represent if the predicted relationship does not exist.
Z-TEST
The parametric procedure used to test the null hypothesis for a single-sample experiment when the true standard deviation of the raw score population is know.
SIGNIFICANT
Describes results that are too unlikely to accept as resulting from sampling error when the predicted relationship does not exist; it indicates rejection of the null hypothesis.
- results ARE in the region of rejection.
NONSIGNIFICANT
Describes results that are considered likely to result from chance sampling error when the predicted relationship does not exist; it indicates failure to reject the null hypothesis.
- results are NOT in the region of rejection.
TYPE I ERRORS
Deciding to reject the null hypothesis when the null hypothesis is true (that is, when the predicted relationship does not exist)
- conclude that a treatment has an effect, when it doesn’t.
TYPE II ERRORS
Deciding to retain the null hypothesis when the null hypothesis is false (that is, when the predicted relationship does exist)
- test fails to detect a treatment
- can’t determine probability for it.
- represented by β (beta)
POWER
The probability that we will detect a true relationship and correctly reject a false null hypothesis; the probability of avoiding a Type II error.
Closely related to Type II error.
Power = 1 - β
Power of 0.8 = good.
EFFECT SIZE ESTIMATE
Hypothesis testing doesn’t tell us how big the effect size is, so use effect size estimate. Measured using Cohen’s d.
COHEN’S D
Tells us the degree of separation between two distributions.
- how far apart the means are (in standardised units).
d = mean difference / standard deviation
MAGNITUDE OF D
- 2 = small effect
- 5 = medium effect
- 8 = large effect
STEPS IN HYPOTHESIS TESTING
- State the hypothesis (eg. µH1: blah blah ≠ 100)
- Set a critical region (At α = 0.5, critical region z=±1.96)
- Collect data and compute sample statistics (sample score z-score = 2.33)
- Make a decision (reject the null hypothesis?)
ALPHA
Is the probability of committing a Type I error.
- concluding a treatment has an effect when it doesn’t.
ONE-TAIL TEST
Null hypothesis: µBlah ≤ 100
Alternative hypothesis: µBlah > 100
Alpha is 0.5, but only at one end.
ONE-TAIL TEST vs TWO-TAIL TEST
One:
- use when theory or previous studies predict direction. Or logic says.
- allows you to reject null with a smaller difference in the specified direction
Two:
- competing theories predict opposing outcomes
- you want a conservative assessment
- no strong expectation either way
Two tail is more common.
INCREASING POWER
- Use a higher alpha level.
1. 0 is greater than 0.5 = bigger critical region - Use a one-tail test
- Increase your sample size
- A larger treatment effect will also result in greater power
ASSUMPTIONS FOR HYPOTHESIS TESTING USING THE Z-TEST
- Random sampling
- Independent observations (no event has any influence on another)
- The SD is not changed by the treatment
- Normal sample distribution.
