Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
22 Cards in this Set
- Front
- Back
|
limitation of z-scores in hypothesis testing
|
the population standard deviation (variance) must be known
|
|
|
A sample mean(M) us expected to approximate its population mean(µ).
|
This permits us to use the sample mean to test a hypothesis about the population mean.
|
|
|
Standard error
|
provides a measure of how well a sample mean approximates the population mean
σ(M)=σ/√n |
|
|
compare sample mean(M) with the hypothesized population mean(µ) by
|
a z-score test statistic
z=M-µ/σ(M) |
|
|
goal of the hypothesis test
|
determine whether or not the obtained result is significantly greater than would be expected by chance
|
|
|
estimated standard error
|
used as an estimate of the real standard error σ(M) when the value of σ is unknown
s(M)=√(s^2/n) RECALL s^2=sample variance s^2=SS/df |
|
|
single-sample t statistic
|
used to test hypotheses about an unknown population mean µ when the value of σ is unknown
t=M-µ/s(M) |
|
|
difference between t formula and the z-score formula
|
z-score uses the actual population variance, σ^2 (standard deviation), and the t formula uses sample variance s^2
|
|
|
t distribution will have more variability than the normal z distribution because
|
the standard error in the t formula is estimated and will vary with the sample
|
|
|
as the value for df increases, the t distribution
|
becomes more similar to a normal distribution
|
|
|
A repeated-measures approached may be preferred
|
when one wants to observe changes in behavior in the same subjects.
|
|
|
In general, if the variance of the difference scores increases, then the value of the t statistic will:
|
decrease (move toward 0 at the center of the distribution).
|
|
|
An advantage of a repeated-measured design (compared to an independent-measures design) is
|
that it reduces the contribution of error variability due to individual differences
|
|
|
define r^2
|
r^2=t^2/t^2+df
r^2 measures the percentage of variability that is accounted for by the treatment effect .01<r^2<.09 small .09<r^2<.25 medium .25<r^2 large |
|
|
pooled variance
|
Under the assumption of equal population variances, the pooled variance represents the best estimate of this equal but unknown population variance. It is a weighted average of the variance within each group.
|
|
|
4-step process for hypothesis testing
|
1. State the null hypothesis, and select an alpha level. State alternative hypothesis.
2. Locate the critical region, the area where sample outcomes would be very unlikely to occur if null hypothesis is true. 3. Collect the data, and compute the test statistic. 4.Make a decision to reject or fail to reject the null hypothesis. |
|
|
Type II error is defined
|
the failure to reject a false null hypothesis
|
|
|
Type I error is defined
|
rejecting a true null hypothesis and is determined by the alpha level
|
|
|
cohen's d
|
mean difference/std. deviation
-effect size can be standardized by measuring the mean difference in terms of the std. deviation 0<d<.2 small effect .2<d<.8 medium effect d>.8 large effect |
|
|
two assumptions for hypothesis tests with the t statistic
|
1. values in the sample must consist of independent observations - occurrence of the first event has no effect on the probability of the second outcome
2. sampled population must be normal - assumption can be violated without affecting the validity with a large enough sample size |
|
|
estimated standard error
|
an inferential value that describes how accurately the sample mean represents the unknown population
|
|
|
homogeneity of variance assumption
|
assumption is that the two population variances are equal
|
