Exam 3

power

of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists.

level of significance

or the alpha level, is a probability value that is used to define the concept of "very unlikely" in a hypothesis test.

normal distribution

relatively large, around 30 or more.

stages

state hypothesis predict experiment collect data

null hypothesis

states that in the general population there is no change, no difference, or no relationship. In the context of an experiment, predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population.

alternative hypothesis

states that there is a change, a difference, or a relationship for the general population. In the context of an experiment, predicts that the independent variable (treatment) does have an effect on the dependent variable.

percentage of variance accounted for by the the treatment (r *squared)

t *squared / t*squared + df

alpha level and type 1 error

the alpha level determines the probability of type I error.

directional test

the statistical hypothesis specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.

in a research report, the term significant is used when the null hypothesis is rejected(true/false)

true

type I error

occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation, a type I error means that the researcher concludes that a treatment does have an effect when, in fact, it has no effect.

as sample size increases, the value of expected value also increases. (true/false)

False. the expected value does not depend on sample size

as sample size increases, the value of the standard error also increases. (true/false)

False. the standard error decreases as sample size increases.

Central limit theorem

For any population with mean and standard deviation, the distribution of sample means for sample size n will have a mean of u and a standard deviation of ( stand devi / sq. root of n) and will approach a normal distribution as n approaches infinity.

Distribution of sample means

Is the collection of sample means for all of the possible random samples of a particular size (n) that can be obtained from a population.

Sampling distribution

Is the distribution of statistic obtained by selecting all of the possible samples of a specific size from a population.

Sampling error

Is the natural discrepency, or amount if error, between a sample statistic and its corresponding population parameter.

Law of large numbers

States that the larger the sample size (n), the more probable it is that the sample mean is close to the population mean.

Expected value of M

The mean if the distribution of sample means is equal to the mean of the population of scores, u

Standard error of the M

The standard deviation of the distribution of sample means. Provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (u)

significant

a result is said to be significant, if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject the null.

as the power of a test increases, what happens to the probability of a type II error?

as power increases, the probability of a type II error decreases

degrees of freedom

describe the number of scores in a sample that are independent and free to vary. Because the sample mean places a restriction on the value of one score in the sample, there are n-1 degrees of freedom for a sample with n scores.

in a research report, the results of a hypothesis test include the phrase z=3.15, p< .01. this means that the test failed to reject the null hypothesis (true/false)

false.

if the alpha level is increased from a=.01 to a=.05, then the boundaries for the critical region move farther away from the center of the distribution. (true/false)

false. A larger alpha means that the boundaries for the critical region move closer to the center of the distributions.

if the sample data are sufficient to reject the null hypothesis for one tailed test then the same data would also reject null for two tailed test (true/false)

false. because a two tailed test requires a larger mean difference, it is possible for a sample to be significant for a one tailed test but not for a two tailed test.

anova is a statistical procedure that compares two or more treatment conditions for differences in variance. (true/false)

false. goal is to find differences in means between treatments.

if a sample mean is in the critical region with a = .05, it would still (always) be in the critical region if alpha were changed to a=.01.(true/false)

false. with a=.01 the boundaries for the critical region move farther out into the tails of the disturb. it is possible that a sample mean could be beyond the .05 boundary but not beyond the .01 boundary.

alpha level

for a hypothesis test is the probability that the test will lead to a type I error. That is, the alpha level determines the probability of obtaining sample data in the critical region even though the null hypothesis is true.

how does increasing sample size influence the out come of a hypothesis test

increasing sample size increases the likelihood of rejecting the null hypothesis.

Hypothesis test

is a statistical method that uses sample data to evaluate a hypothesis about a population.

confidence interval

is an interval, or range of values, centered around a sample statistic. The logic behind a confidence interval is that a sample statistic, such as a sample mean, should be relatively near to the corresponding population parameter. Therefore, we can confidently estimate that the value of the parameter should be located in the interval.

critical region

is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. if sample data fall in the critical region, the null hypothesis is rejected.

effect size

is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.

t distribution

is the complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). the t distribution approximates the shape of a normal distribution.

estimated standard error

is used as an estimate of the real standard error, when the value of o is unknown. It is computed from the sample variance or sample standard deviation and provides and estimate of the standard distance between a sample mean, M, and the population mean, u.

t statistic

is used to test hypothesis about an unknown population mean, u, when the value of o us unknown. The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator.

estimated d

mean difference / sample standard deviation (s)

cohen's d

mean difference/standard deviation

type II error

occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect.

a z score value in the critical region means that you should reject the null hypothesis. (true/false)

true.

if it were switched then it would be

true.

if a researcher predicts that a treatment will increase scores, then the critical region for one tailed test would be located in the right hand tail of the disturb. (true/false)

true. a large sample mean, in the right hand tail, would indicate that the treatment worked as predicted.

if other factors are held constant, increasing the size of the sample increases the likelihood of rejecting the null hypothesis. (true/false)

true. a larger sample produces a smaller standard error, which leads to a larger z score.

a small value (near zero) for the z score statistic is evidence that the sample data are consistent with the null hypothesis. (true/false)

true. a score near zero indicates that the data support the null hypothesis.

beta

type II error is represented by the symbol beta.

under why circumstances is a type II error likely to occur?

when the treatment effect is very small, in this case, a research study is more likely to fail to detect the effect.