Stats Chapter 7

Type II Error

(beta error) retain false null hypothesis

calculation for the degrees of freedom for the two-independent-sample t test:

(n^1-1) + (n^2-1)

medium d

.2<d<.8

what three factors can be increased to increase power (probability of rejecting a (false) null)?

1) alpha level 2) sample size 3) effect size

3 measures used to estimate effect size for a one or two-sample t test

1) cohen's d 2) eta squared 3) omega squard

Three steps to estimation:

1) compute sample mean and standard error 2) choose the level of confidence and find the critical values at that level of confidence 3) compute the estimation formula to find the confridence limits

e steps to estimation for a two-indpendent-sample t test

1) compute the sample mean and SEM 2) choose the level of confidence and find the critical values at that level of confidence 3) compute the estimation formula to find the confidence limits

what 3 factors can be decresed to increase the power (probability that a randomnly selected sample will show that the null is false) of detecting an effect (difference between sample and population mean) in a given population

1) decrease beta error 2) decrease population standard deviation 3) decrease standard error

two ways to calculate size of effect

1) how far scores shift in the population 2) % variance that can be explained by a given variable

to report the results of estimation for the one-sample t test, report these 3 things:

1) level of confidence 2) point estimate 3) interval estimate of each confidence interval

for two-independent-sample t tests, we make 4 assumptions:

1) normality 2) random sampling 3) indepenence 4) equal variances

4 steps of hypothesis testing

1) state hypothesis 2) set criteria for a decision 3) compute test statistic 4) make a decision

to report the results of a one-sample t-teset, state these 4 things:

1) test statistic 2) degrees of freedom 3) p value 4) effect size

when reporting the results of a one sample t test and a two-independent sample t test, state these 4 things:

1) test statistic 2) degrees of freedom 3) p value 4) effect size

3 assumptions for a one-sample t test:

1)normality 2) random sampling 3) independence

estimation formula for the two-independent -sampel t test

M1-M2 +/- t(sM1-sM2)

Cohen's D

a measure of the effect size in terms of the number of standard deviations scores shift above/below the population mean stated by the null. Larger d value -> larger effect in the population

normality

assume data in the population being sampled are normally distributed; particularly important in small samples. In larger samples (n>30), the standard error is smaller, and this assumption becomes less crtiical as a result

small d

d<.2

large

d>.8

effect

difference between the sample and population mean in the null hypothesis

independence

each outcome/observation is independent; one outcome doesn't influence another

estimated standard error

estimate of the standard deviation of a sampling distribution of sample means selected from a population with an unkown variance An estimate of the standard error or standard distance taht sample means deviate from the value of the poopulation mean stated in the null hypothesis

power

in hypothesis testing, the probability of rejecting a false null hypothesis. The probability that a randomnly selected sample will show a null hypothesis is false when it is.

interval estimate/confidence interval is a statistical prcoedure i which a sample of data is used to find the _______ of possbile values within which a _______ is likely to be contained

interval/range; population parameter

alpha level

level of significance/criterion for hypothesis; largest probability of comitting a Type I error that we allow and still reject the null

test statistic

mathematical formula that allows researchers to determine the likelihood or probability of obtainig sample outcomes if the null hypothesis were true. The value of a test statistic can used to make inferences concering the value of a population parameter stated in the null hypothesis.

cohen's d

measure of the effect size in terms of the number of standard deviations that mean scores shift above/below the population mean stated by the null hypothesis. The larger the value of estimated cohen's d, the larger the effect in the population

are the degrees of freedom required for a z test

no, because the populaton variance is known

do we know the population variance for a t test?

no; the sample variance is used to estimate the population variance

what distribution is used to locate the probability of obtaining a sample mean for a z test?

normal distribution

eta-squared tends to ____the size of an effect in a population. Omega squared ____for this bias

overestimate; correct

As sample size increases, the sampel variance more closely estimates the _____

population variance

Type III Error

possible with 1-tail tests a result would've been significant in one tail, but the researcher retains the null hypothesis because the rejection region was placed in the wrong/opposite tail

p-value

probability of obtaining a sample outcome, given the value of the null hypothesis is true. the P-value for obtainign a sample outcome compared to a level of significance

the less overlap in scores between groups in a between subjects design, the more likely we are to decide to ____ the null

reject

Type I Error

rejecting a true null

between subjects design

research design in which different participants are observed in each group or at each level of one factor; with 2 groups, compare differences between the groups

point estimate is a statistical procedure that involves the use of a _____ to estimate a _______

sample statistic (e.g., sample mean); population parameter (e.g., population mean)

one-sample t test is specifically ised to test hypotheses concerning the mean in a ___ population with an ___ variance

single; unkown; compars a mean value measured in a sample to a known value in the population

effect size

statistical measure of the size of the effect in the population, allows researchers to describe how far scores shift in the population

estimation

statistical procedure in which a sample statistic is used to estimate the value of an unkown population parameter

what distribution is used to locate the probability of obtaining a sample mean for a t test?

t distribution

one-sample z test

test uses a single population, mean variance

critical value

the cut off value, defines the boundaries beyond which 5% sasmple means can be obtained if the null is true. The sample means obtained bneyond a critical value will result in a decision to reject the null

larger the value of the test statistic, ______

the less likely a sample mean would be to occur if the null hypothesis were true, adn the more likely we are to reject the null hypothesis

rejection region

the region beyond a critical value in a hypothesis test

obtained value

the value of the test statistic. Compared to the critical value of the hypothesis teset to make the decission. When the obtained value is greater than the critical value, you rejeect the null; otherwise, retain the null

how are the rejection regions, the probability of a Type I error, the level of significance, adn the alpha level related?

they all describe the same thing. The level of significance is represented by alpha, which defines the rejection region or the region associated with the probability of committing a Type I error.

z-statistic

used to determine the number of standard deviations from the population mean stated in the null

t statistic

used to determine the number of standard deviations in a t distrubution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis

do we know the population variance for a z test?

yes

are the degrees of freedom required for a t test?

yes, the degrees of freedom for a t test are equal to the degrees of freedom for sample variance for a given sample: n-1