PSYC10 Midterm #2 Conceptual

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Z critical value for a two-tailed test at alpha = 0.05

+/- 1.96

A researcher reports with 90% confidence interval that 31-37% of Americans believe in ghosts. What is the point estimate for this interval?

34%

T/F: Increasing the sample size reduces the likelihood of committing a Type 1 error.

False

T/F: the sample mean is an unbiased estimator of the population mean

True

t statistic is used to determine number of standard deviations in a t distribution that a sample mean deviates from....

a population mean or mean difference stated in the null hypothesis

inferential task

ability to correctly reject null hypothesis

increase in n, standard error

decreases

bigger the sample: easier or harder to reject null?

easier

related samples: what does a difference score achieve (2)

eliminates source of error; reduces standard error, increasing power to detect an effect

sampling w replacement

ensure each individual or item has the same probability of being selected

how to find degrees of freedom of a related 2-sample t-test

n (pooled) - 1

can a p value be negative

no, only between 0 and 1

experimental sampling, 2 features

order does not matter, sample w/o replacement

variance of normal distribution has to be a ____ number

positive

central limit theorem

probability distribution for obtaining a sample mean from a population is normal; at least 95% of all possible sample means are within 2 SD of the population mean

In hypothesis testing, a researcher can never

prove that his or her hypothesis is correct

if value inside CI, ___ null

retain

omega-squared for one sample t test

t^2 - 1/ t^2 + df

related sample: assume independence __ groups

within

3 characteristics of sample mean that make it a good estimator of value of population mean

1. sample mean = unbiased estimator = mean of population (w random choices) 2. distribution of sample means follows central limit theorem; distribution of sample means approaches shape of normal distribution 3. distribution of sample mean has minimum variance

sampling error

2 random samples selected from same population can produce different estimates of same population mean

What is the central limit theorem?

Explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution of in the population

T/F: The smaller the error variance, the more overlap there is in scores between groups

False

The test statistic for the related samples t test is equivalent to the test statistic for the two-independent sample t test

False

T/F: A study in which 26 participants are observed two times is associated with 26 degrees of freedom for a related samples t-test

False; 25

z score formula for sampling distribution

M - pop. mea / (SD/sqrt n)

t stat equation

M - u / sM

What is the level of significance for a hypothesis test?

Probability to incorrectly reject the null, the Type 1 error, and the alpha level

An advantage of computing difference scores in the related samples t test is that:

Reduces standard error, reduces variability, increases power

What is Type 1 error?

Researcher incorrectly decides to reject a null hypothesis that is actually true

Type 3 error

Result would have been significant in one tail, null is retained because the rejection region was placed in the wrong or opposite tail (only possible for 1 tailed tests)

If the sample mean is equal to the null hypothesis, what does that mean in terms of significance?

Retain the null

estimated standard error equation (sM)

SD / sqrt n

standard error of the mean formula

SD/sqrt(n)

Does the p value need to be less than or greater than alpha to reject?

Smaller

T/F: A one-sample t-test will be = 0 when the mean difference is equal to 0

True

T/F: Cohen's d has a different formula for different types of t-tests, but Eta-squared are the same for each test

True

T/F: Effect size measures are an estimate of the size of an effect in the population

True

T/F: The smaller the error variance, the less overlap there is in scores between groups

True

T/F: You can use a confidence interval to make a judgement about whether you can reject or retain the null hypothesis

True

T/F: the degrees of freedom for the related samples t-test is the number of pairs of participants minus one, and not always the total number of participants minus one

True

T/F: To estimate the population mean for the two-sample t, the sample size must be known

True (can't build confidence intervals without sample sizes

T/F: A one-sample t-test will be undefined (denominator = 0) when the same score is recorded for all participants in a study

True because standard deviation will be 0, leading the denominator to = 0

Suppose you obtained a sample form a population different from the one specified by the null hypothesis. On the basis of a t test, you failed to reject the null hypothesis. This error is:

Type 2

What elements, when decreased, will increase power?

Type 2 error, standard deviation, standard error

What elements, when increased, will increase power?

alpha, Cohen's d, and sample size

values in a sampling distribution of the sample mean...

are approximately normally distributed

sampling w/o replacement used in what research

behavioral

experimental sampling is most used in

behavioral research

steps to estimate value of population mean

compute sample mean and standard error, choose level of confidence and find critical values, compute estimation formula to find confidence limits

In reporting results of z-test, what is not reported?

critical values

effect size equation

d = M - u / standard deviation

decrease alpha, power

decreases

as sample size increases, standard error ____. why?

decreases; larger the sample, more data, the closer estimate of population mean; law of larger numbers

as standard deviation decreases, standard error ____. why?

decreases; less scores in a population deviate from the mean = less possible sample means will deviate from population mean

independent sample

different participants are independently observed one time in each group

sampling distribution

distribution of mean and variance for all possible samples of a given size from a population

if sample size increases, effect size

does not change

when it is a 2 tailed test, the p value must be ____

doubled

what 2 variables represent proportion of variance

eta squared and omega squared

type II error

failing to reject a false null hypothesis (look at distribution)

what does a larger test statistic mean

farther the distance/ number of sample means from population mean stated in the null hypothesis

when it is a 2 tailed test, the alpha level must be

halved

is it easier or harder to reject the null w 2 tailed test? why?

harder; need to get a value past a bigger z score (1.645 vs 1.96)

Measures of effect size allow researchers to describe:

how far scores shifted in the population, and also the % of variance that can be explained by a given variable

The related-samples design can _______ the power to detect an effect by making the standard error __________

increase / smaller

does an increase or decrease in standard deviation lead to an increase in standard error?

increase in SD = increase in SE

as effect size increases, power ___

increases

increase alpha, power

increases

sample size increases, power

increases

Power in hypothesis test:

is the probability of rejecting a false null hypothesis (correct rejection)

is a 2 tailed test more or less powerful than 1 tailed test

less

what is power

likelihood to detecting an effect

A researcher hypothesizes that parents read to their children less than the recommended 30 minutes each day. The alternative hypothesis should be:

mean time that parents spend reading to their children is les than 30 minutes

A researcher hypothesizes that parents read to their children less than the recommended 30 min each day. The alternative hypothesis should be ______.

mean time that parents spend reading to their children is less than 30 min

sampling without replacement

method of sampling in which each participant or item selected is not replaced before the next selection

standard error of the sampling distribution of sample means is...

minimal (does not get larger as the sample size increases)

advantages to related samples instead of independent (3)

more practical, reduces standard error, increases power

is Cohen's d affected by sample size

no

assumptions of one sample t test (3)

normality, random sampling, independence

4 assumptions about 2 independent sample t tests w 2 populations

normality, random sampling, independence, equal variances (larger s^2/smaller s^2 < 2)

rejection of null is easier under a one or two tailed test?

one tailed test

if value outside CI, ___ null

reject

type 1 error

rejecting the null hypothesis when it is true (false positive)

inferential stats

researchers select sample or portion of data from a much larger population

What are the two decisions that researchers can make in hypothesis testing?

retain or reject null

unbiased estimator

sample mean equals the value of the population mean on average

the ___________ are distributed along the x - axis for a sampling distribution of the sample mean

sample means

T distribution has greater variability in the tails of distribution because...

sample variance is substituted for the population variance to estimate standard error in the distribution

Distribution of all possible sample means that could be obtained in samples of a given size from the same population is called...

sampling distribution

2 ways to select independent samples

select sample from 2 populations (quasi experiments, levels of factor pre-existing); one sample from same population and randomly assign participants in the same to groups (experiments that use randomizations, manipulation, comparison/control group)

theoretical sampling, 2 features

selection order matters, sample w replacement

power

sensitivity of a test, how well the test is doing it's job

how to calculate standard error

standard deviation divided by the square root of the sample size

standard error of the mean

standard deviation of a sampling distribution; square root of variance; SEM = square root of standard deviation squared

interval estimate/ confidence interval

stated within a given level of confidence (likelihood that interval contains unknown population mean); M +/- t(sM)

Theoretical sampling is the basis for

statistical theory

eta-squared for one sample t test

t^2 / t^2 + df

test statistic

tells us how far/how many deviations the sample mean is from population mean (z score, t score, etc.)

A researcher computes a test statistic and determines that the probability of obtaining a sample mean, given that the value stated in the null hypothesis is true, is .02. The .02 refers to what value?

the p value

One-sample t tests can only be computed when...

the population being sampled from is normally distributed

how to find standard deviation from variance

the square root of the variance= standard deviation

Standard error of the mean is:

the standard deviation for the sampling distribution; a measure of the distance the sample means deviate from the population mean; equal to the population standard deviation divided by the sqaure root of the sample size

Characteristics of the sampling distribution of the sample mean

unbiased estimator of population mean; approximately normally distributed; has minimum variance

point estimate

unbiased estimator, measures sample mean

Can determine probability of obtaining a sampl mean from a population with a given population by...

using a sampling distribution


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