PSYC10 Midterm #2 Conceptual
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