Psych 210 (Stats) Exam 2

What is one benefit of increasing the sample size when using t distributions

Larger sample sizes reflect the parameters of the population more closely.

conficence interval formula

M +/- t* (sm) sample mean - critical t value * standard error

how do you find critical t?

N-1 for df, then look on t table

for a paired samples t test, df=

N1+N2-2

Is it necessary to correct for error when calculating the standard error for a t test?

No; we already corrected the standard deviation and are now reflecting the size of the sample.

An effect size of 0.58 was calculated for data after performing a hypothesis test with a single-sample t statistic in which the null hypothesis was rejected. What can we conclude about the results based on this information?

The sample data are significantly different from what was expected based on the population, with the sample mean being 0.58 standard deviation greater than the population mean.

When there is uncertainty about the parameters of a population of interest, a t distribution is used instead of a z distribution. Is the t distribution wider or thinner than the z distribution and why?

The t distribution is wider because we are less certain of the findings compared to the z distribution.

what is the difference between z and t tests?

The t test uses the estimated standard error while the z statistic uses the actual standard error of the population of means.

increasing the size of your sample will have no impact on your effect size?

True

According to the video game industry's statistics, the average gamer is 32 years old. Imagine the standard deviation for age is 7.7 years. Yahzid collected data on video gaming among people with new tablets or iPads to see if the mean age of that group is older or younger. He finds an average age of 36.5 years based on a sample size of 57. His 95% confidence interval is:

[ 34.5 ; 38.5 ]

it is hypothesized that there will be a significant difference in aggression scores after caffeine consumption as compared to before caffeine consumption. This hypothesis best illustrates what type of t test?

a paired samples t test

effect sixzes are calculated ___ the study

after

A small difference between means may not be statistically significant with a small sample, but it could reach statistical significance with a large sample because:

as N increases, the standard error gets smaller, reflecting less variability in sample means, which allows greater sensitivity for detecting small but significant differences.

In calculating pooled variance, why are adjustments made for sample size?

because estimates from smaller samples tend to be less accurate than those from larger samples

an independent samples t test is used with which type of research design?

between groups

When the population mean falls in our confidence interval, we conclude that the sample:

comes from the same population

When the population mean falls in our confidence interval, we conclude that the sample

comes from the same population.

Published literature tends to include significant findings, where the data were sufficient to reject the null hypothesis. This can lead to an inflated estimate of effect size when performing a meta-analysis. Rosenthal suggested that researchers test the level of inflation of their effect size calculations by:

computing a file drawer analysis to see how many null findings would be needed to remove the statistical significance found.

If a researcher runs the same study 30 times, the researcher would expect to find a mean in (or at) the _____ 95% of the time, with a p value of 0.05.

confidence interval

The t statistic is more _____ than the z statistic because the researcher is less likely to observe an extreme t statistic.

conservative

For the paired-samples t test, the comparison distribution:

contains means of difference scores.

formula for calculating effect size for a single sample t test

d = (M-mew) / s

Critical t values _____ as the degrees of freedom _____.

decrease; increase

a paired samples t test is also known as:

dependent samples t-test

Which of the following is NOT a way to resolve issues with the file drawer problem?

eliminating unpublished studies from analysis

in general, the larger the sample variance, the greater the likelihood of rejecting the null hypothesis

false

the null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment)

false

as the sample size increases, the shape of the t distribution

gets wider

under what circumstances can a very small treatment effect be statistically significant?

if the sample size is big and the sample variance is small

ways to increase statistical power?

increase alpha, turn two tailed hypothesis into one, and increase N

As the overlap between distributions being compared decreases, the effect size:

increases

A researcher is comparing two groups, labeled as "depressed" and "anxious." The independent variable is diagnosis, and the dependent variable is accuracy. Which statistical test should the researcher use

independent samples t test

In which statistical test are mean differences compared to a distribution of differences between means?

independent samples t test

If a researcher wants to use a control group as well as an experimental group, which type of t test is MOST appropriate and why?

independent-samples t test; it is a two-sample, between-groups design

In a(n) _____ t test, the samples of participants are from different groups, while in the _____ t test, participants are from the same group.

independent-samples; paired-samples

when N is small (less than 30), how does the shape of the t distribution compare to the normal distribution?

it is flatter and more spread out that the normal distribution

An independent-samples t test compares sample _____ differences

mean

A Cohen's d of -0.49 is what type of effect size?

medium (negative does not matter)

how many groups are compared in an independent samples t test?

only 2

In which statistical test do you calculate a difference score for each individual, take the mean of the difference scores, and perform a test on them to compare two sample means?

paired-samples t test

the weighted average of the two estimates of variance (one from each sample) that are calculated when conducting an independent-samples t test is referred to as:

pooled variance

paired samples t tests are well suited for:

research studies examining learning or other changes that occur over time

the symbol used to designate the standard deviation when estimating from a sample is:

s

In calculating confidence intervals in a z distribution, you start by finding the z scores centered on the:

sample mean

A researcher calculates a confidence interval for a paired-samples t test. That interval is centered on -6.35, which is the:

sample mean difference

____ is a measure of our ability to reject the null hypothesis given that the null hypothesis is false

statistical power

The _____ indicates the distance of a sample mean from a population mean in terms of the estimated standard error. You Answered

t statistic

the the population variance or standard deviation is not known, you must use a ___ instead of a z-statistic for a hypothesis test?

t statistic

correct APA format for reporting statistical results:

t(27)= 3.5, p < 0.05

When comparing the difference between means for two distributions, what happens to the effect size as the variability within each distribution becomes smaller?

the effect size increases

A researcher is comparing two groups. The population mean from which the samples come is known, but not the population standard deviation. Which test should be used?

the t test because standard deviation for the population must be estimated

Why is it necessary to use pooled variance rather than variance when conducting an independent-samples t test

there are two samples

Why is it necessary to use pooled variance rather than variance when conducting an independent-samples t test?

there are two samples

According to APA standards, why is it recommended to report descriptive statistics for the two samples in addition to reporting the p value?

they provide additional information about the group differences that often interests readers

What needs to be known to determine the critical values for an independent-samples t test?

total degrees of freedom

Two samples drawn from the same population will probably have different t statistics even if they are the same size and have the same mean- true or false?

true

confidence interval provide more information than hypothesis tests- true or false?

true

if both studies use an alpha level of .05, a study with an N of 100 is just as likely to result in a type 1 error as a study of N of 20- true or false?

true

if the 99% confidence interval for mew is 40 to 50, then the sample mean is M=45, true or false?

true

in a repeated measures study, a small variance for the difference scores indicates that the treatment effect is consistent across participants- true or false?

true

counterbalancing minimizes order effects by:

varying the order of presentation of different levels of the independent variable from one participant to the next

The major difference between the paired-samples t test and the single-samples t test is that in the paired-samples t test:

we must create difference scores for every individual.

Can you ever have too much power and would that be a problem? (short answer quesiton)

yes. every variable becomes significant

What are the advantages of using a within-subjects design over a between-subjects design? (Short answer question)

- can use a smaller sample size - no need for extra control group - increase in statistical power

Statistical power can be enhanced by decreasing the standard deviation in the sample. This can be accomplished by:

- using a more reliable measure - sampling a more homogeneous (alike) group - working with a less variable distribution of scores

Dividing SS by "n-1" results in a "sliding" adjustment, yielding an unbiased estimate of σ2. Explain the adjustment made by "n-1", especially as it relates to sample size (short answer quesiton)

-By subtracting 1 from N, we will get a slightly larger and more accurate standard deviations value - As the value of N increases, we will approach z and it will be closer to the actual normal z distribution of the population (sliding adjustment) -A larger sample will more likely be similar to that of the entire population than one derived from a smaller sample

Cohen's d (effect size) guidelines

.2= small .5= medium .8 = large

Steps in Hypothesis Testing

1. identify population, distributions, & assumptions 2. state hypothesis 3. characteristics of the comparison distribution 4. determine critical values or cutoffs 5. calculate the test statistic 6. make a decision

A researcher believes that a new math training program will increase test scores. Previous research shows that test scores increase 5 points between the first and second administration of the test being used. This researcher believes his training program will cause a significant increase, beyond the expected 5 points. If a paired-samples t test is used by this researcher, what value would he expect to be at the center of the comparison distribution, a distribution of mean differences?

5

The interval estimate for two values overlaps. What might this indicate?

Both points may actually have the same value in the general population, although one appears slightly higher, possibly due to uncertainty of the sample.

if the null hypothesis states that mew=70 and a researcher obtains a sample M=73 and s^2 = 9, then cohens d= .33 True or false?

False because d= 73-70/ 3 = 1 (we use SD not variance)