Psych 210 Exam #2
what is r squared?
-another measure of effect size -accounts for variance
Meta-analysis
-considers many studies simultaneously -allows us to think of each individual study as just one data point in a larger study
Increasing effect size does what to amount of overlap?
-decreases amount of overlap -means farther apart -less variability
What is statistical power?
-measure of our ability to reject the null hypothesis, given that the null is false -the probability that we will reject the null when we should -the probability that we will avoid a type 2 error -want 0.8 or better
what is effect size?
-size of a difference that is unaffected by sample size -ignores sample size, how big of a difference do we really have? -standardization across studies -cohen's d
if a hypothesis test is found to have a power = 0.70, what is the probability that the test will result in a type 2 error? A. 0.30 B. 0.70 C. 0.05 D. cannot be determined without more info
0.30
a paired samples t test is also known as:
Dependent samples t-test
counterbalancing
minimizes order effects by varying the order of presentation of different levels of the independent variable from one participant to the next -can reduce order effects in within-groups research designs
Increasing sample size will make us more or less likely to find a statistically significant effect?
more
when sample size increases, s approaches sigma and t and z become (more or less) equal?
more
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.
A researcher calculates a confidence interval for a paired-samples t test. That interval is centered around -8.32, which is the:
sample mean difference
What are Cohen's effect sizes?
small- 0.2 medium- 0.5 large-0.8
Cohen's d estimates effect size by assessing the difference between means using the __________________ instead of ________________
standard deviation; standard error
What is the difference between the z and t tests?
t test uses the estimated standard error while the z statistics uses the actual standard error of the distribution of means
Reporting the statistics
t(df) = tcalc, p < 0.05
what do t tests tell us in general?
tells us how confident we can be that the sample differs from the larger population -t distributions more versatile than z distributions because we can use them when (a) we don't know the population standard deviation, and (b) we compare two samples.
degrees of freedom
the number of scores that are free to vary when we estimate a population parameter from a sample df= N-1
p < 0.05 vs p > 0.05
there is a difference between means (reject the null) no difference between means (fail to reject null)
True or false: if the sample data are in the critical region with alpha = 0.01, then the same sample data would still be in the critical region if alpha were changed to .05
true
True or false: t distributions are wider and flatter compared to standard, normal z distributions
true
true or false: a type 1 error occurs when a treatment has no effect but the decision is to reject the null hypothesis
true
true or false: for a hypothesis test using a t statistic, the boundaries for the critical region will change if the sample size is changed
true
true or false: in a repeated measures study, a small variance for the difference scores indicates that the treatment effect is consistent across participants
true
true or false: paired samples t tests are particularly well suited to research studies examining learning or other changes that occur over time
true
true or false: the null hypothesis is stated in terms of the population even though the data comes from a sample
true
true or false: two samples draw from the same population will probably have different t statistics even if they are the same size and have the same mean
true
true or false: when the population variance or standard deviation is not known, you must use a t statistic instead of a z statistic for a hypothesis test
true
Number of samples and comparison distribution for independent-samples t test
two (different participants); distribution of differences between means
Number of samples and comparison distribution for paired-samples t test
two (same participants); distribution of mean difference scores
paired samples t-test
two sample means and a within-groups design *the major difference in the paired-samples t test is that we must create difference scores for every participant (i.e. mean of the differences)
why is sample standard deviation a biased estimator?
underestimates true variability in population
Power can be thought of as the percentage of the distribution of means, centered around the sample mean, that falls: A. outside of the null hypothesized distribution. B. above two standard deviations from the sample mean. C. within the critical cutoff regions, where the null hypothesis can be rejected. D. below the mean of the null hypothesized distribution.
answer: C
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 computing a meta-analysis. Rosenthal suggested that researchers test the level of inflation of their effect size calculations by: A. conducting additional research that would more clearly assess the relationship between variables. B. pressuring scholarly journals to publish more null findings. C. computing a file drawer analysis to see how many null findings would be needed to remove the statistical significance found. D. including studies in their meta-analysis that have strong effects only.
answer: C
The _____ estimate acknowledges the amount of uncertainty in the _____ estimate by reporting the margin of error. A. interval; standard error B. point; interval C. interval; point D. point; standard error
answer: C
Would an independent-samples t test be appropriate when using three groups (a control group and two experimental groups) to compare differences on an IQ test? Explain. A. Yes; IQ test scores is a scale variable. B. Yes; the participants belong to different groups C. No; there are more than two groups. D. No; the independent variable should be a scale variable.
answer: C
Would an independent-samples t test be appropriate when using three groups (a control group and two experimental groups) to compare differences on an IQ test? Explain. A. Yes; IQ test scores is a scale variable. B. Yes; the participants belong to different groups. C. No; there are more than two groups. D. No; the independent variable should be a scale variable.
answer: C
a psychologist has conducted a study of how well students remember the content of advertisements when the ads are embedded in violent TV shows vs. nonviolent TV shows. she finds a statistically significant difference between the two conditions. the probability of a type 2 error is: A. 1- alpha B. 0.05 C. zero D. 1-beta E. cannot be determined from the information provided
answer: C
the 95% confidence interval for Mx-My does not include 0. If the H0 that mux- muy = 0 were now being tested, A. the difference between Mx-My would not be significant at the .05 level B. the difference between Mx-My would be significant at the .025 level C. the difference between Mx-My would be significant at the .05 level D. nothing can be said about the significance of the difference at this point
answer: C
what measure of effect size assesses the difference between two means in terms of standard deviation?
cohen's d
As effect size increases, the overlap between distributions being compared increases, decreases, or stays the same?
decreases
dependent sampling generally results in a more powerful statistical test than independent sampling because:
dependent procedures reduce the variability in the sampling distribution
Sample size can affect whether statistically significant differences are found, but sometimes in extremely large samples differences are found that are significant but of no real value or interest. What standardized value helps measure the size of the difference in relation to the variability of the data rather than to that of sample size?
effect size
true or false: in general, the larger the sample variance, the greater the likelihood of rejecting the null hypothesis
false
true or false: we construct our 95% confidence interval around the null hypothesized mean value
false
True or false: we never use z scores when doing power calculations
false: ALWAYS use z scores when doing power calculations
What is a new assumption for the independent-samples t test?
homogeneity of variance -the two populations from which are the samples are selected must have equal variances (SD) - same variability
order effects
how a participants behavior changes when the dependent variable is presented for a second time -function of practice effects (i.e. better 2nd time because already did it)
relate effect size to the concept of overlap between distributions
if two distributions overlap a lot, then we would probably find a small effect size and not be willing to conclude that the distributions are necessarily different. if the distributions do not overlap much, this would be evidence for a larger effect or a meaningful difference between them
What type of test: reward vs. punishment
independent samples t test
what type of tests: chalkboard vs. powerpoint
independent samples t test
what does effect size tell us?
indicates the size of a difference and is unaffected by sample size
Six Steps of Hypothesis Testing
1. Identify the populations, distribution, and assumptions and then choose the appropriate hypothesis test 2. State the null and research hypotheses in both words and symbolic notation 3. Determine the characteristics of the comparison distribution 4. Determine the critical values, or cutoffs, that indicate the points beyond which we will reject the null hypothesis 5. Calculate the test statistic 6. Decide whether to reject or fail to reject the null hypothesis
How to calculate power:
1. determine the info needed to calculate power: population mean, population std. dev., sample mean, sample size, standard error (based on sample size) 2. determine a critical z statistic and raw mean 3. calculate: the percentage of the distribution of the means for population 2 that falls above the critical value
What are the ways we can get more power? Which 2 do we not do? (*)
1. larger sample size increases power *2. alpha level (higher level increases power) *3. one-tailed tests have more power than two-tailed tests 4. decrease standard deviation (by exerting more experimental control) 5. increase difference between the means (changes size of manipulation)
What are the 3 assumptions that underlie parametric tests?
1. scale data 2. normal distribution 3. random sampling
When is it appropriate to use the independent-samples t test?
An independent-samples t test is used when we do not know the population parameters and are comparing two groups that are composed of unrelated participants or observations.
Why do the t distributions merge with the z distribution as sample size increases?
As the sample size increases, we can feel more confident in the estimate of the variability in the population. Remember, this estimate of variability (s) is calculated with N 2 1 in the denominator in order to inflate the estimate somewhat. As the sample increases from 10 to 100, for example, and then up to 1000, subtracting 1 from N has less of an impact on the overall calculation. As this happens, the t distributions approach the z distribution, where we in fact knew the population standard deviation and did not need to estimate it.
The use of probabilities based on prior beliefs is:
Bayesian statistics
why are interval estimates better than point estimates?
Interval estimates provide a range of scores in which we have some confidence the population statistic will fall, whereas point estimates use just a single value to describe the population
point estimate vs. interval estimate
Point estimate: summary statistic - one number as an estimate of the population (i.e. mean) Interval estimate: based on our sample statistic, range of sample statistic we would expect if we repeatedly sampled from the same population (i.e. confidence interval)
How is a paired samples t test different from a single sample t test?
Unlike a single-sample t test, in the paired-samples t test we have two scores for every participant; we take the difference between these scores before calculating the sample mean difference that will be used in the t test.
single sample t test
a hypothesis test in which we compare a sample from which we collect data to a population for which we know the mean but not the standard deviation
why do we calculate confidence intervals?
add details to the hypothesis test. they tell us a range within which the population mean would fall 95% of the time if we were to conduct repeated hypothesis tests using samples of the same size from the same population.
A group of rats ran faster with a steroid drug supplement compared to a group of rats that received no steroid drug supplement. Which type of statistical test should be used to report these results? A. independent-samples t test B. paired-samples t test C. single-sample t test D. z test
answer: A
After performing a paired-samples t test as part of a hypothesis test, it is recommended by the APA that researchers also consider: A. calculating a confidence interval and a measure of effect size. B. performing a power analysis to assess the risk of Type I errors. C. repeating the research with a between-groups design to avoid order effects. D. running a replication to confirm the findings.
answer: A
which of the following is the proper way of writing the null hypothesis for a single sample t test? A. mu = x B. mu1= mu2 C. mu1-mu2= 0 D. all of the above are correct
answer: A
A power analysis reveals that the study being run has low power. Which method is NOT an appropriate way to increase statistical power? A. Increase the alpha. B. Increase the variance of the distributions. C. Increase the N. D. Decrease the standard deviation.
answer: B
By increasing statistical power, the probability of making a _____ error is _____. A. Type I; 0 B. Type II; decreased C. Type I; decreased D. Type II; 0
answer: B
In Cohen's d, the farther apart the means of two distributions, the _____ the effect size, assuming the standard deviation is held constant. A. more variable B. higher C. lower D. less variable
answer: B
Which statement is true about final decisions made from an independent-samples t test A. hypothesis tests provide more information than confidence intervals B. confidence intervals provide more information than hypothesis tests C. hypothesis tests and confidence intervals are the same thing D. effect size cannot be calculated for independent-samples t tests
answer: B
as sample size decreases, the shape of the t distribution: A. gets progressively narrower B. gets progressively wider C. more likely matches the z distribution D. is more accurate
answer: B
if the treatment has a very small effect, then what is the likely outcome for a hypothesis test evaluating the treatment? A. type 1 error B. type 2 error C. a correct rejection of the null D. a correct failure to reject the null
answer: B
when N is small (less than 30), how does the shape of the t distribution compare to the normal distribution? A. it is almost perfectly normal B. it is flatter and more spread out than the normal distribution C. it is taller and narrower than the normal distribution D. there is no consistent relationships between the t distribution and the normal distribution
answer: B
A Cohen's d value of 0.2 indicates how much overlap between distributions? A. no overlap B. 53 percent C. 85 percent D. a medium amount of overlap
answer: C
A researcher is comparing the normal curve for two studies using the standard deviation for individual scores. Study 1 depicts two samples with means close together, while the means in Study 2 are farther apart. Which has a bigger effect size? A. Study 1 because there is more overlap between distributions B. Study 1 because there is less overlap between distributions C. Study 2 because there is more overlap between distributions D. Study 2 because there is less overlap between distributions
answer: D
For the paired-samples t test, the comparison distribution: A. is the same as that for a single-sample t test. B. is the same as that for the z test. C. contains sample means based on samples of the same size. D. contains means of difference scores.
answer: D
In Cohen's d, the closer together the means of two distributions, the _____ the effect size, assuming the standard deviation is held constant. A. more variable B. higher C. less variable D. lower
answer: D
In order to conduct a single-sample t test, one needs to know: A. the population mean and standard deviation, and the standard error of the sample. B. all properties of the sample and the population. C. the mean of the sample and all properties of the population. D.the population mean and the properties of the sample.
answer: D
When conducting a study of gender differences, we have to employ: a. single-sample t test b. paired-samples t test c. dependent-samples t test d. independent-samples t test
answer: D
if a hypothesis test is found to have a power = 0.70, what is the probability that the test will result in a type 1 error? A. 0.30 B. 0.70 C. 0.05 D. cannot be determined without more info
answer: D
the comparison distribution for an independent-samples t test is a distribution of: A. means B. scores C. mean difference scores D. differences between menas E. all of the above
answer: D
A value of 0 within the interval of a confidence interval may indicate: A. an error in the calculation. B. large sample sizes. C. no difference. D. large confidence interval.
answer: no difference
An independent-samples t test is used with which type of research design?
between-groups design
Number of samples and comparison distribution for single-sample t test
one; distribution of means
Number of samples and comparison distribution for z test
one; distribution of means
it is hypothesize that there will be a significant difference in aggression scores after caffeine consumption as compared to before caffeine consumption. what hypothesis best illustrates this?
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
p<0.05 means what?
reject the null
s vs. SD
s uses (N-1)
For a repeated measures study comparing 2 treatments, a researcher obtains a sample of N= 9, difference scores with a Mdiff=4 and a variance of s2= 36. what is the value for the t statistics?
sM= 6/3= 2 t= 4/2
independent samples t-test
used to compare two means in a between-groups design (i.e. each participant is in only one condition) -more variability -samples independent to each other
why is it necessary to use the pooled variance when conducting an independent-samples t test?
we are working with two samples and an estimate of spread based on two samples is likely to be more accurate than an estimate of spread based on a single sample
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
when should we use a t distribution?
when we do not know the population standard deviation and are comparing 2 groups