302 Midterm 2
A researcher randomly assigns participants to two groups. One group slept 8 hours and the other group slept 4 hours the night before an exam. Which of the following statistical tests should he run, if he wants to test the effect of sleep on exam performance?
independent samples t-test
Distribution of differences btwn the means
independent samples t-test
For which of the following tests does the calculation of the t-statistic require a pooled standard deviation measure?
independent samples t-test
A researcher reports the following results from a paired samples t-test (two-tailed, alpha = .05): t(31) = 3.44, p = .021 What should the researcher conclude?
reject the null
If the variation between sample means is large
then there is a significant effect
Distribution of sample means
z-tests and one sample t-tests
sample size does NOT affect
effect size
In ANOVA, what is the most commonly used measure of effect size?
eta squared
In which of these scenarios would a researcher use a one-sample t-test?
A personality psychologist compares whether levels of consciousness in a random sample of college students at her college differ from the known mean of a typical student.
Why don't we just run a bunch of different t-tests when comparing multiple groups?
because every t-test would add more probability of Type I error.
F =
between groups variance/within groups variance
Between groups vs. repeated measures ANOVA
between is an extension of independent samples, repeated measures is an extension of paired samples
Unlike a z-test, in a t-test,
critical values (a=.05) depends on sample size. The smaller the sample, the fatter the tails = small sample, Fcrit must be must be bigger to be considered rare.
To find Tcrit of a paired samples t-test, use
df = n-1
dfAxB
dfA x dfB
In a one-way, repeated-measures ANOVA, the degrees of freedom associated with the remaining variability (after variance due to individual differences and the independent variable are factored out )are called _____.
dfResidual
In a one-way, repeated-measures ANOVA, the degrees of freedom associated with variability due to the independent variable are called _____.
dfTreatment
A researcher administered a measure of extraversion to a group of biology majors and to a group of psychology majors, with the goal to compare the groups. The researcher finds out that his sample contained a few double majors. Which assumption of the independent samples t-test does this violate?
independence
A one-way, between-subjects ANOVA with two groups is identical to the...
independent samples t-test
DFcrit
(DFB,DFW)= x
How do you find N if it is not given?
(n*k)
Compute variance (MS) for the following sample data: 6, 3, 8, 5, 1 Hint: Make sure to use n-1. Round to two decimal points
7.3
Compute variance (MS) for the following sample data: 6, 8, 9, 2, 7 Hint: Make sure to use n-1. Round to two decimal points
7.3
2 levels of one group and 2 levels of another group
= a 2X2 factorial ANOVA
A researcher tests the working memory capacity of 12 world class poker players and plans to run a one-sample t-test to determine if poker players have a higher WMC than the general population (μ = 7). The participants in the study remembered on average 9.17 words from the word list (SD = 3.46). Calculate the estimated standard error of the mean. Round your answer to two decimal places.
1
A typical U.S. adult gets 6.8 hours of sleep per night. A sleep researcher tested if college students sleep less than the general population. He asked 24 college students how much sleep they got the night before (in hours) and found that on average they slept 6.3 hours. The researcher is running a one-sample, one-tailed t-test to test his hypothesis. How many degrees of freedom are there for this test?
23
Given: The total number of participants = 144 Number of groups = 6 SSb = 13 SSw = 274 What is the mean squares within? Round to two decimal points
1.99
Given: Number of participants = 298 Number of groups = 4 SSb = 57 SSw = 168 What is the value of mean squares between? Round to two decimal points
19
A one-way ANOVA is used to test for mean differences between/among ________________________________.
2 or more groups
Given: The total number of participants = 111 Number of groups = 4 SSb = 18 SSw = 261 What is the mean squares within? Round to two decimal points
2.44
A researcher reports the following results from a paired samples t-test: t(27) = 4.56, p < .001 How many participants were in the study?
28
With a sample of 30, the degrees of freedom for a one-sample t-test would be
29
Compute sum of squares (SS) for the following sample data: 0, 4, 8, 3, 4 Round to two decimal points
32.8
For which of the following would a paired t-test be appropriate? Select all that apply.
A researcher is studying neuroticism in parent-child dyads. A researcher is comparing performance before and after a training program. *NOT*: A researcher is looking at the relationship between agreeableness and extraversion on the same individuals.
For which of the following would a paired samples t-test be appropriate?
A researcher measures working memory capacity for each participant before and after a sleep intervention.
when do you calculate the effect size?
Always when calculating an ANOVA
Brenda is interested in the effects of stress on blood pressure. She assesses the blood pressure of 50 females before, during, and after giving a public speech. What would her null hypothesis be?
Average blood pressure would be the same before, during, and after giving a public speech.
Under what circumstances will the absolute value of the t-statistic be the largest?
Big diff between means and large sample size. A t-value of 0 indicates that the sample results exactly equal to the null hypothesis. As the difference between the sample data and the null hypothesis increases, the absolute value of the t-value increases
Under what circumstances will be the absolute value of the t-statistic the largest?
Big differences between means, large sample size
What is the null hypothesis for an independent samples t-test?
The two independent samples are drawn from populations with the same mean.
DFb (factorial ANOVA)
DFb (factorial ANOVA)
To find the t-crit for an independent samples t-test, you need it's degrees of freedom. You get this how?
DFpooled = DF1+DF2 or N-2
In a paired samples t-test, what does SMd mean?
Estimated standard error of the differences SMd =sqrt(variance/n) To get variance: SS/df To get the SS for this, you do (the sum of the difference in scores - Md)^2
Another way to think of F =
F= Variability due to treatment effect + Variability due to individual differences/Variability due to individual differences *Notice that, in the absence of any treatment effect, the F statistic will equal 1.
The researcher conducts a two-tailed test comparing her sample to a population with a mean of 40. Which of these is the null hypothesis?
H0: u=40
Which of the following would violate the independence assumption for a one-sample t-test?
If the same person participated in the study multiple times
SSbestween (factorial ANOVA)
K-1
In factorial ANOVA SStotal DF
N-1
The degrees of freedom for a paired samples t-test is
N-1
Total DF
N-1
SSwithin (factorial ANOVA)
N-K
A researcher runs a one-sample, two tailed, t test (alpha = .05) and reports the following results: t(58) =2.78, p=.023, CI95=[35.4,39.5] What is the correct decision?
Reject the null hypothesis
The researcher runs a one-sample, two-tailed t-test (α = .05) and reports the following results: t(58) = 2.78, p = .023, C I 95= [35.4, 39.5]. What is the correct decision?
Reject the null hypothesis.
A study comparing men and women on empathy reported t(22) = 1.92, p>0.05. What can we conclude?
The results are not statistically significant The null hypothesis was retained
How do you find the estimated standard error of the difference S(M1-M2)
S(M1-M2)= sqrt(variance(pooled) x (N/n1xn2) variance(pooled)= Vp=(n1−1)V1+(n2−1)V2n2/df1+df2
In a Z test, how do you find the population standard error of the mean?
SD/sqrt(N)
SSa and SSb (factorial ANOVA)
SS of factor A and factor B (that between groups is split by)
SSaxb (in a factorial ANOVA)
SS of the interaction btwn factor A and factor B
Mean Squares
SS/df
How do you find the estimated standard error?
Sm= s/sqrt(N)
In a paired t-test, what does Md mean?
The average change for all cases = The sum of the differences for each case/n
What is the Omnibus test?
The main test in a factorial ANOVA
p-value
The probability of of getting the observed test statistic or more extreme, assuming the null hypothesis is true.
In order to calculate the standard error of the difference scores for a paired samples t-test, you need to know
The standard deviation of the difference scores. The sample size.
In a one-way ANOVA, the within-groups degrees of freedom is equal to
The total number of participants - the total number of groups
What is the critical t-value for a two-tailed, one-sample t-test when the alpha level is set at .05?
There is not enough info to answer this Q
When a population standard deviation is known
Use a z-test Z=M-u/SDm
If a 95% confidence interval for the mean difference score in a paired samples t-test includes zero, then
We cannot reject the null
When do you use a paired samples t-test?
When looking at differences Pre-test, Post-test (of the same type) Diff of each person's scores btwn 2 conditions (within-subjects) or how a person's score in one sample differs from their related person in the other sample (matched samples)=mom and kid
Under what circumstances does the t-distribution look nearly identical to the z-distribution?
When the sample size(N) is very large
In repeated measures ANOVA, removing variability due to individual differences reduces the error term in the denominator of the F-ratio. This results in....
a more powerful test
when do you use a post hoc test?
after a significant f-test result
Factor
an IV or QIV that can take on any number of levels
Level
individual conditions (summer, winter, fall, spring)
A repeated measures ANOVA is usually more powerful than between-subjects ANOVA because it can account for the variability in dependent variable that is due to...
individual differences
The MS within is sometimes referred to as the error variance. A key source of error variance is ...
individual differences
Between groups DF
k-1
Variance in ANOVA is referred to as ....
mean squares
DFa (factorial ANOVA)
n levels of A -1
An eta squared value of 0 indicates ________
no effect of group
The assumptions for paired t-test are very similar to the assumptions for a
one sample t-test
Which inference test would we use for comparing conscientiousness score in a sample of UO undergraduates to the known national average?
one-sample t-test
A researcher compares pre and post-therapy depression scores collected from the same individuals. The researcher should analyze the data with a(n)
paired samples t-test
Independent samples t-test
t=(M1-M2)/S(M1-M2) t=difference btwn sample means/the estimated standard error of the difference
You should use a one-way repeated measures ANOVA when
testing for significant differences between groups when the same participants are in each group
Which of the following is a general definition of Cohen's d?
the difference of means divided by the standard deviation
In a one-way ANOVA, the between-groups degrees of freedom is equal to
the number of groups - 1
When do you use an independent samples t-test?
to see if the average score in one population is better or worse than the average in a second population (experimental group w/ control group). Both groups MUST be random sample and independent. Ex. test whether second born children develop language faster than first-born children. Test first borns and second borns at same age from DIFF families.
A researcher tests the working memory capacity of 27 world class poker players and plans to run a one-sample t-test to determine if poker players have a higher WMC than the general population (μ = 7). The participants in the study remembered on average 7.85 words from the word list (SD = 3.34). Calculate the estimated standard error of the mean. Round your answer to two decimal places.
.64
The researcher collects data from 28 people. What will the critical t-value be for a two-tailed, one-sample t-test when the alpha level is set at .01? Use t-table.
2.771
A researcher tests the working memory capacity of 22 world class poker players and plans to run a one-sample t-test to determine if poker players have a higher working memory capacity than the general population (μ = 7). The participants in the study remembered on average 9.02 words from the word list (SD = 2.96). Calculate the t-statistic. Round your answer to two decimal places.
3.2
A researcher tests the working memory capacity of 18 world class poker players and plans to run a one-sample t-test to determine if poker players have a higher working memory capacity than the general population (μ = 7). The participants in the study remembered on average 9.85 words from the word list (SD = 3.26). Calculate the t-statistic. Round your answer to two decimal places.
3.71
A researcher reports these results from an independent samples t-test, t(89) = 3.80, p = .044, C I 95 = [3.05, 12.67], d = .65. What is the value of the test statistic?
3.80
A researcher sampled 24 people who volunteered to pick up trash on the beach. The volunteers filled out a personality survey, and the researcher hypothesized that the volunteers would score higher on the trait agreeableness than the general population. The mean for agreeableness in the general population is considered to be 3, while the sample of volunteers scored a 4.04 (SD = 1.32). Calculate the t-statistic for a one sample t-test. Round your answer to two decimal places.
3.86
A clinician is interested in seeing if her patients have lower depression scores after therapy compared to before therapy. For each of her 40 patients, the clinician subtracts the depression score at time two from the depression score at time one. She finds that the mean of the difference scores is -0.79 (SD = 2). She runs a paired samples t-test with how many degrees of freedom?
39
A researcher sampled 33 people who volunteered to pick up trash on the beach. The volunteers filled out a personality survey, and the researcher hypothesized that the volunteers would score higher on the trait agreeableness than the general population. The mean for agreeableness in the general population is considered to be 3, while the sample of volunteers scored a 4.12 (SD = 1.44). Calculate the t-statistic for a one sample t-test. Round your answer to two decimal places.
4.47
Compute sum of squares (SS) for the following sample data: 1, 2, 10, 2, 3 Round to two decimal points
53.2
Given: The total number of participants = 58 Number of groups = 3 SSb = 7 SSw = 234 What is the degrees of freedom within?
55
Given: The total number of participants = 64 Number of groups = 5 SSb = 20 SSw = 170 What is the degrees of freedom within?
59
The researcher runs a one-sample, two-tailed t-test (α = .05) and reports the following results: t(58) = 2.78, p = .023, C I 95= [35.4, 39.5]. How many people were sampled?
59
Given that the sum of squares between = 20 and the sum of squares total is = 86, what is the sum of squares within?
66
Which of these observed values are more likely to lead to rejecting of the null hypothesis?
A very small p-value A large F-value
Within-groups DF
N-k
Studying the relationship between geographical location and political views, a researcher compared scores on the conservative values questionnaire among samples from New York, South Carolina, Kansas, Montana and Oregon. What in this scenario would be referred to as a level?
New York, South Carolina, Kansas, Montana or Oregon
When will the independent samples t-value be more likely significant?
When there is a small variability within each group When the differences between sample means are large
The shape of F distribution under the null hypothesis is determined by...
both within and between groups degrees of freedom
Bonferroni, Holm, Tukey are all examples of
corrections for multiple comparisons (THEY ARE NOT INFERENCE TESTS
How do you determine effect size?
eta squared! =SSb/SStotal represents the proportion of total variability in the sample that is explained by the treatment effect
The null hypothesis for an independent samples t-test states that the difference between the population means is
exactly zero
Studying the relationship between geographical location and political views, a researcher compared scores on the conservative values questionnaire among samples from New York, South Carolina, Kansas, Montana and Oregon. What variable in this scenario would be referred to as a factor?
geographical location
In a 2-way factorial ANOVA, what are you reporting?
if you have 2 IVs, then you have 2 main effects and 1 interaction = 3 different f tests = 3 nulls, and 3 things to report
Why are repeated measures ANOVAs more powerful?
n a repeated measures ANOVA, we can figure out the individual differences because we test the same people (or groups or whatever) multiple times. So we can remove the variability due to differences between people from the within groups, shrinking the bottom half of the ratio, and making the whole F value larger.
In a one-way, repeated-measures ANOVA, which equation is used to calculate dfSubjects?
n-1
In a one-way ANOVA, the factor is most commonly on which type of scale?
nominal/categorical
Distribution of mean differences
paired samples t-test
One-way, repeated measures ANOVA is an extension of _________
paired t-test
Cohen's D
provides a standardized measure of effect size d= difference in means/SD = M=u/popSD
As t value increases,
pvalue decreases.
Which of the following violates the homogeneity of variance assumption?
s1= 4.76, s2 = 18.45
In an ANOVA f-test (vs t-test)
smaller sample needed to discover an effect
Sample standard deviation
sqrt(SS/N-1)
Population standard deviation
sqrt(ss/N)
In ANOVA, we calculate the mean squares as a ratio of
sum of squares divided by the degrees of freedom
In a one-way ANOVA, the alternative hypothesis is that
the population means are not all equal
In an anova, if there is an effect
the total variability will be greater than the variability in each group. if no effect, it will be about the same.
What is the purpose of a Post Hoc for an f test
to check for between groups variability between different pairs
Why do we use ANOVA instead of T-test?
to control for type 1 errors
Factorial design study
uses 2 different treatments (IVs) in 2 or more groups
When do you use a single sample t-test?
when we do not know the pop SD, instead we infer it based on the sample variability t=M-u/Sm
In an independent samples t-test, t-values can be positive or negative depending on
which group mean is subtracted from the other in the t-statistic formula.
What do post-hoc tests tell us?
which means are significantly different from each other
