Hypothesis Testing
Can a null hypothesis ever be proven?
No, because we always might find evidence of an effect in the future
What are the degrees of freedom for a single-sample t test if you had a sample of 100 participants?
df = 99
How do you know whether to use an independent-samples or paired-samples t test?
With independent samples, there is no relationship between the cases in the two samples. With paired samples, the cases in each group are related in some way. For paired samples, the samples in each case can be the same people or paired up on some basis.
Which of the following is NOT another term for a paired-samples t test?
A) Dual sample
B) Matched pairs
C) Repeated measures
D) Within subjects
A) Dual sample
Refer to the drawing of a scatterplot on the board. What kind of relationship is depicted in the scatterplot?
Negative/inverse
What are assumptions for a statistical test?
The conditions that must be met in order to run that statistical test
When do we do a single-sample t test, rather than a single-sample z test?
When we do not know the population standard deviation
A) s1 = 3.0, s2 = 3.5
B) s1 = 1.0, s2 = 2.2
C) s1 = 4.0, s2 = 7.8
D) s1 = 12.5, s2 = 20.0
B) s1 = 1.0, s2 = 2.2
How do you determine the degrees of freedom for a paired-samples t test?
Subtract 1 from the number of pairs
N - 1
Name the assumptions of a correlation test.
Random sample, independence of observations, normality, linearity
What does it mean for results to be statistically significant?
The sample mean differs from the actual or hypothesized population mean.
Why do degrees of freedom matter for t tests?
The shape of the t distribution changes as sample size increases.
Which of the following is the correct formula for an independent-samples t test?
A) t = M - u / sM
B) t = M1 - M2 / sM1-M2
C) t = M1 - M2 / sMD
B) t = M1 - M2 / sM1-M2
What is the best measure of effect size for a paired-samples t test?
Confidence intervals, because we can't report d or r2
Which of the following is a correct null hypothesis for a one-tailed correlation test?
A) H0: ρ ≤ 0
B) H0: ρ ≠ 0
C) H0: r = 0
D) H0: r ≠ 0
A) H0: ρ ≤ 0
Alpha is also known as the probability of making what type of error?
Type I error
A researcher is interested in how loud music affects typing speed. The website where they have their participants do a typing test mentions that the overall average score across everyone who takes their test is 65 WPM. There is no standard deviation listed. They run a sample on 25 people taking this typing test while listening to loud music. The mean typing score for their sample is 50 WPM, with a standard deviation of 15 WPM. Calculate the test statistic and mention if the researcher should reject or fail to reject the null hypothesis, if they want to do a two-tailed test with an alpha of 0.05.
tcv = 2.064
t(24) = 5.0
Reject the null hypothesis
Calculate Cohen's d for the following independent-samples t test data.
s1 = 4.0
s2 = 3.0
M1 = 10.0
M2 = 8.0
n1 = 20
n2 = 18
d = 0.56
Which measure of variance is used to calculate the test statistic for a paired-samples t test?
A) standard deviation (s)
B) standard error of the mean (sM)
C) standard error of the difference (sM1-M2)
D) standard error of the difference (sMD)
D) standard error of the difference (sMD)
Convert the following r scores to z scores.
A) 0.34
B) -0.86
C) 0.55
A) 0.35
B) -1.29
C) 0.62
Write null and alternative hypotheses for an independent-samples t test, paired-samples t test, and a correlation test for the following situation. A researcher thinks that dancing in the morning will improve mood. Because they believe there will be a positive effect of dancing on mood, they want to do a one-tailed test.
Independent-samples
H0: μ1 ≤ μ2
H1: μ1 > μ2
Paired-samples
H0: μ1 ≤ μ2
H1: μ1 > μ2
Correlation
H0: ρ ≤ 0
H1: ρ > 0
Calculate r2 for a single-sample t test with the following information, mentioning if this is a small, medium, or large effect:
t = 4.0
df = 49
24.62%
Medium, arguably large
Why do we use a pooled weighted variance estimate when computing the standard error of the difference? What is it estimating? What is it pooling? Why is it weighted?
The computation of the standard error of the difference pools together the two sample variances to get a better estimate of the population variability. Each sample variance is weighted by the size of its sample because we know that the larger the sample is the better is the estimate of the population value. So, the larger sample is given more weight in the estimate.
Calculate a 95% confidence interval for the following paired-samples t test results, assuming an alpha level of 0.05 for a two-tailed test.
M1 = 14
M2 = 20
N = 30
sMD = 1.10
95% CIdiff [3.75, 8.25]
Calculate a confidence interval for the following correlation results.
r = 0.87
a = 0.05, two-tailed
N = 30
95% CI [0.74, 0.94]