Module 5 T-test
What is a benefit to using between-subjects study? what is a con?
-the subjects are only in one group or the other, under a single condition -there may be high level of variability between the groups (age, gender, socioeconomic, status, educational background, etc.)
Given the sample statistics: n =11, x bar =107.1818, and s =10.3133. Compare the critical t value for a one-tailed test and a two-tailed test with α=0.05. Why is there a difference?
Answer: In a two-tailed test, the 0.05 is split between the two tails rather than being concentrated on either the left or right side of the distribution. Therefore, the corresponding critical value would change. Specifically, the critical value for a two-tailed test (α=0.05) would be ±2.228 and the critical t value for a one-tailed test is ±1.812.
What is the meaning of the null hypothesis (H0) for a one sample t-test?
Answer: The null hypothesis states that μ is equal to the claimed value.
What is the major difference between a paired samples and independent samples t-test?
Both of these t-tests involve two samples. However, in a paired samples t-test, the members of the two samples are related in some way. Either both samples consist of the same members at two different time points or the samples consist of members who are related (spouses, siblings, pairs, etc.). In an independent samples t-test, the members of each sample are completely independent of one another, and membership is mutually exclusive (members of one sample cannot be members of the second sample). Examples of independent samples include members of different political parties, pet owners vs non-pet owners, men vs women, etc.
True or False: Mathematically, the normal distribution and the t-distribution are very different.
False
If a researcher administers the same medication to a group of teenagers and a group of adults, what type of design is this?
Independent samples design
In what type of experimental design is an assessment administered before and after a treatment condition with the same participants? (a) Observational study (b) Double-test design (c) Blinded design (d) Pre/post-test design
Pre/post-test design
If a researcher states in the alternative hypothesis that μ is greater than the claimed value, what type of test would be performed?
Right-tailed
Define degrees of freedom. What is the formula for calculating the degrees of freedom for a one sample t test? An independent samples t-test? A paired samples t-test?
The term degrees of freedom (df) refers to the number of values that may vary freely until remaining values are determined. One sample and paired samples t-tests have degrees of freedom df = n - 1. Independent samples t-tests have degrees of freedom df = n1 + n2 - 2.
a researcher wants to compare the mean results from a sample of men and a sample of women after each sample receives the same treatment
independent measures design (between-subjects design) BS I'm independent!
university wants to compare the mean exam scores on a biology final given to first-semester freshmen and first-semester sophomores.
independent measures design (between-subjects design) BS I'm independent!
Comparing final exam scores in a statistics course for students who had two hours of sleep to the same final exam scores of students who had eight hours of sleep
independent measures design study The researcher looks for whether or not there is a significant difference in the means between the two treatments
The t-distribution for __________ sample sizes more closely resembles the normal distribution.
large
In this design, participants in two different study groups are "matched" based upon specific variables or criteria that may be relevant to the study. After the treatment is applied to both groups, the results are compared. Cons?
matched pairs study e.g. pairs of spuses, age-gender pairs -One negative side to a matched pair study is that if a participant in Group A drops out of the study, the results of the matched participant in Group B cannot be used.
a researcher wants to compare the mean results from the same sample of men before and after a given treatment
repeated measures design (within-subjects design)
university wants to compare the mean exam scores of a sample of freshmen before and after a study strategies seminar.
repeated measures design (within-subjects design)
Unlike the normal distribution, the t-distribution is sensitive to _________.
sample size
researcher is looking to see if there is any difference between the scores within the same group of participants
within-subjects study
A ______ -test is used if the population standard deviation is known, whereas a ______ -test is used if the population standard deviation is estimated from the sample standard deviation.
z, t