Exam 4 (Chapter 10) Flashcards
An estimate of sampling error that is determined from the standard deviation of the distribution of sample means using the sample standard deviation to represent the population standard deviation
Estimated standard error
List the 5 steps in completing any T-Test for a study.
- State Hypothesis
- Set decision criterion
- Collect sample data
- Calculate statistics
- Make a decision
What is the difference between a z-score and a t-score?
A t-score is used when the population standard deviation is not known. Instead, we will use the sample standard deviation to calculate the t-score. Z-score requires the population standard deviation.
How does the t-distribution differ from the z-distribution?
- The larger the sample size, the closer t is to the value of z.
- The larger the df, the closer the distribution of t-scores is to a normal distribution
- Very large df, t distribution will be the same as the z distribution
- The variability of the distribution increases with a smaller sample size
- Critical regions associated with our alpha level will change with the degrees of freedom.
How can you change the Sig. P value from two-tailed to a one-tailed Sig. P value?
Divide the sig. (2-tailed) in half to get sig. (1-tailed)
What are the assumptions to use a one sample t-test?
1.The population the sample is drawn from must be normally distributed
2. The scores in your sample must be independent observations
How do you use SPSS for a one sample t-test?
- Analyze, compare means, one sample t test
- Select dependent variable data column -> Test Variable box
- Indicate known mean for comparison in the Test Value Box
- Hit ok
How do you conduct a related or paired samples t-test using SPSS
- Analyze, compare means, paired samples t test
- Click the data columns needed as variable 1 and variable 2 -> add them as a paired variable
- Hit ok.
When is a paired samples t-test used?
1.For a within-subjects design if participants are experiencing both conditions.
2. For a between-subjects design if participants are being compared on a certain quality.
What are some assumptions of a paired samples t test?
- The population of different scores must be a normal distribution.
- The scores from different participants or pairs must be independent.
When is an independent samples t test used?
- When comparing two different populations
- When the same population is exposed to different conditions
How do you calculate the statistics for an independent samples t-test?
- Find the mean and sum of squares for each data set
- Calculate df for each sample group
- Calculate pool variance (s squared p)
- Calculate standard error (s x bar 1 minus x bar 2)
- Calculate t score
- The mean Population difference is the expected difference from the null hypothesis (typically 0)
- Calculate total df
How do you conduct an independent samples t test using SPSS?
- Analyze, compare means, independent samples t test
- Select column as test variable and select column as grouping variable
- Define groups coding numbers
- Hit ok.
Independent samples t test assumptions
- The population of difference scores must be a normal distribution
- The scores from different participants within each sample must be independent
- The population that the samples represent must have equal variances
The assumption of independent samples t test and analyses of variance (ANOVAs) that the variance in the scores in the populations is equal across groups
Homogeneity of variances
The combination variance terms for two samples weighted by the sample size of each sample
Pooled variance
When we do not know the population standard deviation (lower case sigma) we use the _________ to calculate estimated standard error.
A. Population mean
B. Sample mean
C. Sample standard deviation
D. Sampling error
C. Sample standard deviation
With a sample size of 25, our degrees of freedom would be?
A. 26
B. 25
C. 24
D. 20
C. 24
In the calculation of a t-score the estimated standard error is an estimate of
A. The population mean
B. the population standard deviation
C. the difference between the sample mean and the population mean
B. The population standard deviation
When we calculate an inferential statistic looking at mean differences, the numerator is the _______ and the denominator is the ______.
A. Actual mean difference, mean difference expected by chance due to sampling
B. mean difference expected by chance due to sampling, actual mean difference
C. population mean, sample mean
D. Sample mean, population mean
A. Actual mean difference, mean difference expected by chance due to sampling.
For a sample of 36 participants and sampled standard deviation of 3, the estimated standard error would be _______.
A. 0.08
B. 0.50
C. 1.0
D. 3.0
B. 0.50
The shape of the T distribution will be normal whenever the population is normal
A. True
B. False
B. False
An assumption of the T test is that the scores must be independent observations
A. True
B. False
A. True
The T table provides the P value for each T score to allow the researcher to compare P with alpha
A. True
B. False
A. True
In the related or paired samples t test, the difference scores typically predicted by the null hypothesis _______.
A. Equal 0
B. Equal 1
C. Equal -1
D. Depend on the alternative hypothesis
A. Equal 0
For a sample size of _________, we do not need to be worried about violating the assumption of a normal distribution for the population.
A. 10
B. 25
C. 30
D. 31 or higher
D. 31 or higher
The dependent variable for a within subject design is ________.
A. accuracy
B. speed
C. difference scores across conditions
D. difference scores across participants
C. Difference scores across conditions
A matched design might involve _____.
A. Couples
B. Twins
C. The same participants completing all the conditions
D. Both A & B
D. Both A & B
The estimated standard error in a related or paired samples t test is based on the standard deviation of the difference scores.
A. True
B. False
A. True
The df for a matched pairs design is based on the total number of participants instead of the number of pairs.
A. True
B. False
A. True
An assumption of the related or paired samples t test is that all scores across conditions are independent.
A. True
B. False
B. False
The pooled variance is _______.
A. The estimated standard error in an independent samples t test
B. The combined variance for two independent samples
C. The variance in the populations the samples were drawn from in a study.
B. The combined variance for two independent samples
The variance of a sample depends on _____ and ______
A. The mean of the sample, the sample degrees of freedom
B. The mean of the sample, the same of squares for the sample
C. The sum of squares for the sample, the sample degrees of freedom
C. The sum of squares for the sample, the sample degrees of freedom
With an independent samples t test, a researcher can draw conclusions about ______.
A. A comparison of two population means
B. A comparison of two population variances
C. Tbe importance of sample size to the sampling error in a test
A. A comparison of two population means
Levene’s test in SPSS will help a researcher know if the assumption of _____ for the independent samples t test holds for their study.
A. A normal population of scores
B. The homogeneity of variances
C. The independent observations
B. The homogeneity of variances
The homogeneity of variances assumption states that the variance in the two samples must be equal.
A. True
B. False
B. False
A between-subjects study with results showing no significant mean difference between conditions supports the null hypothesis that no difference exists between the populations the samples represent.
A. True
B. False
B. False
Like other t tests, the independent samples t test assumes that the scores between participants are independent.
A. True
B. False
A. True
A researcher wants to know if using videos to illustrate concepts in class improves exam scores. He uses the videos before the 1st exam in his course and collects exam scores from the 62 students in his class. On average, they score 78% with a standard deviation of 5%. Use this description to answer the following questions:
A. What else does the researcher need to know in order to use a one- sample t test to test his hypothesis?
B. What is the null hypothesis for this study?
C. What T critical value should the researcher use in this study if his alpha level = 0.05
a) He needs the mean score in the population when videos are not used.
b) Using videos to illustrate concepts in class has no effect or decreases exam scores in the population of students.
c) ~ 1.67
Your instructor tells you that his exam scores always show a 75% average score. But he thinks the class you’re in seems to be grasping the material better than his previous classes. You decide to test this. The reported mean on the exam for your class is 80% with a 10% standard deviation. There are 49 people in your class. Assuming alpha level = 0.05, is he right about your class understanding better than the previous classes (Using the exam scores as a measure of this)?
The t score of 3.5 falls within the critical region, meaning we can reject the null hypothesis. The results suggest the instructor’s claim is accurate.
A researcher wants to know if using videos to illustrate concepts in class improve exam scores. He uses the videos after the 1st exam in his course and then collects exam scores from the 62 students in his class for the 2nd exam. He wants to compare scores on the 1st exam and the 2nd exam to see if the score increased after he started using the videos. On average, the differences in scores between the 1st exam and the 2nd exam was 5% with a standard deviation of 8%. Use this description to answer the following questions:
A. What is the alternative hypothesis for this study?
B. What is the null hypothesis for this study?
C. What T critical value should the researcher use in the study if his alpha level = 0.05?
D. Do the videos seem to help? Explain your answer.
a) The population mean difference score is greater than zero between scores without the videos and scores with the videos.
b) The population mean difference score is less than or equal to zero.
c) tcrit = 1.671
d) Yes, the videos seem to help. The t score (4.92) is in the critical area. We can reject the null hypothesis. The results suggest videos help improve exam scores.
A group of students is tested on their driving ability in a research study that was done to investigate the effect of cell phone use on driving performance. A sample of 25 students drive a test course in a driving simulator to measure their driving accuracy (based on how often they deviate from the course, miss a red light, et cetera). Then, all 25 students are tested on the driving course again while holding a conversation on their cell phone with a researcher. The mean difference score in driving accuracy shows that, on average, accuracy decreases by 25% while talking on the cell phone with a standard deviation of 15%. Does cell phone use cause a significant decrease in driving performance?
Yes. The t score (8.33) is in the critical area. We can reject the null hypothesis. The results suggest cellphone use decreases driving performance.
Suppose you conducted a study to test the hypothesis that social pressure affects memory accuracy. You set up a study in which participants view a person robbing a convenience store. Then, half of the participants watch a video of other participants discussing the crime. In reality, the participants in the video are part of the experiment, and some of the details of the crime that are discussed are inaccurate. The actual participants are told that they should consider other people’s perspectives on the crime because it is difficult for any one person to accurately remember all of the details. The other half of the participants do not view the video discussion of the crime but are also told that it is difficult for any one person to accurately remember all of the details of the crime. 30 minutes after viewing the original crime video, all participants are given a recognition memory test about details of the crime. For this study, answer the following questions:
A. What are the alternative and null hypothesis for this study?
B. Suppose that 10 participants participated in each group in the study. For the recognition accuracy data provided here, conduct an independent samples t test to analyze these data.
Video Discussion Group: 67, 80, 69, 72, 75, 79, 66, 71, 69, 79
No Video Discussion Group: 78, 65, 79, 84, 88, 79, 89, 90, 85, 87
C. From the test result you obtained, what can be concluded about the null hypothesis you stated?
a) The null hypothesis tested in the analysis is that there is no mean difference between video discussion and no video discussion groups in the population. The alternative hypothesis is that is that there is a mean difference between video discussion and no video discussion groups in the population.
b) No answer needed.
c) The video discussion group had mean recognition accuracy of 72.7% (SD = 5.23), and the no video discussion group had a mean recognition accuracy of 82.4% (SD = 7.52). The test indicates that the no video discussion group has a significantly higher mean recognition score than the video discussion group, t(18) = -3.35, p = .004. Because the p value of .004 is less than alpha (.05), we can conclude that the null hypothesis is false and that there is a difference between video and no video groups in the population.
The statistic ______ differs slightly from the statistic z distribution.
A. t score
B. t distribution
C. df
D. t test
B. t distribution
The larger the ______, the closer the t is to the value of z.
A. p value
B. population
C. sample size
D. unit of measure
C. Sample size
The critical region(s) associated with our ______ will change with the degrees of freedom.
A. standard error
B. z score
C. z test
D. α level
D. α level
The default test in SPSS is a(n) ______ test.
A. ANOVA
B. one-tailed
C. two-way
D. two-tailed
D. two-tailed
The one-tailed test has a(n) ______ that is half the ______ for the two-tailed test.
A. p value; α
B. α; p value
C. p value; p value
D. α; α
C. p value; p value
There are two ______ that a researcher must know to be true in order to use a t test.
A. criteria
B. assumptions
C. requirements
D. parametrics
B. assumptions
______ means that the scores cannot be related in some systematic way to each other.
A. Independent variables
B. Independent variances
C. Independent observations
D. Independent case studies
C. Independent observations
In ______ design, participants are paired across the treatment conditions on some variable of interest.
A. post hoc
B. matched
C. pretest–posttest
D. related/paired samples t test
B. matched
A study is considered a ______ design because all the participants will complete the same task in two different environments.
A. within-subjects
B. between-subjects
C. within-groups
D. between-groups
A. within-subjects
Why is setting an alpha level of 0.05 important in studies?
It sets our chance of making a Type I error at 5% or less.
