Measures of Central Tendency and Dispersion
The questions below mainly revolve around measures of central tendencies like mean, median, and mode, as well as measures of dispersion like standard deviation and variance. Some of the questions also touch on hypothesis testing, where we explain different types of hypothesis testing and other concepts.
Measures of Central Tendency
- Determine the test to be used
- State null and alternate hypothesis
- Set the significance level and make the decision criteria
- Compute the test statistic
- Make the decision.
- One sample t-test is useful when we are given the data for one sample and we are comparing it with the population means.
- Paired samples t-test is useful when we are given the data for some individuals. For example, we want to compare the weight loss after a training session. Thus, we compare the weights of the same individuals before and after the training session.
- Independent samples t-test is useful when we have two groups and we want to compare their means. For example, if we want to compare the weights of males and females.
1. A very useful descriptive statistic that we use to see how to spread out a data set is around the mean is called_standard deviation__.
2. If a psychologist summarizes data for a variable in a frequency table, but finds that there are so many values that the table is too cumbersome to be useful, what could he create to make the data easier to view and understand? _Group frequency table or histogram____
3. On a normal curve, where do most scores fall? _In the center of the curve_____
4. What percentage of scores falls in the tails of a normal curve? _5%_
5. The mean of the scores 2, 2, 2, 6 is _3__.
6. The n size of this set of scores is _7_______.6, 7, 7, 8, 10, 2, 1
7. In the following group of scores, which score is the outlier? _2___ 2, 81, 82, 82, 84
8. A deviation score is a difference between the score and the _mean__.
9. In most cases, if you have the variance, how do you compute the standard deviation? __taking the square root of the variance_________
10. Compute the z score in the following scenario: Raw score = 28
Mean = 20
SD = 2
The Z score is _4__.
11. Hypothesis testing is a systematic procedure for determining whether the results of an experiment are significant. List the 5 steps of hypothesis testing:
12. In hypothesis testing, if you find significance, does that mean that your study has meaning?
Statistically significant results indicate that a result from the sample is likely to occur by chance. However, statistical significance is directly linked to the sample size i.e. a large sample size may conclude the study being statistically significant even with a small difference. Thus, it is important to examine the significance or the effect size after the results are statistically significant as the sample size does not influence the practical significance.
13. If you make a Type I decision error in your hypothesis test, what has happened? _In type I error, we reject the null hypothesis when it is actually true i.e. it is a false positive.
14. If your question is that your significant hypothesis test is significant “enough” to have true meaning, what are some other things you can look at to determine practical significance?
In addition to the significance of the hypothesis test, the effect size of the test should also be considered after the results are statistically significant in order to determine the practical significance.
Explaining Three Types of Test
15. You learned about 3 types of t-tests. What are they and briefly describe the types of research scenarios for which they are best suited: