Statistics and Research Design: Conceptual and Problem-Solving Questions

Sampling and research design

1. In research studies, collecting the proper sample is prominent. How is the sample different from the population? In this regard, what is the difference between parameter and statistic? Also, one problem with using a sample is that the sample cannot perfectly represent the population. This discrepancy is called sampling error. Define the term, sampling error, and describe why it occurs in sample statistic. Lastly, a random sampling method is usually recommended in collecting data. What does it mean by random sampling and why is it important?

2. Statistics is often classified into descriptive statistics and inferential statistics. Define these two distinctive statistics. Also, describe the differences (1-2 sentences) between them in your own words. Out of six chapters we have covered, what information (i.e., specific statistical techniques) can be used in descriptive statistics (plus, any examples?) and in inferential statistics (examples)?

3. The goal of an experimental study is to demonstrate a cause-and-effect relationship between two variables. In order to see the true effect of the manipulation, the researcher must rule out any other possible explanation for the difference. Those two general categories are participant variables and environmental variables (also called confounding variables). Define those two categories and explain why it is important to control and consider those variables. Also, describe some techniques to control those confounding variables.

4. In statistics, the most common two terminologies are independent and dependent variables. Define the terms and explain how they are different and related. Also, in this example, “A researcher (Joung, 2018) conducted an experimental study to test the effect of calorie information on the menu board on the customers’ purchase intention of lower-calorie food. He developed two versions of menus (one with calorie information of the menu items and the other one without it) and compared which menu items were selected between two groups.” indicate independent variable (IV) and dependent variable (DV). (Note: “Variables” are “names,” so be careful when you name the variables!)

5. Understanding measurement scales (i.e., nominal, ordinal, interval, and ratio scales) is crucial when developing a research instrument (e.g., survey). Define each of the measurement scales and provide at least one example of each. When you ask respondents their age on the survey, you can ask either “How old are you?” or “Indicate your age in the list: a) Less than 18 years, b) 19-30 years, c) 31-40 years, d) 41-50 years, and e) 51 years or above.” Between two options, which question format would you use (or, is more appropriate)? Why?

Descriptive and inferential statistics

6. What is the difference between discrete and continuous variables? How about categorical vs. continuous variables? Then, where do the four measurement scales from question 5 fall in each category (i.e., discrete vs. continuous and categorical vs. continuous)? For example, a nominal scale is always discrete and categorical variable because….

7. There are various types of frequency distribution graphs (e.g., histogram, polygon, bar graph, etc.). First of all, what is the purpose of presenting a frequency distribution graph? Also, explain which frequency distribution graph is suitable for each measurement scale (i.e., nominal, ordinal, etc.).

8.Almost all distributions can be classified as being either symmetricalor skewed (positive vs. negative). Define those distributions and sketch each distribution.

9. What is the purpose of measuring central tendency? There are three measures of central tendency. What are those? Define each of the three measures of central tendency and explain how to compute them.  Also, explain the circumstances in which each of the three measures of central tendency is appropriate. Does a measurement scale affect your choice when selecting which measure of central tendency? How?

10. What is variability and why is it important to understand variability? There are three measures of variability. What are those? Define each of the three measures of variability and explain how to compute them (it would be great to explain how SS, variance, and standard deviation are related). You also have to understand the concept of an unbiased statistic and the correction for bias that is used in the formula for sample variance. Why is there a bias in sample variance? What correction should be made for sample variance?

11. What is a z-score and how to transform X values into z-scores? Also, why is it important to standardize distributions (i.e., transforming X values into z-scores)? In certain situations, a distribution may be standardized by converting the original X values into z-scores and then converting the z-scores into a new distribution of scores with predetermined values for the mean and the standard deviation (e.g., IQ, SAT, etc.). What is the process of that?

12. The role of inferential statistics is to use the sample data as the basis for answering questions about the population. In this regard, explain why understanding probability is important.

13. A researcher plans to compare two treatment conditions by measuring one sample in treatment 1 and the second sample in treatment 2. The researcher then compares the scores for the two treatments and finds a difference between the two groups.

Briefly explain how the difference may have been caused by the treatments.

Briefly explain how the difference simply may be sampling errors.

14. A survey given to a sample of 200 college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph).

Number of pizzas consumed during the previous week

Size of a T-shirt worn (S, M, L, XL)

Gender (male/female)

Grade point average for the previous semester

College class (freshman, sophomore, junior, senior)