1. 9/7/2015 Research Methods for Counselors COUN 597 University of Saint Joseph Class # 2 Copyright © 2015 by R. Halstead. All rights reserved.

2. 9/7/2015 Class Objectives The Basics of Sampling - Trochim Chapter 2 Review of Descriptive Statistics - Salkind Chapters 2, 3, and 4

3. 9/7/2015 Trochim Chapter 2 - Sampling Sampling is a process by which you select elements from a population that you would like to study. There are a variety of factors that one needs to consider before and during the sampling procedure.

4. 9/7/2015 The Logic of Sampling How you select your sample for a research project is important. The degree to which a sample is representative of some population of interest, determines the degree to which you will be able to generalize your results to that larger population. There are no guarantees that a sample will be representative of the population you wish to study, but there are sampling techniques that can help.

5. 9/7/2015 The Logic of Sampling There are two types of sampling methods - Probability Sampling “Random Sampling” - Nonprobability Sampling - This form of sampling is very common in qualitative research - Reliance on one or more forms of availability of participants for your project

6. 9/7/2015 Non-probability Sampling - Convenience Sampling - based on the use members of a pre-existing group. - Purposeful or Judgmental Sampling - sampling is based on your knowledge of the population. - Snowball Sampling - Find new members for the sample by asking members of the sample from whom you have already collected data. - Quota Sampling - Selecting a sample proportionately to the represented groups in the population.

7. 9/7/2015 Non-probability Sampling Selecting Informants Factor - How well informed are the individuals from whom you are collecting your data about the larger group?

8. 9/7/2015 Probability Sampling - As the name suggests, probability sampling relies on probability theory to help insure we work with a sample that represents the larger population. - Remember that the population from which a sample drawn will have an amount of heterogeneity. So the must be large enough to be representative. - A sample that is not fully representative of the population from which it was selected, it said to have either Sample Error or Sample Bias. Sometimes a sample will have both.

9. 9/7/2015 Sampling Error and Sampling Bias Sample Error - results from the sample differing significantly from the population by chance. - Sample Error - - is associated with probability limitations of sampling. Sample Bias - results from the sample differing significantly from the population because of something that the researcher did or did not take into account. - Sample Bias – can be associated with probability or non- probability sampling.

10. 9/7/2015 Sampling Concept and Terminology Random Sampling - A process where by every individual from a population has an equal chance of being selected for the study. - This sampling technique relies on principles of probability to help ensure the sample is representative. - A random numbers chart is often used to guide the selection process to ensure sample selection is truly random.

11. 9/7/2015 Sampling Concept and Terminology Stratified Random Sampling - A process of randomly selecting from within sub-groupings contained in a population so as to ensure that the sample represents members of those sub- groupings in the same proportion as they exist in the population.

12. 9/7/2015 Sampling Concept and Terminology Cluster Sampling - A process whereby whole groups are randomly selected instead of randomly selecting individuals. - Selecting all students from 10 randomly selected high schools as a representative sample of all high school students in a region.

13. 9/7/2015 Sampling Concept and Terminology Systematic Sampling - The sample is constructed by selecting every N th name from a list such as phone book or voting records. Example: I will randomly pick one person and then every 12th name on the list there after. - This differs from random sampling in that not every person on the list has an equal and independent chance of being selected. Once you pick the first individual the other members of your list will have been determined.

14. 9/7/2015 Drawing Generalizations from a Study: Process of Sampling Population Sample Generalizeback Generalizeback (Trochim, W. 2001)

15. 9/7/2015 Drawing Generalizations from Research: Proximal Similarity OurStudy TimesPeople Places Settings Lesssimilar Less similar Lesssimilar Lesssimilar Gradients of similarity (Trochim, W. 2001)

16. 9/7/2015 External Validity External validity is the degree to which the conclusions from your study would hold for other people in other places at other times.

17. 9/7/2015 Examples of Threats to External Validity Maybe it is just these people. Maybe it is just these places. Maybe it is just these times. Interaction of selection and treatment Interaction of setting and treatment Interaction of history and treatment (Trochim, W. 2001)

18. 9/7/2015 How Can We Improve External Validity? Population Sample OurStudy People Places Times Random sampling Replicate, Replicate, Replicate (Trochim, W. 2001)

19. 9/7/2015 Appropriate Sample Size can also Increase External Validity There are thought to be several primary factors that need to be taken into account when determining what your sample size should be. - The level of precision being required between the sample and the population - The variability (standard deviation) of the population - The sampling technique employed to obtain the sample

20. 9/7/2015 Sample Size The general rule is that the larger the sample size the more representative it will be of the population. Sample size and Type of Research Conducted - There are many factors that come into play when one is establishing an adequate sample. Most of those factors depend largely on the type of research being conducted and/or the methods that will be employed for data analysis.

21. 9/7/2015 Descriptive Statistics – A Review: Measures of Central Tendency The Mean - Computing and Understanding the Average  verage = The Sum of All Values in a Distribution Divided by the Number of Values in that Distribution

22. 9/7/2015 The Mean - A Measure of Central Tendency 3572835728 + 25 Divided by 5 = 5 Distribution Sum N Mean

23. 9/7/2015 Other Members of Central Tendency Median - The physical center of a distribution. 50% of the cases in the distribution are found to be above the median point and 50% of the cases are found be below the median point. 1 2 3 4 5 6 7 8 9 10 Median = 5.5

24. 9/7/2015 Other Members of Central Tendency Mode - The most frequently occurring value in a distribution 3 3 4 5 6 6 8 8 8 10 15 18 25 Mode

25. 9/7/2015 Why Do We Need to Concern Ourselves with Central Tendency? Answer: Computing measures of central tendency is the first step toward understanding variability.

26. 9/7/2015 Why Do We Need to Concern Ourselves with Variability? zAnswer: Understanding how distributions of interest vary helps to describe an aspect the group we are encountering. zWhat? zLet’s look at an example.

27. 9/7/2015 Variability and Depression Every client that seeks services at a group practice, as part of the intake, is administered an instrument that measures depression. Ten items with a 5 point Likert scale (0 - 4) Severity of depression is marked by quartiles - Scores - 0-10 none to mild - Scores - 11-20 mild to moderate - Scores - 21-30 moderate to sever - Scores - 31-40 sever

28. 9/7/2015 Variability and Depression - Continued So lets look at the 13 new clients’ scores that came to the practice in the month of December. There are several things we can do to describe this group of individuals. 20 32 5 11 26 33 16 14 20 37 24 18 7

29. 9/7/2015 Variability and Depression - Continued The first thing you should do with any distribution you encounter is to compute the: - Mean = 20.23 - Median = 20 - Mode = 20 This establishes the central tendency for the distribution 5 7 11 14 16 18 20 20 24 26 32 33 37

30. 9/7/2015 Variability and Depression - Continued After establishing a picture of central tendency, you should begin to wonder about how the scores within the distribution vary.

31. 9/7/2015 Variability and Depression - Continued First you would compute the range of distribution. The Range tells us how much spread there is between the highest and lowest score in the distribution. 37 - 5 = The Exclusive Range 32 20 32 5 11 26 33 16 14 20 37 24 18 7

32. 9/7/2015 Variability and Depression - Continued Although the range tells us how much spread there is between the highest and lowest score in the distribution, it does not tell us about any of the other scores in the distribution. To get a fuller picture of variability you must compute the standard deviation.

33. 9/7/2015 Variability and Depression - Continued The standard deviation gives us a more detailed account of the variability within a distribution than does the range. The standard deviation is the average distance that scores in a distribution deviate from the mean.

34. 9/7/2015 Variability and Depression - Standard Deviation 5 - 20.23 = -15.23 7 - 20.23 = -13.23 11 - 20.23 = -9.23 14 - 20.23 = -6.23 16 - 20.23 = -4.23 18 - 20.23 = -2.23 20 - 20.23 = -0.23 24 - 20.23 = 3.77 26 - 20.23 = 6.77 32 - 20.23 = 11.77 33 - 20.23 = 12.77 37 - 20.23 = 16.77 239.95 175.03 85.19 38.81 17.90 4.97 0.05 14.21 45.83 138.53 163.07 281.23 The sum of the squared deviations = 1204.82 The sum of the squared deviations divided by n-1 = 100.4 Take the square root s = 10.02

35. 9/7/2015 Variability and Depression - Standard Deviation - So What! The standard deviation allows us to compare scores from different distributions even when their means and deviations are different. Why would we want to do that? To answer that question we need to look at another piece of our original example.

36. 9/7/2015 Variability and Depression - Continued You will remember our December intake data was as follows. Now lets look at data from the intake data from July of the same year. 5 7 11 14 16 18 20 20 24 26 32 33 37 3 4 6 8 11 11 11 14 15 18 23 25 30

37. 9/7/2015 Variability and Depression - Continued December Descriptive Statistics - Mean = 20.23 Median = 20 Mode = 20 - Range = 33 SD = 10.04 July Descriptive Statistics - Mean = 13.76 Median = 11 Mode = 11 - Range 28 SD = 7.96 3 4 6 8 11 11 11 14 15 18 23 25 30 5 7 11 14 16 18 20 20 24 26 32 33 37

38. 9/7/2015 Variability and Depression - Continued Now that we have standard deviations for our December and July data we can compare them even though they are different distributions that have different means. December July 5 7 11 14 16 18 20 20 24 26 32 33 37 3 4 6 8 11 11 11 14 15 18 23 25 30

39. 9/7/2015 Variability and Depression - Continued “Why would anyone want to compare the December and July data? I work with individual clients and each one is special.” Right! We must always be careful not to generalize pass what the data or our research design will allow (more on the later). Let’s consider, however, possible questions that might help to enhance your work with clients.

40. 9/7/2015 Variability and Depression - Research Questions Research Questions -Are there significant differences between our December and July client groups. -What might account for the differences in variability between the two sets of clients who seek counseling in the months of December and July? - Why are some December clients showing higher levels of depression than others?

41. 9/7/2015 Variability and Depression - Research Questions - What happens to mean depression levels of the July clients during the month of December? - If depression levels increase, what proactive/preventive programs would be effective? - If you were to track individual clients over time, would you find that your interventions were effective?

42. 9/7/2015 Research Questions - It is likely that the research questions posed above would not have emerged had descriptive statistics not been tracked. - To actually find answers to those questions, however, you will need to learn a bit more about inferential statistics and research design. So come back next week!!