PSA 2006 Session Title: Teaching Statistics to Undergraduates


Teaching Undergraduate Statistics Experientially Using Per...
Paper Presented at the
Pacific Sociological Association Annual Meeting
April 20- 23, 2006
Hollywood, CA


Draft Copy: Not ...
INTRODUCTION


       "For true knowledge to occur it must be experienced."       (Peck 1978) The


practice of acquiring ...
order to understand how the legal system can protect or hinder the needs of the poor.


Entering medical students at anoth...
depends partly on the adult’s belief that the reading and discussion and other


educative activities can actually contrib...
design, sampling, hypothesize testing, and summary statistics of central tendency and


variability. The course is require...
For section one of the portfolio, each student selects the first of two samples


of 10 dating ads from a source they choo...
calculates a sampling interval.”


       “The data is being collected to investigate a hypothesis associated with the
   ...
percentages, ratios and rates. They also practice visually presenting their data in


comparative formats such as double b...
Range, Number of years younger willing to date, and Number of years older willing


to date (Appendix C).


Summary Statis...
The last five sections (Sections 7-11) of the portfolio focus on more complex


calculations of inferential statistics. Wi...
“The mean of means is 7.91 for women seeking years older, with a standard
       deviation of 2.01. What this means is tha...
Conclusions


       Because students can relate to the data they have collected in a very


meaningful way, the statistic...
this decline intensifies with age (Schatzel in Knowles 1984:435). In fact, there


appears to be a clear distinction betwe...
appreciate the relevance of statistical measures for applied social science fields and


are less shy about reading such f...
"For true knowledge to occur it must be
experienced."   (Peck 1978)
While the specific experiential approaches to
learning may differ in content and technique, they
are centered around the f...
Sample One                    Sample Two




Femal      Desire Desire   Femal       Desire Desire
e     Age -Low    -Hi   ...
To illustrate from one student’s portfolio:



“The raw data sample I collected came from the source,
Match.com, an online...
states that men tend to seek women who are younger than
they are to marry.”


“On average men desire to date younger women...
As we continue to read from the portfolio quoted earlier, we find the


following excerpts in Section Ten on, “Generalizin...
The final section (Section 11) of the portfolio is on correlation of Pearons’s r.


The correlation table lists the case n...
Handouts for PSA 2006 Session
       Title: Teaching Statistics to Undergraduates

       Teaching Undergraduate Statistic...
Portfolio Contents
Section One: Research Design and Sample Selection
(This data has already been done as homework during t...
Section Six: Second sample
1. Draw a second sample of dating ads using the same sampling frame as before. Or, you
can use ...
Section Ten: Generalizing to the Population
1. Gather the means and standard deviations for each class member=s first samp...
Teaching undergradutae statisitcs using dating ads
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Teaching undergradutae statisitcs using dating ads

  1. 1. PSA 2006 Session Title: Teaching Statistics to Undergraduates Teaching Undergraduate Statistics Experientially Using Personal Dating Ads Sharon Warner Methvin, PhD Department of Sociology Clark College Vancouver, Washington 98663 Email: Smethvin@clark.edu Web: http://web.clark.edu/smethvin Phone: 360.992.2976 Cell: 503.888.4337
  2. 2. Paper Presented at the Pacific Sociological Association Annual Meeting April 20- 23, 2006 Hollywood, CA Draft Copy: Not Proofread
  3. 3. INTRODUCTION "For true knowledge to occur it must be experienced." (Peck 1978) The practice of acquiring knowledge and mastering skills through one's personal experiences is a teaching technique employed in academic fields as diverse as health care and legal specialties, to wildlife management and archaeology as well as psychology, anthropology and sociology. The specific approach and duration of the experiential learning projects are nearly as diverse as the courses in which they are used. The assignments can involve simulated learning experiences such as collaborative games, hypothetical (or sometimes real) case studies, role plays, and computer models. Or, they can involve real life laboratories such as practicums, ethnographic observations, field schools, and natural experimental or other research settings. The duration of the experiential learning assignment can be as short as one class period, as long as an entire semester or somewhere in between. Examples of such strategies abound in discipline specific and in education journals. For example, entering year law students are staying with poor families in
  4. 4. order to understand how the legal system can protect or hinder the needs of the poor. Entering medical students at another school are required to "sit with" the terminally ill for a period of several weeks at the beginning of a their traditional laboratory training. And sociology is no exception to using experiential methods as a teaching modality. In this paper I discuss using personal dating ads as an example of one such experiential method for teaching undergraduate social science statistics. While the specific experiential approaches to learning may differ in content and technique, they are centered around the fundamental premise that students learn best when the information can be understood in a personally meaningful way. And what might be personally meaningful to an undergraduate social science major you might be inclined to ask? Certainly an analysis of dating advertisements would fit nicely into this category and offer the opportunity for a student to understand that statistics is not merely a dreaded rite of passage that all undergraduates must endure, but is a useful tool that helps us make sense of real world events. Knowles (1984:455) states that the success of learning and problem-solving strategies
  5. 5. depends partly on the adult’s belief that the reading and discussion and other educative activities can actually contribute to the achievement of any important personal goals. It seems that the demonstration of statistics through dating personals is particularly well suited to providing such a contribution to the goals of an undergraduate college student. METHODOLOGY The course in which I use this technique is part of a combined two course sequence on research methods and statistics. The majority of students in this sequence are interested in applied fields in sociology and do not plan to continue their education beyond the bachelor’s degree. Many have “put off” statistics until the very end of their academic experience; often citing, “math anxiety” as their reason for doing so. The course sequence focuses on the interrelationship between data collection and analysis and is designed to equip the social science and psychology major with knowledge of the basic research methodologies and statistics used in the human sciences. During the first course in the sequence students learn about research
  6. 6. design, sampling, hypothesize testing, and summary statistics of central tendency and variability. The course is required for all social science majors. The second course goes more in-depth into the presentation and interpretation of data, reviews descriptive statistics, and introduces statistics. It is this term during which the dating ads are used to illustrate these concepts. TECHNIQUE At the beginning of the course, each student is asked to purchase a loose leaf type notebook. Each major section of the portfolio is then identified and set apart with a tab so it is easy to thumb through it in the future. Each section in the student’s portfolio shows all the work (if applicable) for that topic/problem as well as an interpretation or explanation for that topic/problem. This portfolio forms the basis for their grade in the course and is divided into eleven sections that cover all the key summary and inferential statistics (Appendix A). The portfolio contents are based on the dating ad database that the students develop and continue to analyze for the duration of the course.
  7. 7. For section one of the portfolio, each student selects the first of two samples of 10 dating ads from a source they choose by using one of the sampling strategies discussed in class. The second sample of 10 is selected later in the course and is based on the initial comparative sample selection strategy that the student designed. The only requirement imposed in regard to the sample selection strategy is that each ad, in order to be considered as part of the project, must specify the gender and exact age of the advertiser and the gender and exact age range for the desired dating partner (Appendix B). The sampling strategy and source (s) are developed and justified by the student in part One of the portfolio. To illustrate from one student’s portfolio, “The raw data sample I collected came from the source, Match.com, an online dating service. I chose ten love seekers within the age brackets of 26 to 38 years of age. The method of sampling I utilized was a quota sampling technique. This is a sampling method where the researcher specifies specific categories of people, such as specific gender and age range.” ”I also used systematic sampling, as I chose page ‘10’ out of 20 pages from each of the female and male love seekers in my cohort. Systematic sampling according to Neuman (2003) is, simple random sampling with a short cut for random selection. In other words, instead of random numbers, the researcher
  8. 8. calculates a sampling interval.” “The data is being collected to investigate a hypothesis associated with the cultural rule of hypergamy. This rule states that men tend to seek women who are younger than they are to marry. “On average men desire to date younger women while on average women desire to date older men…is my directional hypothesis.” The student goes on to discuss the research method of content analysis and the theoretical approach she is using as symbolic interactionism but also includes an excellent discussion of Rational Choice theory. She identifies her level of measurement as Interval level categories and explains why. Finally, she identifies her unit of analysis at the “individual” level and struggles with what she refers to as, “the various angles of the project” that include broader units of analysis such as gender and culture. Sections Two and Three of the portfolio are the organization and presentation of the raw data. The students organize and present their data in this section and practice collapsing data into frequency tables and cross tabulations. They discuss
  9. 9. percentages, ratios and rates. They also practice visually presenting their data in comparative formats such as double bar graphs and frequency polygons. At this stage (about three weeks) in the course, I find students are beginning to develop ownership of their data samples and the conversations around the “water cooler” so to speak, are peppered with discussions of ads they consider to be outliers, expectations of what might occur when they draw their second sample of ads, and what differences, if any, would be found in a different age cohort or sample. This discussion often overshadows their anxiety of next week’s statistical technique to be mastered and is reminiscent of the kind of discussions that go on at the graduate level among students involved in writing theses. By the end of this section of the portfolio, each student has generated a database for their sample. The database spread sheet has six important pieces of information for each case in their sample and it is these numbers from which all their summary and inferential statistics are calculated. These data are: Age of Advertiser, Youngest Age willing to date, Oldest Age willing to date, Dating Age
  10. 10. Range, Number of years younger willing to date, and Number of years older willing to date (Appendix C). Summary Statistics Sections Four and Five cover measures of central tendency and measure of variability. These means and deviations are calculated from the data on their spread sheet. They are determined for the “number of years older” and “number of years younger” a person is willing to date. For example, a 28 year old female advertiser may be willing to date a person 27 to 38, so she is willing to date a person “1” year younger and “10” years older. These calculations are then added to the spreadsheet (Also on Appendix C). These calculations provide all rest of the data needed to perform the statistics for the duration of the course. At this point in the course (Section Six in Portfolio), students draw their second set of data and organize and present it in a comparable format in the database. Inferential Statistics
  11. 11. The last five sections (Sections 7-11) of the portfolio focus on more complex calculations of inferential statistics. With two sets of personal ads data drawn and the lowest versus highest number of years a person is willing to date beyond their own age calculated, students can now calculate the key inferential statistics covered in this course like Z scores, T’tests, Chi Square, Confidence Intervals (they collect all the students’ means in order to do this), and correlation. For example, to investigate confidence intervals and the generalizability of their sample, students collect the means of the other students in the class and then calculate the mean of means in order to estimate their confidence intervals and a probability distribution. Returning to the student’s portfolio from earlier, we find the following excerpts in Section Ten on, “Generalizing to the Population.” “These small circles represent the mean scores obtained from each classmate’s data set and represent the average number of years older and younger the advertisers are willing to date. Constructing the sampling distribution of means becomes a frequency distribution of the means from the data sampling ads”
  12. 12. “The mean of means is 7.91 for women seeking years older, with a standard deviation of 2.01. What this means is that it is likely on average, 68% of females are seeking men 5.9 years older and 9.92 older than they are.” As in the above statement, sometimes their interpretation in not correct or what they choose to measure is not appropriate and does not work out, so this is discussed the next class and simply becomes anther learning opportunity for the entire class. The final section (Section 11) of the portfolio is on correlation of Pearons’s r. The correlation table lists the case numbers, age of the advertiser, and dating age range; it tests the correlation that as the age of the advertiser increases, the gap in the age range for a desired dating partner will also increase. The student from before states, “For my correlation model, I used the Age Range as the Y axis and Age of Advertiser as the X axis. I then graphed my scores as a scatter plot. I then calculated Pearson’s r to be 0.42. To test the significance of r at the .05 level, I went to table F…therefore I can reject the null hypothesis." ”What this all means is that the research hypothesis regarding the cultural rule of hypergamy is coupled with an additional rule: the older the advertiser, the wider the net!
  13. 13. Conclusions Because students can relate to the data they have collected in a very meaningful way, the statistical concepts seem to have greater registration in their memory. Second, students seem to better understand the relevance and application of “numbers” to real world events. And, importantly they have a greater ability to transfer the knowledge learned through the dating ad analysis to other situations which is the best measure that they have grasped the meaning of the concepts and true learning has occurred. The important first step that connects the statistical concept in its abstraction and the student's ability to grasp its meaning experientially and master its transference is that of memory registration. Research by Knowles, Schatzel, and others (May 1991:68) suggests that long-term memory is tied to personal significance and the strength of the initial registration of the information. When the material committed to memory is not meaningful, there is a marked decline in the long-term retention of the material, and
  14. 14. this decline intensifies with age (Schatzel in Knowles 1984:435). In fact, there appears to be a clear distinction between primary storage for immediate and short- term memory, such as until the exam hour is over, and storage for intermediate and long-term memory. Moreover, forgetting what was once learned and stored in short- term memory depends on the strength of the original registration. And, the likelihood of a strong registration seems to result from the frequency, degree of individual engagement, and the personal importance of the exposure. Using dating personals to register statistical concepts is one example that certainly fits these criteria! As evidenced in the course evaluations and “water cooler” conversations, students typically leave the course with a high level of self confidence in their ability to understand how statistics are calculated and how they can be used to interpret real world events. I have found that during the course, students tend to develop a personal investment in their samples and the results and will often be comparing their findings before and after class. I also have found that students begin to
  15. 15. appreciate the relevance of statistical measures for applied social science fields and are less shy about reading such findings in popular and professional literature. Importantly, students become less anxious about math as the term proceeds and develop an understanding of the interrelationship between methods, statistics and real world events.
  16. 16. "For true knowledge to occur it must be experienced." (Peck 1978)
  17. 17. While the specific experiential approaches to learning may differ in content and technique, they are centered around the fundamental premise that students learn best when the information can be understood in a personally meaningful way.
  18. 18. Sample One Sample Two Femal Desire Desire Femal Desire Desire e Age -Low -Hi e Age -Low -Hi 6 24 23 25 1 52 50 58 8 24 24 34 2 27 25 35 2 27 25 35 3 67 62 73 7 41 35 50 4 63 58 68 9 44 38 52 5 51 45 60 10 47 45 52 6 24 23 25 5 51 45 60 7 41 35 50 1 52 50 58 8 24 24 34 4 63 58 68 9 44 38 52 3 67 62 73 10 47 45 52 10
  19. 19. To illustrate from one student’s portfolio: “The raw data sample I collected came from the source, Match.com, an online dating service. I chose ten love seekers within the age brackets of 26 to 38 years of age. The method of sampling I utilized was a quota sampling technique. This is a sampling method where the researcher specifies specific categories of people, such as specific gender and age range.” ”I also used systematic sampling, as I chose page ‘10’ out of 20 pages from each of the female and male love seekers in my cohort. Systematic sampling according to Neuman (2003) is, simple random sampling with a short cut for random selection. In other words, instead of random numbers, the researcher calculates a sampling interval.” “The data is being collected to investigate a hypothesis associated with the cultural rule of hypergamy. This rule
  20. 20. states that men tend to seek women who are younger than they are to marry.” “On average men desire to date younger women while on average women desire to date older men…is my directional hypothesis.”
  21. 21. As we continue to read from the portfolio quoted earlier, we find the following excerpts in Section Ten on, “Generalizing to the Population.” “These small circles represent the mean scores obtained from each classmate’s data set and represent the average number of years older and younger the advertisers are willing to date. Constructing the sampling distribution of means becomes a frequency distribution of the means from the data sampling ads” “The mean of means is 7.91 for women seeking years older, with a standard deviation of 2.01. What this means is that it is likely on average, 68% of females are seeking men 5.9 years older and 9.92 older than they are.”
  22. 22. The final section (Section 11) of the portfolio is on correlation of Pearons’s r. The correlation table lists the case numbers, age of the advertiser, and dating age range; it tests the correlation that as the age of the advertiser increases, the gap in the age range for a desired dating partner will also increase. The student from before states, “For my correlation model, I used the Age Range as the Y axis and Age of Advertiser as the X axis. I then graphed my scores as a scatter plot. I then calculated Pearson’s r to be 0.42. To test the significance of r at the . 05 level, I went to table F…therefore I can reject the null hypothesis.” “What this all means is that the research hypothesis regarding the cultural rule of hypergamy is coupled with an additional rule: the older the advertiser, the wider the net!
  23. 23. Handouts for PSA 2006 Session Title: Teaching Statistics to Undergraduates Teaching Undergraduate Statistics Experientially Using Personal Dating Ads Sharon Warner Methvin, PhD Department of Sociology Clark College Vancouver, Washington 98663 Email: Smethvin@clark.edu Web: http://web.clark.edu/smethvin Phone: 360.992.2976 Cell: 503.888.4337 Handouts are for the course: complete syllabus can be found at the above web site in “Basics.” RESEARCH AND STATISTICS IN THE SOCIAL SCIENCES INSTRUCTOR: Dr. Sharon Warner Methvin TEXT: Elementary Statistics in Social Research, by James Alan Fox and Jack Levin, 9th ed., 2003 Social Research Methods, by W. Lawrence Neuman, 5th ed., 2003. ASSIGNMENT DETAILS Portfolio: (210 pts.) Each student is to purchase a loose leaf type notebook. Each major section of the portfolio is to be identified and set apart with a tab so it is easy to thumb through it in the future. Within each section may be several assignments of problems and they should be numbered and identified with the appropriate heading. Each section in the portfolio should show all the work (if applicable) for that topic/problem as well as an interpretation or explanation for that topic/problem. In other words, what do the numbers, data, or concept mean, in plain English. Parts one through five of the portfolio are due week three of class. These are a review of the first course in this sequence and ensure that all of us are at the same skill level. The other sections of the portfolio are due as listed on the course outline and are designed to apply class lectures as we proceed through the course. The portfolio is based on the dating ad data base that we have been and will continue to be developing. Bring your ads with you for discussion in class next week.
  24. 24. Portfolio Contents Section One: Research Design and Sample Selection (This data has already been done as homework during the first term) 1. Use your former ads or draw an appropriate raw data sample of male and female dating ads from a specific population using our sampling frame. Discuss the sampling frame, sampling elements, and sampling method used. 2. Discussion of Type of Research Method 3. Discussion of Theory 4. Statement of Hypothesis, Dependent and Independent Variable (s) based on your sampling strategy 5. Level of Measurement 6. Unit of Analysis Section Two: Organization and Presentation of Data for Male and Female Samples (The data has already been done during the first term) 1. Sort Data by Age of Advertiser (IV) into a Frequency Table 2. Create a Cross Tabulation Table of the age of the advertiser tabulated across gender 3. Calculate the specific number of years younger and older a person is willing to date and present in table format. 4. Create a double Bar Graph for males and females showing the number of years older they are willing to date (showing males and females on the same graph) 5. Create a double Frequency Polygon for males and females showing the number of years younger they are willing to date (showing males and females on the same graph) Section Three: Summary Statistics (Number of Years Younger and Older a person is willing to date) 1. Create a Table Showing the Cumulative Frequencies/Percentages 2. Proportions/Percentages at three years older and younger 3. Ratios for males to females at three years older and youger 4.What is the Range for the ages they are willing to date younger and older Section Four: Measures of Central Tendency (Number of Years Younger and Older a person is willing to date) 1. Mode 2. Median 3. Mean Section Five: Measures of Dispersion (Number of Years Younger and Older a person is willing to date) 1. Mean Deviation 2. Variance 3. Standard Deviation
  25. 25. Section Six: Second sample 1. Draw a second sample of dating ads using the same sampling frame as before. Or, you can use the dating ads I have drawn that are posted on the class web page as your second set of ads. 2. Sort Data and Calculate the Average Years Younger and Older a Person is willing to date 3. Calculate the mean for both samples (aver. Age older and younger) 4. Calculate the standard deviation for both Section Seven: Z Scores 1. Calculate graph the percentage of females that desire a dating partner five or more years older than themselves. 2. Present in a graph form the area for Z 3. Calculate the percentage of males that desire a dating partner five or more years older than themselves 4. Present in a graph form the area for Z 5. Calculate and graph using the addition rule, the probability that a man would desire a dating partner either three years older or three years younger than him. Discuss how the multiplication rule might work. Section Eight: T=tests 1. Graph the means for your sample as in Figure 7.1 and find the mean difference. 2. What type of t=test would you use and why to test the difference between the two samples. 3. What would be the degrees of freedom for your test. 4. Set a confidence interval for alpha and explain it to me. 5. Set up a null hypothesis using the symbols and interpret it for me (p. 212). 6. Set up a research hypothesis as well. 7. Describe how you would conduct the test. 8. Assuming that the t=test found a true difference, tell me what it might say about your two samples. Section Nine: Chi Square 1. Follow the steps to create a table of age intervals for advertisers for both of your samples/M/F. 2. Calculate the Chi-Square and find the critical value. 3. Set up a hypothesis. 4. Tell me what your values mean for each situation. 5. For the brave, try creating a three by three table for the practice.
  26. 26. Section Ten: Generalizing to the Population 1. Gather the means and standard deviations for each class member=s first sample (sample A). We will consider this our population. 2. Calculate the mean of means and standard deviation (standard error of the mean) for the classes sample distribution. 3. Diagram the sample distribution of means as a bell shaped curve, p. 177. 4. Plot the means in graph form to see how they might approximate the normal curve, p. 179. 5. Draw the sampling distribution of means as a probability distribution showing three standard deviations on either side of the curve and plug in your numbers from #2, p. 181. 6. Calculate the standard error of the mean for your own sample A using the standard deviation for the class means of means. Calculate the 95% CI as a probability that the mean of your sample reflects the true population mean. 7. Discuss how the mean of means is representative of the true population mean; how about the standard deviation. Discuss how your sample might be generalizable to the population and your original research hypothesis of cultural hypergamy. Section Eleven: Correlation 1. Construct a correlation table for males and females using the following information from your first sample. (Could be done as one correlation with gender as a subgroup.) 2. The age of the advertiser and the age range he/she specified for a desired dating partner. 3. Calculate r. 4. Construct a scatter plot with a mean axis for x and y and plot the scores. 5. Interpret the findings of your Pearson=s r score and scatter plot. 6. Set up a test of significance hypothesis to see if the findings are generalizable to the rest of the population of dating advertisers. 7. Calculate p (rho) and tell me your findings. 8. Tell me how you can evaluate correlations while controlling for other (ordinal) variables and give examples

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