PSA 2006 Session Title: Teaching Statistics to Undergraduates

Teaching Undergraduate Statistics Experientially Using Personal Dating Ads

Sharon Warner Methvin, PhDDepartment of Sociology

Clark CollegeVancouver, Washington 98663 Email: Smethvin@clark.edu

Web: http://web.clark.edu/smethvin Phone: 360.992.2976 Cell: 503.888.4337

Paper Presented at the Pacific Sociological Association Annual MeetingApril 20- 23, 2006Hollywood, CA

Draft Copy: Not Proofread

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 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 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

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.

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 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 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 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

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”

“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!

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 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 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.

"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 fundamental premise that students learn best when the information can be understood in a personally meaningful way.

Sample One Sample Two

Female Age

Desire-Low

Desire-Hi

Female Age

Desire-Low

Desire-Hi

6 24 23 25 1 52 50 588 24 24 34 2 27 25 352 27 25 35 3 67 62 737 41 35 50 4 63 58 689 44 38 52 5 51 45 6010 47 45 52 6 24 23 255 51 45 60 7 41 35 501 52 50 58 8 24 24 344 63 58 68 9 44 38 523 67 62 73 10 47 45 5210      

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 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.”

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.”

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!

Handouts for PSA 2006 Session Title: Teaching Statistics to Undergraduates

Teaching Undergraduate Statistics Experientially Using Personal Dating Ads

Sharon Warner Methvin, PhDDepartment of Sociology

Clark CollegeVancouver, 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 MethvinTEXT: Elementary Statistics in Social Research, by James Alan Fox and Jack

Levin, 9th ed., 2003Social Research Methods, by W. Lawrence Neuman, 5th ed., 2003.

ASSIGNMENT DETAILSPortfolio: (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.

Portfolio ContentsSection 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 Method3. Discussion of Theory4. Statement of Hypothesis, Dependent and Independent Variable (s) based on your sampling strategy5. Level of Measurement6. 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 Table2. Create a Cross Tabulation Table of the age of the advertiser tabulated across gender3. 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/Percentages2. Proportions/Percentages at three years older and younger3. Ratios for males to females at three years older and youger4.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. Mode2. Median3. Mean

Section Five: Measures of Dispersion (Number of Years Younger and Older a person is willing to date)1. Mean Deviation2. Variance 3. Standard Deviation

Section Six: Second sample1. 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 date3. Calculate the mean for both samples (aver. Age older and younger)4. Calculate the standard deviation for both

Section Seven: Z Scores1. 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 Z3. Calculate the percentage of males that desire a dating partner five or more years older than themselves4. Present in a graph form the area for Z5. 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=tests1. 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.

Section Ten: Generalizing to the Population1. 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