Quantitative Analysis of Survey Data and Other Assessments for Non-Experts: How to do SoTL without a statistician on retainer June 2, 2011 Gintaras Duda Creighton University

My Background I am a theoretical particle physicist Came to SoTL (PER) as a junior faculty member –New faculty workshop experience Huge roadblocks: no experience with 1.How educational research is conducted 2.Quantitative or qualitative analysis 3.Weak background in statistics

Areas of SoTL interest Attitude of introductory physics students –Particularly how it affects learning Online discussion behavior Realism in physics Problem-Based Learning in upper division courses Student note taking How students use the internet to learn physics

Workshop Purpose As SoTL matures, publication requires more and more rigorous measures and evidence –Sophisticated statistical tests –Careful survey design and analysis –Mixed method research –Evidence, evidence, evidence! But, many of us are untrained in these things

Who are you? Please share with the group: 1.Name, institution, and discipline 2.Why you picked this workshop 3.What you hope to gain

Workshop Purpose continued … Leave you with some simple tools to analyze: 1.Likert scale surveys 2.Effects of instruction 3.Survey reliability and validity No stats class or methods courses required

Part I. What to do with Likert Scales Likert scale instruments seem ubiquitous in SoTL work Particularly useful in measuring students’ attitudes, feelings, opinions, dispositions, etc. –Can use pre-post scheme to see changes and growth/deterioration –Of interest in Jesuit Pedagogy (another workshop)

Example from physics Attitudinal surveys –Measure students’ changes in attitude towards physics due to instruction –Instruments: VASS, MPEX, C-LASS, Attitude II, and others These instruments all show a similar trend –Students have more negative attitudes towards physics after instruction

Example Questions from Attitude II Instrument 1.Physics is irrelevant to my life 2.I can use physics in my everyday life 3.I will did find it difficult to understand how physics applies in the real-world 4.I see and understand physics in technology and the world around me 5 point Likert scale: Strongly agree, weakly agree, neutral, weakly disagree, strongly disagree

One of my Likert Scale Instruments

What do I do with Likert Scale Data? Two camps on analyzing Likert scale data 1.Interval Approach 2.Ordinal Approach Methods for data analysis differ between the two methods

Interval Data Basic philosophy: differences between responses are all equal –i.e. Difference to a student between strongly disagree and weakly disagree is the same as the difference between a neutral response and weakly agree Basic technique: Sum the data and do some statistics

Ordinal Data Basic philosophy: Differences between responses are not equal –i.e. Students tend not to distinguish highly between strongly and weakly statements –3 pt Likert scale more appropriate? Basic technique: Examine statistically the number of students who agreed or disagreed

Controversy over neutral response Good debate in the literature about the neutral/neither agree nor disagree response Some claim it’s crucial Some claim you should get rid of it Not going to discuss it here

Analyzing Ordinal Data One method is to reduce the problem to a “binomial analysis” –Lump all disagrees together, all agrees together, and don’t worry about neutral responses Visual method: Agree-disagree (Redish) plots Redish, J. Saul, and R. Steinberg, “Student expectations in introductory physics,” Am. J. Phys. 66, 212–

Agree-Disagree Plots Introduced by Redish et al. in their MPEX paper - called “Redish” plots Change from pre to post must be > 2σ to be considered significant (at 5% probability level) New Agree Percentage New Disagree Percentage Standard Deviation Redish, J. Saul, and R. Steinberg, Am. J. Phys. 66, 212–

Example of an Agree-Disagree Plot Duda, G., Garrett, K., Am. J. Phys. 76, 1054 (2008).

Analyzing Interval Data Basic idea here is assign a numerical value to each response Strong Disagree = -2 (or 0) Weakly Disagree = -1 (or 1) Neither Agree/Nor Disagree = 0 (or 2) Weakly Agree = 1 (or 3) Strong Agree = 2 (or 4) Sum the responses then analyze using standard statistical techniques

Simple (student) t-test The t-test is a simple (but robust) statistical test Tests a hypothesis: Is there a difference between two sets of data? –Are differences statistically significant? –95% confidence level, i.e. only a 5% probability the difference is due to statistical fluctuations

Example: The “Gender Gap” in Intro Physics StudentsNormalized GainStatistically Significant? Control Group Males (n=82)0.67 Females (n=63)0.50 Experimental Group Males (n=50)0.63 Females (n=96)0.56 Is there a difference between male and female students?

Which image is random? Sometimes our eyes can deceive us! And sometimes we think things are true because we’d like them to be true …

The “Gender Gap”: FMCE Gains StudentsNormalized GainP-value Control Group Males (n=82)0.67< 0.05 Females (n=63)0.50(significant) Experimental Group Males (n=50) Females (n=96)0.56(not significant) In the experimental group, there is no statistically significant difference between the two genders.

Student’s t-test Assumptions: –Each data set follows a normal distribution Parameters: –One-tailed vs. two-tailed –Types: paired, two-sample equal variance, and a two-sample unequal variance test Can have different # of data points if conducting an unpaired test

Demo

Two Sample t-test Group AGroup B t-test outputGroup AGroup B Mean Variance Observations9.000 Pooled Variance0.054 Hypothesized Mean Difference0.000 df t Stat3.404 P(T<=t) one-tail0.002 t Critical one-tail2.583 P(T<=t) two-tail0.004 t Critical two-tail2.921 Here p < 0.05, so the null hypothesis is falsified – statistical difference between Group A and Group B

Measuring Effects of Instruction Suppose you apply some educational innovation –Control group and experimental group –Or pre-test and post-test How do you know if it’s effective? Say you give some sort of standard assessment –How big do the changes need to be to be statistically significant?

Method #1: Use a t-test You can always use a t-test Compare scores of control vs. experimental group or Compare pre vs. post tests –More difficult due to other variables

Method #2: Effect Size Effect Size (ES) is a method to quantify how effective an educational intervention has been relative to a control group Extremely useful when there is no familiar scale to judge outcomes

A thought experiment Suppose we do a study to see if children learn better in the morning or afternoon Morning trial: 15.2 average on assessment Afternoon trial: 17.9 average on assessment Is this a big difference? It depends on overlap! Robert Coe: “What is an Effect Size: A guide for users”

Two distributions If the distributions of scores looked like this, you would think the result is quite significant Robert Coe: “What is an Effect Size: A guide for users”

Two distributions But if the distributions of scores looked like this you wouldn’t be so impressed Robert Coe: “What is an Effect Size: A guide for users”

Effect Size Continued The Effect Size –Compares the difference between groups in light of the variance of scores within each group ES= (mean of experimental group) – (mean of control group) Standard Deviation Actually quite simple to calculate Robert Coe has great information online about ES

How to Interpret Effect Size Effect Size% of control group below mean of experimental group Probability you could guess which group an individual belongs to based on their score 0.050% % % % % % %0.84 Robert Coe: “What is an Effect Size: A guide for users”

How to Interpret Effect Size Effect SizeHow Large?Equivalent to the height differences between 0.2Small15 and 16 yr old girls 0.5Medium14 and 18 yr old girls 0.8Large13 and 18 yr old girls IQ differences between typical freshmen and Ph.D.s corresponds to an effect size of 0.8 Robert Coe: “What is an Effect Size: A guide for users”

Effect Size Example Duda, G., Garrett, K., Am. J. Phys. 76, 1054 (2008).

Making a better survey In my experience surveys and assessment instruments are difficult to write How do you know your instrument is 1.Reliable 2.Valid Are there alternatives to writing your own instruments?

Reliability: Cronbach Alpha Cronbach Alpha: measure of how closely items in a group are related Cronbach Alpha is often used for instruments which are not marked right or wrong –Think Likert Scale Measures if students responses are the same for similar types of questions

How to Cronbach Alpha You could calculate it by hand or you buy SPSS and figure out how to use it or you could download an excel spreadsheet which is programmed to do this: Reliability and validity/reliabilitycalculator2.xls

Cronbach Alpha Values Typically a Cronbach Alpha (α) > 0.8 is considered good –At this level survey is “reliable” However, there are exceptions: –Different types of surveys/instruments may have different natural levels of reliability –Experimental instruments may be still useful even if α~0.6

Warning! Common Mistakes with Cronbach Alpha Paper: “Calculating, Interpreting, and Reporting Cronbach’s Alpha Reliability Coefficient for Likert-Type Scales” by Joseph A. Gliem and Rosemary R. Gliem Lesson –Use Cronbach Alpha for Likert scale surveys –Draw conclusions based on clusters of items –Single item reliability is generally very low

Instrument Validity Validity is never universal –“Valid” for a certain population and for a specific purpose Three general categories of validity: 1.Content validity 2.Predictive validity 3.Concurrent validity

Ideas for Establishing Validity 1.Establish content or face validity –Correlate with other independent measures such as exam scores, course grades, other assessment instruments 2.Predictive validity –Longitudinal studies and student tracking are needed here 3.Concurrent validity –Compare with other assessment instruments or calibrate with the proper groups

Survey/Assessment Creation Tips Build in measures to show reliability –e.g. multiple questions within a survey on the same topic (both positive and negative) –Questions that establish that students are taking the survey seriously For content driven assessments, research student difficulties Beta-version: open ended questions Correlations can help show validity

An Example of evidence for Validity Duda, G., Garrett, K., Am. J. Phys. 76, 1054 (2008).

Buros Institute of Mental Measurement “By providing professional assistance, expertise, and information to users of commercially published tests, the Institute promotes meaningful and appropriate test selection, utilization, and practice.”

Conclusion Some simple statistical tests can provide rigorous evidence of –Student learning –Instructional effectiveness –Improvements in attitude All of these methods are extremely effective when coupled with qualitative methods Stats involved can be done with little or no training

My SoTL advice Plan a throw-away semester in any SoTL study –“trial” period to tinker with your study design –Flexibility to alter your study design when you find it doesn’t work Involving students in SoTL work can be very effective Try to publish in discipline specific journals When in doubt, ask your students!

Good References Analysis of Likert Scales (and attitudinal data in general) – CLASS survey – Effect Size: –“What is an Effect Size: A guide for users” by Robert Coe (easily found by google) –Coe also has an excel spreadsheet online to calculate effect size

Good references Reliability and Validity: – nstrument%20Reliability%20and%20Validity/ Reliability.htmhttp:// nstrument%20Reliability%20and%20Validity/ Reliability.htm – nstrument%20Reliability%20and%20Validity/ validity.htmhttp:// nstrument%20Reliability%20and%20Validity/ validity.htm T-test –Step by step video on excel: o

Good References The FLAG: Field-Tested Learning Assessment Guide – –Contains “broadly applicable, self-contained modula classroom assessment techniques (CATs) and discipline-specific tools for STEM instructors”

Good References John Creswell’s books (and courses) have been highly recommended to me