Commonly Used Statistics in Survey Research

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This is a version of our "commonly used statistics" presentation that has been modified to address the commonly used statistics in survey research and analysis. It is intended to give an *overview* of …

This is a version of our "commonly used statistics" presentation that has been modified to address the commonly used statistics in survey research and analysis. It is intended to give an *overview* of the various uses of these tests as they apply to survey research questions rather than the point-and-click calculations involved in running the statistics.

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  • Null Hypothesis: The hypothesis that a difference or relationship between the variables does not exist. You are trying to reject this hypothesis in your test.Alternative Hypothesis: The hypothesis that a difference of relationship between the variables does exist. What you are trying to “prove” in statistical tests.Mean: A measure of central tendency that is the arithmetical average of a group of numbers. Standard Deviation: A measure of spread that quantifies how much the scores in a sample vary around the sample’s mean.Correlation: Implies a relationship (usually linear) between two variables. Terminology appropriately used when testing relationships between variables, but is commonly misused in other contexts.Confidence Interval: Derived from statistical tests. Provides 95% (usually) confidence that the true statistic of interest (i.e. mean, relationship, risk, etc.) lies within a given range. Greatly affected by things such as sample size and measurement error.
  • Etc: sample size, spherecity…

Transcript

  • 1. Patrick Barlow and Tiffany Smith
  • 2. Descriptive StatisticsParametric StatisticsNon-Parametric Statistics
  • 3.  Null Hypothesis Alternative Hypothesis Mean Standard Deviation Correlation Confidence Interval
  • 4.  Fitthe statistics to the research question, not the other way around! First, ask yourself, “Am I interested in….  Describing a sample or outcome?”  Looking at how groups differ?”  Looking at how outcomes are related?”  Looking at changes over time?”  Creating a new scale or instrument?  Assessing reliability and/or validity of an instrument? Second, “How am I measuring my outcomes?”
  • 5.  Descriptive Statistics Parametric Statistics  Common tests of relationships  Pearson r  Linear/multiple regression  Common tests of group differences  Independent t-test  Between subjects analysis of variance (ANOVA)  Common tests of repeated measures  Dependent t-test  Within subjects ANOVA Tests of categorical data  Odds Ratio / Chi Square  Logistic Regression Common Psychometric tests  Cronbach’s Alpha  Principal Components and Factor Analysis
  • 6.  Numbers used to describe the sample They do not actually test any hypotheses (or yield any p-values) Types:  Measures of Center -  Mean  Median  Mode  Measures of Spread -  Quartiles  Standard Deviation  Range  Variance  Frequencies
  • 7.  Most powerful type of statistics we use Researchers must make sure their data meets a number of assumptions (or parameters) before these tests can be used properly.  Some key assumptions  Normality  Independence of observations Inresearch, you always want to use parametric statistics if possible.
  • 8. Pearson r correlationLinear/Multiple Regression
  • 9.  What is it?  A statistical analysis that tests the relationship between two continuous variables. Commonly Associated Terms:  Bivariate correlation, relationship, r-value, scatterplot, association, direction, magnitude.
  • 10. Strong Relationship: r > .50 Weak Moderate Relationship: No Relationship: Relationship: r ≈ |.00| |.10| r ≈ |.30| 10
  • 11. Each has a Pearson Correlation of r=.82, is & is statistically significant 11Anscombe, F.J., Graphs in Statistical Analysis, American Statistican, 27, 17-21
  • 12.  What you read:  Study found a relationship between GPA and sense of belonging, r=.35, p = .03. What to interpret:  Results show r = .35, p = .03, R2=.12 How to interpret:  There is a weak, significant positive relationship between college GPA and students’ sense of belonging to the university. As sense of belonging increases, GPA also increases.
  • 13.  What is it?  A statistical analysis that tests the relationship between multiple predictor variables and one continuous outcome variable.  Predictors: Any number of continuous or dichotomous variables, e.g. age, anxiety, SES  Outcome: 1 Continuous variable, e.g. ER visits per Month Commonly Associated Terms:  Multivariate, beta weight, r2-value, model, forward/backward regression, sequential/hierarchical regression, standard/simultaneous regression, statistical/stepwise regression. 13
  • 14. Independent t-testBetween Subjects Analysis of Variance (ANOVA)
  • 15.  What is it?  Tests the difference between two groups on a single, continuous dependent variable. Commonly associated terms:  Two sample t-test, student’s t-test, means, group means, standard deviations, mean differences, group difference, confidence interval, group comparison.
  • 16.  What to interpret?  p-values (<.05)  Mean differences and standard deviations  Confidence intervals How to interpret?  There is a significant difference between the two groups where one group has a significantly higher/lower score on the dependent variable than the other.
  • 17.  What you read:  Students who were put on academic probation (M=1.50, SD=.40) had lower sense of belonging than students who were not put on academic probation (M=3.50, SD=.75), p = .02. What to interpret:  p-value: .02  Mean sense of belonging for both groups: academic probation = 1.50 & non-academic=3.50.  Standard deviations for both groups: on academic probation =.40 & not on academic probation=.75. How to interpret:  Participants on academic probation had significantly lower sense of belonging than students who were not put on academic probation.
  • 18.  What is it?  Tests the difference among more than two groups on a single, continuous variable.  Post-Hoc tests are required to examine where the differences are. Commonly associated terms:  F-test, interactions, post-hoc tests (tukey HSD, bonferroni, scheffe, dunnett).
  • 19.  What to interpret?  p-values (<.05)  Main effect: Shows overall significance  Post-hoc tests: shows specific group differences  Mean differences, standard deviations How to interpret?  Main Effect: There was an overall significant difference among the groups of the independent variable on the dependent variable.  Post-Hoc: Same interpretation as an independent t- test
  • 20.  What you read:  A researcher looks at differences in average satisfaction on three different reading interventions (A, B, and C).  Main effect: Overall F=20.10, p=.01  Post-hoc: Comparison of Intervention “A” to Intervention “B” shows average satisfaction to be 4.32 (SD=.50) and 3.56 (SD=1.2), respectively, p=.04. What to interpret:  Main effect: p-value=.01  Post-hoc: p-value=.04, group means show Intervention “A” has higher satisfaction ratings than Intervention “B”. How to interpret:  Main effect: There is a significant overall difference among the three interventions on satisfaction.  Post-hoc: Students who received Intervention “A” have significantly higher satisfaction than those who received Intervention “B”
  • 21. Dependent t-testWithin Subjects Analysis of Variance (ANOVA)
  • 22.  What is it?  Tests the differences for one group between two time-points or matched pairs Commonly Associated Terms:  Pre and posttest, matched pairs, paired samples, time. What to interpret?  p-values (<.05)  Mean change between measurements (i.e. over time or between pairs) How to interpret:?  There is a significant difference between the pretest and posttest where the score on the posttest was significantly higher/lower on the dependent variable than the pretest.
  • 23.  What you read:  An article shows a difference in average test score before (M=79.50, SD=8.00) and after (M=85.25, SD=7.90) an educational intervention, p=.08. What to interpret:  p-value=.08  Mean change=7.75 more points after the educational intervention. How to interpret:  Average test score did not significantly change from before the intervention to after the intervention; however, there may be a practically relevant difference.
  • 24.  What is it?  A statistical analysis that tests differences of one group between two or more time-points or matched pairs (e.g. pretest, posttest, & follow-up or treatment “A” patient, treatment “B” matched patient, & placebo matched patient). Commonly Associated Terms:  Multiple time-points/matched pairs, repeated measures, post- hoc. What to interpret?  Main effect: p-values  Post-hoc: p-values, mean change, direction of change. How to interpret:  Main Effect – There was an overall significant difference among the time points/matched pairs on the dependent variable.  Post-Hoc: Same as a dependent t-test.
  • 25.  What you read:  An article shows a difference in average classroom comfort before (M=1.5, SD=2.0), after (M=3.30, SD=.90), and six months following a cohort-building intervention (M=4.20, SD=3.0).  Main effect: Overall F=3.59, p=.02. What to interpret:  p-value=.02, statistically significant  Mean change=1.8 higher classroom comfort at post- intervention How to interpret:  Classroom comfort significantly increased from baseline to six-months following a cohort-building intervention; however, post-hoc tests will be needed to show where that differences lies.
  • 26.  Mixed ANOVA: Used when comparing more than one group over more than one time-point on a measure  Example – Males vs. female students, before and after a foreign language course – Average score on an assessment Factorial ANOVA: Comparing two or more separate independent variables on one dependent variable.  Example – Who taught the course (Ms. Lang, Mr. Beard, or Ms. Brinkley), AND which teaching method was used (online, face to face) – Average post-test assessment score Analysis of covariance (ANCOVA): Examining the differences among groups while controlling for an additional variable  Example – Online or face to face course, controlling for baseline knowledge – Average post-test assessment score All of these methods are used to test interaction effects
  • 27. Odds Ratio / Relative Risk (Chi-square test of independence) Logistic Regression
  • 28.  What is it?  A statistical analysis that tests the odds or risk of an event occurring or not occurring based on one or more predictor variables (independent). Commonly Associated Terms:  Unadjusted odds ratio (OR), relative risk (RR), 2x2, chi-square, absolute risk reduction, absolute risk, relative risk reduction, odds, confidence intervals, protective effect, likelihood, forest plot. What to interpret?  If a 2x2 table: interpret the OR or RR and confidence intervals rather than the p-value.  If more than a 2x2 table, then the p-value and frequencies may be more useful. How to interpret:  Odds Ratio < 1: For every unit increase in the independent variable, the odds of having the outcome decrease by (OR) times.  Odds Ratio > 1: For every unit increase in the independent variable, the odds of having the outcome increase by (OR) times.  Odds Ratio = 1 or CI crosses 1.0 or p > .05: You are no more or less likely to have the outcome as a result of the predictor variable. (this would be non- significant)
  • 29.  What are the odds of leaving college if a student has been placed on academic probation?  IV: Academic probation (Y/N)  DV: Completion (Y/N) What you read:  The odds ratio (95% CI) for college completion and academic probation showed OR=2.00 (95% CI=1.44 - 2.88), p <.05. What you interpret:  OR > 1 (2.00)  95% CI is small, and does not cross 1.0 (1.44 to 2.88)  p-value is below .05 How you interpret:  Students are two times more likely to leave college if they were placed on academic probation.
  • 30.  What is it?  A statistical analysis that tests the odds or risk of an event occurring or not occurring based on one or more predictor variables (independent) after controlling for a number of other confounding variables. Commonly Associated Terms:  Adjusted odds ratio (AOR), multivariate adjusted odds ratio, likelihood, protective effect, risk, odds, 95% confidence interval, classification table, dichotomous DV. What to interpret?  OR (these are your measures for risk of the outcome occurring given the predictor variable), p-value for OR, confidence intervals for OR (should not cross over 1.0, should not be overly large e.g. 1.2 – 45.5), classification table (if it is provided). How to interpret:  Odds Ratio < 1: For every unit increase in the independent variable, the odds of having the outcome decrease by (OR) times after controlling for the other predictor variables.  Odds Ratio > 1: For every unit increase in the independent variable, the odds of having the outcome increase by (OR) times after controlling for the other predictor variables.  Odds Ratio = 1 or CI crosses 1.0 or p > .05: You are no more or less likely to have the outcome as a result of the predictor variable after controlling for the other predictor variables. (this would be non-significant)
  • 31.  Does age, male sex, and time spent playing video games, increase the odds of being on academic probation?  Predictor Variables: age (scale), sex (M/F), Gaming (ordinal, 0hrs, 1- 3hrs, 4-6hrs, etc.)  DV: Probation (Y/N) What you read:  The ORs (95% CI) for each predictor variable are:  Age: OR=1.40 (95% CI=0.88 to 6.90), ns  Sexmale: OR=3.00 (95% CI=2.22 to 5.20), p <.001  Gaming: OR=6.75 (95% CI=4.69 to 8.80), p <.001 What you interpret:  The OR, CI, and p-value for each predictor. How you interpret:  Both sex and time spent gaming increase the odds of being on academic probation. Specifically, men are 3.00 times more likely to be on academic probation than females, and for every unit increase in gaming time, the odds of being on probation increases by 6.75 times.
  • 32. Questions? 
  • 33. Work together (in groups of 3-4) to create surveyresearch scenarios / questions that could beaddressed using the analyses you have learned aboutin class.Use your “Commonly Used Statistics” handout as aresource! Be prepared to share your answers 
  • 34. Cronbach’s AlphaPrincipal Component Analysis / Factor Analysis Other psychometric tests
  • 35.  Psychometric tests are used to examine the characteristics and performance of a survey or assessment instrument. Reasons to use these tests  Reliability  Validity  Dimension reduction (constructing new instruments)  Item analysis (objective tests)
  • 36.  Cronbach’s alpha is one of the most common psychometric tests used by survey researchers. Looks at the internal consistency of the items in a certain scale or instrument.  In other words, how responses to items in the scale relate to one another. What to interpret  The overall alpha value for the scale  The “alpha if item removed” table How to interpret  For the Alpha values: > .90 is excellent, .80-.90 is good, .70-.80 is acceptable, .60-.70 is questionable, between .50-.60 is poor, and <.50 is unacceptable. If you see a negative value, then recheck your data for coding errors.  For the “alpha if removed” table: Look at the values that the scale would have if the item was removed. If dropping an item makes a meaningful improvement (e.g. from .75 to .80), then consider dropping the item and rerunning the analysis.
  • 37.  More items More participants Increase the “good” type of redundancy Drop poor items (those that affect alpha) Clarify item stems Double check coding
  • 38.  PCA and FA are both dimension reduction techniques that are used when either pretesting a new instrument (exploratory) or gathering validity evidence for an existing instrument (confirmatory). Both methods look at how items cluster together as latent (not directly measured) “factors” or “components”.  Examples: “depression”, “anxiety”, or “sense of belonging”
  • 39.  Number of items Number of subjects Technique used  PCA  FA Extraction methods  Orthogonal  Oblique SO many others!
  • 40. Remember: Just because a finding is not significant does not mean that it is not meaningful. You should always consider the effect size and context of the research when making a decision about whether or not any finding is relevant in practice.