Workshop: Statistical Consulting & Research Center November 1, 2012

Introduction Randy Kolb Coordinator of Statistical Consulting Group, LR&TS, Statistical Assistants: Two Graduate Assistants: Sara Brodeur and Kristin Brietzke Two Student Assistants: Damien Traore and Patrick Ilboudo Office: Miller Center, Room 212 Randy’s Phone: Stats Office:

Services Provided by the Statistical Consulting and Research Center It’s free! Reviewing Surveys before using them for your research Assistance in creating online surveys Keying the data from paper surveys Programming support using SPSS and/or Minitab Assistance with statistical analysis and interpretation (if needed)

Useful Tips for Survey Design Follow the 6 steps of successful surveys 1. Clearly define objective(s) and goal(s) of the survey 2. Ask the right questions, get information needed to achieve survey objectives 3. Select target audience (and method of communication to them) 4. Solicit participation 5. Test the survey 6. Execute and analyze *** Contact us early (before survey is finalized) ***

Good and Bad Examples

Types of Questions Multiple Choice with no response Fill in the blank (ex: Age) Categories with ranges (ex: Income) Statement with range of agreement Open-ended Check all that apply ***Mutually exclusive and collectively exhaustive!***

Type of Study Defines what Type of Analysis is Needed Descriptive Analyses Mean Median Mode Frequency Tables Standard Deviations Use of graphs and 2-way tables

Type of Study Defines what Type of Analysis is Needed cont. Comparative/ Inferential Analysis T-test Paired-samples Independent Samples Analysis of Variance (ANOVA) Chi-Squared (sufficiently large sample size) Regression Correlation Hypothesis Testing (Critical to understand)

What is Hypothesis Testing? Formal procedures used to determine the probability that a given hypothesis is true. Six general steps 1. State the hypotheses. 2. Formulate a plan for analysis. Decide on level of significance (sig.) and sample size. 3. Select and compute the appropriate test statistic. 4. Interpret results. 5. Apply decision rule. 6. State conclusion.

Hypotheses Null Hypothesis Hypothesis that observations made are the result of pure chance. In statistics, the only way of supporting your hypothesis is to refute the null hypothesis H o (ex: H o : M 1 = M 2 ; the mean of group 1 is equal to the mean of group 2) Alternative Hypothesis Researcher wants to prove Observations made are influenced by some non-random cause. H a (ex: H A : M 1 ≠ M 2 ; the mean of group 1 is not equal to the mean of group 2 In Hypothesis Testing, the goal is usually to reject H o. Decision to reject or accept H o is based on Alpha and the appropriate test statistic when applied to the data.

Alpha (α) A result is deemed statistically significant if it is unlikely to have occurred by chance, and thus provides enough evidence to reject the null hypothesis. Levels of Alpha used in Research: p <.10 90% confident in the decision to reject H o and conclude H A p <.05 (most common) 95% confident p <.01 99% confident

T-Test (Paired Samples/Within Cases) Assesses whether the means of two groups are statistically different from each other H o = M 1 = M 2 H a = M 1 ≠ M 2 Pair 1: t = , sig. =.000 If sig. > α, H O If sig. < α, H a thus, rejecting the null hypothesis (Support of H A )

T-Test (Independent/Group) H o = M 1 = M 2 Ha = M 1 ≠ M 2 Levene’s Test for Equality of Variances Decision To determine which t-test formula should be used, either the “equal variances assumed” formula or the “equal variances not assumed” formula If Sig. > α, Equal Variances Assumed If Sig. ≤ α, Equal Variances Not Assumed Since Sig =.007, H A, Must use Equal Variances Not Assumed t = 1.257, p >.238, thus, unable to reject H o

Analysis of Variance (ANOVA) Used in designs that involve two or more groups Will tell whether the values significantly vary across the groups, but not precisely which group is significantly different from the others. If significance is found, post tests must be computed to determine where the differences are. F ratio – Variance due to manipulation of Independent Variable (IV) (between) Error Variance (within) Hypotheses H o = µ 1 = µ 2 = µ 3 µ = population mean H a = at least one mean is different from the others

One Way ANOVA (Between Subjects) F(1, 149) = 4.567, sig. <.05 Compassion Score by Gender

Chi-Square This test is used when you wish to examine the relationship between two categorical variables that each contains two or more levels. Compares the observed frequencies or proportions of cases that occur in each of the levels within each category, with the values that would be expected if there was no association between the two variables

Chi-Square 3x3 Witnessed Abduction (Witnessed, Assumed Abduction, Inapplicable) by Outcome Status (1-Homocide, 2-Still Missing, 3-Recovered)

Chi-Square Interpretation H o : There is not a relationship between “witnessed abduction” and “outcome status” H a : There is a relationship between “witnessed abduction” and “outcome status” Chi-Square = , sig. =.000 Conclusion: H a

Regression Regression is used for estimating the relationship between a continuous dependent variable (DV) and one or more continuous or discrete independent, or predictor, variables. Builds a predictive model of the dependent variable based on the information provided in the independent variable(s). Value of the regression, simple or multiple approach, lies in its capacity to estimate the relative importance of one or several hypothesized predictors and its ability to assess the contribution of the combined variable(s) to change in the DV.

Regression cont. The R 2 value is an indicator of how well the model fits the data R (or the correlation coefficient) is an indication of the relationship between two variables R squared is a goodness of fit for a formula (usually a straight line) to the data. Models: Simple: Uses 1 independent variable (predictor) in the equation to predict the dependent variable Multiple: Forces all predictors (2 or more) into equation to build best representation of relationship between the dependent variable and the independent variables in the equation Stepwise: Builds a step-by-step regression model to predict the DV by examining the set of IVs and using the most significant variable remaining in the list.

Pearson r Corrleation Describes relationships between variables -1 ≤ r ≤ +1 *sign and size matter (direction of relationship)* The closer r is to ±1, the stronger the relationship

Simple Linear Regression Example H o : Model is not useful H a : Model is useful H o : IV is not significantly useful in predicting the DV Ha: IV is significantly useful in predicting the DV

Multiple Linear Regression Example (Stepwise)

Multiple Linear Regression Example (Stepwise) cont.

Demonstration Online Survey Minitab Demo software Availability: (6 month rental $30, 12 month rental $50, and perpetual license $100) -- Minitab.com SPSS Demo software using recent project Availability: Contact the SCSU computer store (Miller Learning Center basement)

Ready, Set, GO! Getting ready for analysis Using online survey Transitioning from paper surveys Analyzing the data to answer research questions Keywords in research questions Is there a relationship.. Is there a difference between… Does factor (ex: Gender) influence… Hypothesis Testing Interpreting the statistical analysis Demonstration of data analysis using a recent project

Conclusion Questions? Statistical Consulting and Research Center Miller Center, room 212 (north side of large computer lab in east wing) Hours: Mon-Fri, Phone: General Office: (320) Randy: (320)