Download Hypothesis Testing - St. Cloud State University

Workshop: Statistical
Consulting &
Research Center
November 1, 2012
Introduction
• Randy Kolb
• Coordinator of Statistical Consulting Group, LR&TS,
[email protected]
• 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: 320-308-6506
• Stats Office: 320-308-4709
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
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•
•
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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
•
•
•
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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
• Ho
(ex: Ho: M1 = M2; 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.
• Ha
(ex: HA: M1 ≠ M2; the mean of group 1 is not equal to the mean of group 2
• In Hypothesis Testing, the goal is usually to reject Ho.
• Decision to reject or accept Ho 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 Ho and conclude HA
• 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
• Ho = M1 = M2
• Ha = M1 ≠ M2
• Pair 1:
t = -12.173, sig. = .000
• If sig. > α , HO
• If sig. < α , Ha
• thus, rejecting the null hypothesis
(Support of HA)
T-Test (Independent/Group)
• Ho = M1 = M2
• Ha = M1 ≠ M2
• 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, HA, Must use Equal Variances Not Assumed
• t = 1.257, p > .238, thus, unable to reject Ho
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
• Ho = µ1 = µ2 = µ3
µ = population mean
• Ha = 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
• Ho: There is not a relationship between “witnessed abduction”
and “outcome status”
• Ha: There is a relationship between “witnessed abduction”
and “outcome status”
• Chi-Square =157.614, sig. = .000
• Conclusion: Ha
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 R2 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
Ho: Model is not
useful
Ha: Model is useful
Ho: 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, 8-4
Email: [email protected]
Phone: General Office: (320)-308-4709
Randy: (320)-308-6506