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Outline• The Null Hypothesis• Type I and Type II Error• Using Statistics to test the Null Hypothesis• The Logic of Data Analysis
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Research Questions and Hypotheses• Research question: – Non-directional: • No stated expectation about outcome – Example: • Do men and women differ in terms of brand loyalty?• Hypothesis: – Statement of expected relationship • Directionality of relationship – Example: • Women will have greater brand loyalty than men
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Grounding Hypotheses in Theory• Hypotheses have an underlying rationale: – Logical reasoning behind the direction of the hypotheses (theoretical rationale – explanation) – Why do we expect women to have better brand loyalty?• Theoretical rationale based on: – 1. Past research – 2. Existing theory – 3. Logical reasoning
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The Null Hypothesis• Null Hypothesis - the absence of a relationship – E..g., There is no difference between men’s and women’s with regards to brand loyalty• Compare observed results to Null Hypothesis – How different are the results from the null hypothesis?• We do not propose a null hypothesis as research hypothesis - need very large sample size / power – Used as point of contrast for testing
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Hypotheses testing• When we test observed results against null: – We can make two decisions: • 1. Accept the null – No significant relationship – Observed results similar to the Null Hypothesis • 2. Reject the null – Significant relationship – Observed results different from the Null Hypothesis – Whichever decision, we risk making an error
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Type I and Type II Error• 1. Type I Error – Reality: No relationship – Decision: Reject the null • Believe your research hypothesis have received support when in fact you should have disconfirmed it • Analogy: Find an innocent man guilty of a crime• 2. Type II Error – Reality: Relationship – Decision: Accept the null • Believe your research hypothesis has not received support when in fact you should have rejected the null. • Analogy: Find a guilty man innocent of a crime
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Potential outcomes of testing Decision Accept Null Reject NullRE No 1 2A RelationshipLI RelationshipT 3 4Y
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Potential outcomes of testing Decision Accept Null Reject Null CorrectRE No decision 2A RelationshipLI RelationshipT 3 4Y
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Potential outcomes of testing Decision Accept Null Reject NullREA No Relationship 1 2LI RelationshipTY Correct 3 decision
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Potential outcomes of testing Decision Accept Null Reject NullRE No 1 Type I ErrorA RelationshipLI RelationshipTY 3 4
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Potential outcomes of testing Decision Accept Null Reject NullRE No 1 2A RelationshipLI RelationshipTY Type II Error 4
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Potential outcomes of testing Decision Accept Null Reject Null Correct Type I Error decisionRE NoA RelationshipLI RelationshipTY Correct Type II Error decision
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Function of Statistical Tests• Statistical tests determine: – Accept or Reject the Null Hypothesis• Based on probability of making a Type I error – Observed results compared to the results expected by the Null Hypotheses – What is the probability of getting observed results if Null Hypothesis were true? • If results would occur less than 5% of the time by simple chance then we reject the Null Hypothesis
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Start by setting level of risk of making a Type I Error• How dangerous is it to make a Type I Error: – What risk is acceptable?: • 5%? • 1%? • .1%? – Smaller percentages are more conservative in guarding against a Type I Error• Level of acceptable risk is called “Significance level” : – Usually the cutoff - <.05
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Conventional Significance Levels• .05 level (5% chance of Type I Error)• .01 level (1% chance of Type I Error)• .001 level (.1% chance of Type I Error)• Rejecting the Null at the .05 level means: – Taking a 5% risk of making a Type I Error
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Steps in Hypothesis Testing• 1. State research hypothesis• 2. State null hypothesis• 3.Set significance level (e.g., .05 level)• 4. Observe results• 5. Statistics calculate probability of results if null hypothesis were true• 6. If probability of observed results is less than significance level, then reject the null
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Guarding against Type I Error• Significance level regulates Type I Error• Conservative standards reduce Type I Error: – .01 instead of .05, especially with large sample• Reducing the probability of Type I Error: – Increases the probability of Type II Error• Sample size regulates Type II Error – The larger the sample, the lower the probability of Type II Error occurring in conservative testing
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Statistical Power• The power to detect significant relationships – The larger the sample size, the more power – The larger the sample size, the lower the probability of Type II Error• Power = 1 – probability of Type II Error
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Statistical Analysis• Statistical analysis: – Examines observed data – Calculates the probability that the results could occur by chance (I.e., if Null was true)• Choice of statistical test depends on: – Level of measurement of the variables in question: • Nominal, Ordinal, Interval or Ratio
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Logic of data analysis• Univariate analysis – One variable at a time (descriptive)• Bivariate analysis – Two variables at a time (testing relationships)• Multivariate analysis – More than two variables at a time (testing relationships and controlling for other variables)
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Variables• Dependent variable: – What we are trying to predict – E.g., Brand preference• Independent variables: – What we are using as predictors – E.g., Gender, Product usage history
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Commonality across all statistical analysis procedures• Set the significance level: – E.g., .05 level • Means that we are willing to conclude that there is a relationship if: – Chance of Type I error is less than 5%• Statistical tests tell us whether: – The observed relationship has less than a 5% chance of occurring by chance
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Summary of Statistical ProceduresVariables ProcedureNominal IV, Nominal DV Chi-squareNominal IV, Ratio DV T-testMultiple Nominal IVs, Ratio ANOVADVRatio IV, Ratio DV Pearson’s RMultiple Nominal IVs, Ratio ANCOVADV with ratio covariatesMultiple ratio Multiple Regression
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