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    Houser ppt chapt16 Houser ppt chapt16 Presentation Transcript

    • Chapter 16 Analysis and Reporting of Quantitative Data
    • Inferential Analysis
      • Enables inference of results from a carefully selected sample to an overall population
      • Quantifies the potential effects of error on the results
    • General Rules for Quantitative Analysis
      • Statistical tests are selected a priori
        • The acceptable level of significance is also selected before analysis begins
      • Run all of the identified tests
      • Report all of the tests that were run
        • Selective reporting is a source of bias
    • Type of Analysis Driven By…
      • The goals of the analysis
      • Assumptions of the data
      • Number of variables in the analysis
    • Statistical Inference
      • Intended to answer two fundamental questions:
        • How probable is it that the differences between observed results and those expected on the basis of the null hypothesis have been produced by chance alone?
        • How reliable are the results obtained?
    • Statistical Inference
      • Questions about reliability answered by setting confidence limits
      • Questions about probability answered by hypothesis testing
      • Conclusions concerned with probability of drawing an erroneous conclusion
    • Estimation
      • Point estimate : this sample statistic equals the population parameter
      • Interval estimate : the range of numbers we believe will include the population parameter
      • Statistical estimation allows for determination of the amount of uncertainty in the estimate
    • Confidence Interval Two numerical values defining an interval that we believe, with an identified level of confidence, actually includes the estimated population parameter
    • Calculation of Confidence Interval for the Mean
      • Determination of an acceptable confidence level a priori (1-  )
      • Identification of coefficient Z 
      • Calculation of standard error (s /  n)
      • Determination of the mean
    • Hypothesis Testing
      • Statistical test of significance
        • Between a sample and a known population
        • Between two samples
        • Between two variables in a sample
      • Can be used to test differences between:
        • Means
        • Proportions
        • Variances
    • Inferential Statistics
      • If a difference is detected, may be due to:
        • Experimental treatment caused the effect
        • Sampling error caused the effect (chance)
      • We cannot prove the experiment caused the difference
      • We can estimate the probability it was caused by error
    • Steps in Hypothesis Testing
      • 1. State research question as a statistical hypothesis
      • 2. Select the level of significance for the statistical test (alpha)
      • 3. Decide on the appropriate test statistic
      • 4. Determine the value the test statistic must attain to be declared significant (critical value)
      • 5. Perform the calculations for the test statistic
      • 6. Apply decision rule and draw conclusions
    • Hypotheses
      • H 0 : The null hypothesis
        • e.g. H 0 :  = 30
      • H A : The alternative hypothesis
        • e.g. H A :  30
      • The null hypothesis is rejected only if data presents sufficiently strong evidence to support the alternative
    • Steps in Hypothesis Testing
      • 1. State research question as a statistical hypothesis
      • 2. Select the level of significance for the statistical test (alpha)
      • 3. Decide on the appropriate test statistic
      • 4. Determine the value the test statistic must attain to be declared significant (critical value)
      • 5. Perform the calculations for the test statistic
      • 6. Apply decision rule and draw conclusions
    • Level of Significance
      • Level of Significance:
        • Preset standard that is considered significant in determining differences
        • Compare to p value: the probability of a type I error that the researcher is willing to risk
        • Most common: .05 and .01
      • Set a priori (alpha)
    • Steps in Hypothesis Testing
      • 1. State research question as a statistical hypothesis
      • 2. Select the level of significance for the statistical test (alpha)
      • 3. Decide on the appropriate test statistic
      • 4. Determine the value the test statistic must attain to be declared significant (critical value)
      • 5. Perform the calculations for the test statistic
      • 6. Apply decision rule and draw conclusions
    • Most Inferential Tests...
      • Based upon difference between parameter estimates in the sample and the population or between two samples
      • Difference between n and N estimates
      • Standard error
    • Steps in Hypothesis Testing
      • 1. State research question as a statistical hypothesis
      • 2. Select the level of significance for the statistical test (alpha)
      • 3. Decide on the appropriate test statistic
      • 4. Determine the value the test statistic must attain to be declared significant (critical value)
      • 5. Perform the calculations for the test statistic
      • 6. Apply decision rule and draw conclusions
    • Distributions for Probability
      • Each parameter has its own distribution
        • Variance: F
        • Proportion:  2
        • Mean: t
        • Correlation: t
      • Each finite sample will have its own unique probability distribution
      • Closer to normality as sample size increases
    • Steps in Hypothesis Testing
      • 1. State research question as a statistical hypothesis
      • 2. Select the level of significance for the statistical test (alpha)
      • 3. Decide on the appropriate test statistic
      • 4. Determine the value the test statistic must attain to be declared significant (critical value)
      • 5. Perform the calculations for the test statistic
      • 6. Apply decision rule and draw conclusions
    • Hypothesis test of means
      • One sample tests of means
      • H 0 : x = 
      • H A : x 
      • Calculate test statistic: t = x - 
      •  SE (x)
      • Compare to critical value from t distribution
      • Apply decision rule to reject / do not reject the null hypothesis
    • Steps in Hypothesis Testing
      • 1. State research question as a statistical hypothesis
      • 2. Select the level of significance for the statistical test (alpha)
      • 3. Decide on the appropriate test statistic
      • 4. Determine the value the test statistic must attain to be declared significant (critical value)
      • 5. Perform the calculations for the test statistic
      • 6. Apply decision rule and draw conclusions
    • Decision Rules
      • All possible values of the test statistic are divided into 2 regions
      • Rejection region
        • Those values of the test statistic with a low probability of occurrence if H 0 is true
        • Statistically constructed at 5%
        • Critical value: cut point for the rejection region
    • Possible Decisions
      • A significant difference is detected between the actual values and the hypothesized values:
        • Reject the H 0
      • A significant difference is not detected between the actual values and the hypothesized values
        • Do not reject the H A
    • Type I and II Errors
    • Type I and II Errors
      • Type I Error: Treatment doesn’t work, but we think it does
        • Leads to unwarranted change
        • Control by appropriately setting 
      • Type II Error: Treatment works, but we think it doesn’t
        • Leads to missed opportunities
        • Designated as  , controlled by sampling
    • The t test of means
      • Differences between mean values:
        • Between a sample and a known population value
          • One sample t
        • Between two independent samples
          • Independent samples t test
        • Between two time periods for the same group
          • Paired samples t test
    • The Chi Square test
      • Tests for differences in rates, proportions, or probabilities
        • Between a sample proportion and a known population proportion
          • Chi square test of model fit
        • Between two independent samples
          • Chi square test of independence
        • Between two variables in a single sample
          • Chi square test of association
    • Analysis of Variance
      • Tests for differences in means in more than two groups
        • Single dependent variable
          • ANOVA
        • Single dependent variable with potential covariates
          • ANCOVA
        • Single dependent variable measured over more than two time periods
          • Repeated Measures ANOVA
    • Most Common Reported Statistics
      • Descriptive statistics about sample and variables
      • Analysis of group equivalency
      • Statistics about the role of error
      • Statistics to evaluate magnitude of effect
      • Statistics to determine confidence level