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# NUR307: Chapter 15- Houser

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• 1. Chapter 15 Analysis and Reporting of Quantitative Data
• 2. Inferential Analysis
• Enables inference of results from a carefully selected sample to an overall population
• Quantifies the potential effects of error on the results
• 3. 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
• 4. Type of Analysis Driven By…
• The goals of the analysis
• Assumptions of the data
• Number of variables in the analysis
• 5. 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?
• 6. Statistical Inference
• Conclusions concerned with probability of drawing an erroneous conclusion
• 7. 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
• 8. Confidence Interval Two numerical values defining an interval that we believe, with an identified level of confidence, actually includes the estimated population parameter
• 9. 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
• 10. 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
• 11. 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
• 12. 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
• 13. 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
• 14. 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
• 15. 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)
• 16. 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
• 17. 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
• 18. 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
• 19. 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
• 20. 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
• 21. 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
• 22. 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
• 23. 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
• 24. 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
• 25. Type I and II Errors
• 26. Type I and II Errors
• Type I Error: Treatment doesn’t work, but we think it does
• Control by appropriately setting 
• Type II Error: Treatment works, but we think it doesn’t
• Designated as  , controlled by sampling
• 27. 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
• 28. 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
• 29. 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
• 30. 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