• Like
NUR307: Chapter 15- Houser
Upcoming SlideShare
Loading in...5
×

NUR307: Chapter 15- Houser

  • 1,259 views
Uploaded on

 

More in: Technology , Business
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads

Views

Total Views
1,259
On Slideshare
0
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
76
Comments
0
Likes
1

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 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
    • Questions about reliability answered by setting confidence limits
    • Questions about probability answered by hypothesis testing
    • 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
      • 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
  • 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