exam 2

• what are the 3 sources of variation

  • random error variation
  • treatment effects
  • experimental artifacts
• sample vs tails

  sample- number of groups

  tails - side of distribution

  • can be 1 or 2
• what to do if one of the assumptions of normally parametric tests are violated?

  first test for normality

  if tests arent normal, transform data:

  • log
  • square root
• what is psuedoreplication? 


  • data that is not independent
  • artificially inflates sample size
• Tranformations of Data 


  • alter data scale
  • improve normality
  • log transformations
  • squareroot transformation
  • F-Test
• Post Hoc Test


  • Never run a post hoc unless anova shows a significant P-value
• Steps for post hoc analysis


  1. Order means largest to smallest
  2. Determine Psnk
  3. Calculate Sab
  4. calculate q
  5. DF- form anova table
  6. Find q crib
  7. Determine significance
• Sab equal sample size


  $√(mserror/n)$
• Sab for an unequal sample size


  $√(mserror/2)(1/na+1/nb)$
• equation for q post hoc equation


  q=(Xa-xb)/sab
• Statistical Inference


  • makes an estimate, prediction, or decision about a population based on a sample
  • ex: hypothesis testing
• Descriptive Statistics 


  • organize, summarize and present data
  • usually graphical or numerical
  • ex: frequency distribution, central tendency, variability of data set
• Presenting Data 


  • never report raw
  • present summaries of data - descriptive statistics
  • Tables and FIgures
  • Table - arranges data in rows and colomns
  • Figure- graphical representation
• How does the width of the interval change as alpha changes?


  • as alpha decreases , interval gets larger (table 2.)
• Confidence Interval


  • interval values computed from the sample
  • table 2
  • width of the interval chages as alpha changes
  • as alpha gets smaller interval gets larger
• How to Interpret 95% confidence interval

  • we are 95% confident that the true population mean is between these values
• Parametric Statistics Assuptions


  • data are normally distributed
  • Data are independent
  • variances are equal
• Factors that confidence interval depends on

  1. Sample mean
  2. Level of confidence
  3. SE
• Scientific Hypothesis 


  • Testable and falsifiable
• F-Test 


  • compares 2 sample variances
  • F= Sa^2/Sb^2
  • equal variance F=1
• One sample T-Test


  • compares sample mean(x) to proposed population mean (u)
  • tdf= X-u/se
• T-Test


  • only compares 2 groups
  • looks at means
• Paired sample T-Test equation


  • tdf= d-u/se
  • H0- no difference
  • u=0
  • d= avg difference
• Measurements of Distribution 


  • Central Tendency
  • Dispersion
  • Changing mean (u) shifts distribution left or right
  • changing Sd (s) increases or decreases the spread
• Common test for normality 


  H0= distribution is normal, no effect

  1. shapiro wilk
  2. Anderson- Darling
  3. Kolmogrov- Smirnov
  4. Lillefors
• Features of a good Research Design 


  1. random variation
  2. estimation of treatment effects
  3. High degree of accuracy and precision
  4. Absence of bias
  5. Simplicity in execution and analysis
• Presenting Tables


  • Properly labeled
  • data organized within a row
  • descriptive caption above table
  • includes AVG, SE, n
• Inferential Statistics 


  • analysis and interpretation of data to make general conclusions and inferences
  • draws conclusions and makes predictions about population data
• Descriptive Statistics 


  • summarization of data
  • displayed in tables and Figures
• How to minimize Random Error Variation and Experimental Artifacts?

  1. high degree of precision and accuracy
  2. effective controls
  3. Abscence of bias
• Experimental Artifacts


  • variation due to factors other than the experimental treatment or condition
• Random Error Variation 


  • results from influences of independent events
  • existing variation - gentotypic variation
  • measurement error
  • random chance events
• Presenting Figures

  • graphical
  • X-axis has IV
  • Y axis has DV
  • labeled axis
  • Inlcudes units
  • no title
  • descriptive captions below
• Treatment Effects 


  • variation that is a result of your treatments
  • Experimental Differences
• Anova Comparision 


  • compares population variance
  • Factor / Error
  • factor- based on means
  • error - based on individuls
  • F=1
• Sources of Variation 


  • Random error variation
  • treatment effects
  • experimental artifacts
• Statistical Hypothesis 


  • Statments about whether or not a pattern or trend or difference is present in data
  • simply statements about whether or not a pattern or trend exists
• Paired sample t-test equation


  • tdf=d-u/se
• Confidence Interval equation


  • x+,-(tcrit)(SE)

  or

  • u-Tvalue*SE<x<u+Tvalue*SE
• Confidence Interval Depends on

  1. Sample mean (x)
  2. SE
  3. level of confidence (95%)