Data

• Nominal / Categorical Data


  
  

  • Classes
  • categories
  • ex- flower color
• Ranked/Ordinal Data


  • Integers that reflect a heirarchy
  • ex- birth order
• Measurement Data


  • Discrete
  • numerical and fixed in nature
  • ex- number of flower petals
• Continous Data 


  • any number of values between two points
  • ex - height, length, mass
• Observational Studies


  • compares variables measured from different conditions
• Comparative Studies


  • Independent variable varies within a system
  • ex- soil, temp
  • tests hypothesis
  • limits: small sample size
• Perturbation/Response studies


  • Utilizes natural conditions
  • Large scale disturbances
  • ex- natural disasters
• Manipulative


  • impose treatments
  • observe responses to treatments
  • I.V- predictor
  • D.V - response
• Deductive Studies


  • specifies values for variables or conditions
• Sources of Varition 


  • random error variation
  • treatment effects
  • experimental artifacts
• How to minimize randon error variation and experimental artifacts

  • high degree of accruacy and precison
  • effective controls
  • absence of bias
• Bias


  • can occur at sampling, treatment application, measurement protocol
• Replicates


  • Controls and quantifies random variation
  • each replicate must be indepenednt
  • increase replicates means more population
• Randomization


  • eliminates sources of bias
  • insures independence of data
• Features of a good research design

  • random variation
  • high degree of accuracy and precision
  • abscene of bias
• Descriptive statisistics 


  • displayed as tables and figures
• Inferential Statisitcs


  • draws conclusions and makes predictions about population
• Central tendency


  • mean
  • median
  • mode
• Dispersion 


  • scattering of values of a frequency distribution
  • variance
  • standard deviation
• Confidence Interval


  • can interpret as: We are 95% confident that the true population mean is between these values
  • as alpha gets smller interval gets larger
• Confidence Interval Depends on

  • Sample mean
  • SE
  • Level of confidence
• Parametric Statisitcs Assumptions


  • data are normally distributed/Independent
  • count data
  • Equal variance
• Regression


  • simple linear model
  • dependent variable is distributed about the line
  • describes the relationship b/w the dependent and independent variable
• Regression equation:


  1. Yi=a+bx
  2. where:
  3. yi= dependent variable
  4. Bx= slope
  5. a=y-intercept
  6. X= independent variable
• Correlation


  • No cause/ effect
  • describes the linear relationship b/w two variables
  • no line drawn just dots
  • computes "r"
• Regression


  • looks at cause/ effects relationships
  • computes "r^2" or R^2
  • manipulates IV
  • Finds line of best fit
• Regression Line how to interpret Y intercept

  • If B=0 then there is no relationship b/w x and y
  • --> X does not affect Y
  • If B≠0 then there is a relationship b/w X and Y
  • --> X does affect Y
• Deviations 


  • deviations about the mean
  • eq: Xi-x̄
  • sum of square deviations eq: ∑ (x-x̄)^2
• Residuals 


  • deviations about the Line
  • eq: Yi-Ŷ
  • sum of squares residuals eq: ∑(yi-Ŷ)^2
  • where Ŷ becomes 1/2 b/c x becomes y
• Covarinace 


  • part of the variance of one variable (y) depends upon the variance of another variable (x)
  • how much total variation is due to X and how much is unexplained
• Line of best fit Regression model

  • results in smallest ss residuals
  • not due to X
• r^2 coefficient of determination

  • ss regression/ ss total =1
  • Total variation = Variation Regression+ variation of residuals value cant be >1
  • higher r^2= more variation
• R^2


  • coefficent of determination
  • no critical value
  • R^2= 1 matches line and data points
  • R^2= 0 there are no linear relationship b/w X and Y
• Overview correlation


  • correlation≠ causation
  • computes "r"
  • no cause or effect relationships
• Overview Regression


  • Linear Regression quantifes goodness of fit
  • computes R^2 or r^2
  • reports as ANOVA
  • Fn,d,=crit, P-value
• X^2


  • ∑(O-E)^2
  • --------
  • E
• X^2 with two groups

  • includes yates correction
  • ∑(|O-E|-0.5)^2/E
• X^2 assumptions


  • data are count data
  • independence of data
• Advantages of X^2


  • does not assume normal distribution
  • variance is not an issue
• How to report X^2

  • X^2 df= value, p-value