Week 3

• Confounding variable

  an extraneous variable in an experimental design that correlates with both the dependent and independent variables.
• Case study


  An investigation that looks intensily and in depth at a single individual or very small number of individuals

  • their usefulness is determined by how far scientific investigation has advanced in a particular area
  • useful in early stages of investigation
  • not useful in later stages, cannot confirm/disconfirm evidence
  • isolated and lack comparative information to rule out alternative explanations (like in experiments with control/comparison groups)
• Problems with Testimonials

  • Placebo effect: The tendency of people to report that any treatment has helped them, regardless of whether it has a real therapeutic element
  • Vividness effect: vividness of personal testimony often overshadows other information of much higher reliability.
• Biases


  • Single personal cases, testimonials
  • Image evidence, rather than just numbers and stats
• The third variable problem

  the fact that the correlation between the two variables may not indicate a direct causal path between them but may arise because both variables are related to a third variable that has not even been measured (spurious correlation)

  • multiple regression , partial correlation , and path analysis (statistics developed in part by psychologists) allow the correlation between two variables to be recalculated after the influence of other variables is removed, or “factored out” or “partialed out.”
• Directionality problem


  Before immediately concluding that a correlation between variable A and variable B is due to changes in A causing changes in B, we must first recognize that the direction of causation may be the opposite, that is, from B to A.
• Selection bias


  the relationships between certain subject and environmental variables that may arise when people with different biological, behavioral, and psychological characteristics select different types of environments.

  • creates a spurious correlation between environmental characteristics and behavioral-biological
• Managing confounding variables: Sample

  Randomization

  • Assign participants randomly to experimental groups.
  • Ensures confounders are evenly distributed across groups.

  Matching

  • Pair participants in groups based on similar confounding characteristics.

  Restriction

  • Limit the study to participants with specific characteristics
• Managing confounding variables: Experimental

  Standardization

  • Keep all non-experimental conditions identical across groups.

  Use of Controls

  • control group that doesn’t receive the stimulus to compare with IV

  Statistical Techniques

  • Use statistical methods to adjust for confounders:
  • Regression analysis: Adjusts for multiple confounding variables.
  • ANCOVA (Analysis of Covariance): Controls for confounders while analyzing the main effects.

  Measure and Control

  • Identify potential confounders in advance and measure them during the study.
  • Include these as covariates in the analysis.
• Fixed effects 


  factors that the researcher intentionally manipulates or chooses and are of primary interest in the study.

  • Levels are deliberately selected and do not change across samples.
  • The goal is to study their effect on the DV.
  • Results apply only to the specific levels tested
• Random effects


  factors that represent a random sample from a larger population, and their specific levels are not of primary interest.

  • Levels are considered random and vary across samples.
  • The goal is to generalize findings beyond the sampled levels.
  • Results apply to the entire population of possible levels.
  • i.e randomly selecting schools in a district to study teaching effectiveness (schools are random effects), PPS are drawn randomly.
• Mixed-effects models


  a design includes both fixed and random effects, it’s called a mixed-effects model.

  • Example: A study examining the effect of different teaching methods (fixed) in various randomly chosen schools (random).
• Features of a good model

  1. Describe the data we have
  2. Generalise to new datasets
• When a model is wrong

  • Incomplete
  • Limited performance by measurement error (noise)
• Variability of dispersion (population)

  SSE = sum of squared errors

  N = no. of individuals in population

  μ = population mean

  
• Variability of dispersion (sample)

  s² = sample variance

  SSE = sum of squared errors

  n = no. of individuals

  
• Defining Z-scores

  x = individual data point

  +ve Z score = above the mean

  -ve Z score = below the mean

  
• Non-linear functions

  
• Equation


  Mathematical expression that tells us two quantities on either side are equal
• Linear equations


  The relationship they describe are on the same line

  • ax = b
  • a and b are constants