Quantitative Research Methods - Probability and Transformations

Interpreting P Values

• P=probability
• Probability of null hypothesis being true
• Null hypothese for Shapiro- Wilk - normal distribution
• Lets set alpha = 0.05 (cut off for significantly unlikely results)
• If p>0.05 we do not have sufficent evidence to reject null hypothesis (that distribution is normal)
• This does not mean we are certain that it is normal

Probability Distributions

Many different types, Important to estimate:

• event propabilities - p values, outliers
• Uncertainty - p values, confidence intervals

Common types in Psychology

• Normal
• Log-normal
• Binormal
• Poisson

Log-Normal Distribution

• Where logarithm of data is normally distributed
• Asymmetrical with right skew (long tail)
• Parameteres: mean, SD
• Higher chance of high values than normal
• Common in biology, finance, natural events
• Log transformations yields normal data
• When underlying data includes multiplicative processes for example - stock market swings, earthquake magnitudes, city sizes
• Psychological examples - social network sizes, lengh of internet discussion comments, dwell time on online articles, human reaction time

Binary Data

• Only two values possible, ussualy recorded as 0 and 1
• Examples: coin toss (head /tails); binary outcomes (success/failure); human accuracy (correct/wrong)
• Key parameter: probability of success (p)
• Often analused as normal percentage data
• Problem - largest variance around p=0.5, little variance as we go towards p=0 or p=1, hence skewed distribution

Count Data

• Count of events in a fixed period of time or space
• Only whole numbers are possible
• Examples - blinks per minute, number of red cars parked on a street, number of times a book was sold in one day
• Key parameter - number of events counted
• Often also analysed as normal data
• Problem - asymetrical (skewed) distribution when average count is very low (0-5)

Poisson Distibution

• Probability that a given number…