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Summary Distributions Notes

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  • January 18, 2024
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  • 2021/2022
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Statistical methods

Normal distribution :
 When data I symmetrical around central scores
 Mean, median and mode are equal
 Data should fit along a ‘gaussian curve’

Skewed distributions:
 Can have positive, negative skew and a symmetrical distribution
 Calculating skew
o Can calculate Pearson’s coefficient of skew using the median and the mean:
 Skew = 3(mean-median) / standard deviation
o Interpretation
 If skew is <0, the data is negatively skewed
 If skew is >0, the data is positively skewed

Testing for distribution
 Normality tests e.g. Shapiro -Wilk, Kolomogorav – Smirnov
 Simply ask: “is your data normal?” Y/N

Gaussian curve
 From the mean and standard deviation of the data alone, we can predict value of y
for any value of x
 This has big implication, as most of our tests are based on normal distributions

Why is the distribution shape important?
 Parametric tests assume values such as the mean and standard deviation accurately
reflect the population distribution.
o 68% of the population are within (mean +/-1SD)
o 95% of the population are within (mean +/- 2 SD)
o 99.7% of the population are within (mean+/- 3SD)

Transforming data into z scores
 This can help standardise data and reduce the impact of skewness
o Z= individual point – group mean / standard deviation
 This tells us exactly how many standard deviations someone was from the mean
o 68% of the population are within a z score of +/- 1
o 95% of the population are within a z score of =/- 1.96 (rounded up to 2)
o 99.7 of the population are within a z score of +/- 2.96 (rounded up to 3)
 Using a standardised z table – “values represent proportion to the left of the
individual score”
 Pros of z scores
o Can transform data to a standardised scale
o Scale adheres to normal distribution
o Can compare things relative to their own population
o Use the entire data set

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