Distributions, Normality, and Data Transformations Do not trust - - PowerPoint PPT Presentation

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Sep 22, 2022 114 likes •170 views

Distributions, Normality, and Data Transformations Do not trust statistics you did not fake yourself. Winston Churchill (PM of the UK) Measures of Shape Skewness asymmetry within data Frequency Left skewed Normal Right skewed

SLIDE 1

Distributions, Normality, and Data Transformations

“Do not trust statistics you did not fake yourself.”

Winston Churchill (PM of the UK)

SLIDE 2

Measures of Shape

Skewness “asymmetry within data”

Median Mean

Left skewed

negatively skewed

Normal

perfectly symmetric

Right skewed

positively skewed

Represented as a boxplot

Bi-Modal

Two different modes Not necessarily symmetric

Frequency Frequency Mode Mode Mean Median

SLIDE 3

Measures of Shape

Leptokurtic

Positive (+) excess kurtosis – tall and skinny curve (sharper peak, fatter tails)

Mesokurtic

Zero excess kurtosis – e.g. Normal distribution

Platykurtic

Negative (-) excess kurtosis – flat curve (broader peak, thinner tails)

Kurtosis “how steep is the data peek? how fat are the distribution tails”

SLIDE 4

The Normal Distribution

𝑡2 = 𝑦𝑗 − 𝑦 2

𝑜 𝑗=1

𝑜 − 1 SD = 𝑡2

Based on this curve:

68.27% of observations are within 1 stdev of 𝑦
95.45% of observations are within 2 stdev of 𝑦
99.73% of observations are within 3 stdev of 𝑦

For confidence intervals:

95% of observations are within 1.96 stdev of 𝑦