Assumptions and normal distributions

Performing Experiments in Python

Luke Hayden

Instructor

Summary stats

Mean

Sum divided by count

Median

Half of values fall above and below the median

Mode

Value that occurs most often

Standard deviation

Measure of variability

Normal distribution

Density plot of a perfect normal distribution

Sample distribution

print(p9.ggplot(countrydata)+ p9.aes(x= 'Life_exp')+ p9.geom_density(alpha=0.5))

Density plot of life expectancy per country

Accessing summary stats

Mean

print(countrydata.Life_exp.mean())

73.68201058201058

Median

print(countrydata.Life_exp.median())

76.0

Mode

print(countrydata.Life_exp.mode())

78.4

Normal distribution

Density plot of a perfect normal distribution

Q-Q (quantile-quantile) plot

Normal probability plot

Use

Distribution fit expected (normal) distribution?

Graphical method to assess normality

Basis

Compare quantiles of data with theoretical quantiles predicted under distribution

Quantile-quantile plot for a perfect normal distribution

Creating a Q-Q plot

from scipy import stats
import plotnine as p9

tq = stats.probplot(countrydata.Life_exp, dist="norm")

df = pd.DataFrame(data = {'Theoretical Quantiles': tq[0][0], 
                         "Ordered Values": countrydata.Life_exp.sort_values() })

print(p9.ggplot(df)+ p9.aes('Theoretical Quantiles', "Ordered Values") +p9.geom_point())

Q-Q plot for sample

Distribution Density plot of life expectancy per country

Q-Q plot

QQ plot of life expectancy per country

Let's practice!

Performing Experiments in Python