• This presentation will in broad strokes cover P Values.
• We will look at some examples of graphs in both two dimensions and three dimensions that have a normal distribution.
• We will also look at the formula for how to calculate standard deviation and the general formula for determining a Z Score.

Standard Deviation: \(\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}\).

• The above formula above is how we can calculate Standard Deviation given a data set

• \(x_i\). = Each of the values of Data.

• \(\bar{x}\). = The mean of \(x_i\).

• \(n\).= The Number of Data Points

• Next we will look at a graph in 3d that has a normal standard deviation distribution.

• How to determine Z Score: \(z = \frac{x - \mu}{\sigma}\)
• \(x\) = Observed Value
• \(\mu\) = Population Mean
• \(\sigma\) = Population Standard Deviation
• Z Scores are used in a Z-Test which is used in Hypothesis Testing

ggplot(mtcars, aes(x = hp, y = mpg, color = factor(cyl))) +
  geom_point(size = 3) +
  labs(title = "Miles per Gallon vs Horsepower",x = "Horsepower (hp)",
    y = "Miles per Gallon (mpg)",color = "Cylinders" ) +theme_minimal()

• After we look at the graph in the previous slide we can compare and evaluate the significant results by using our P value.
• The standard P Value for studies historically has been \(0.05\)
• P values are in essence a measure of statistical significance
• A large P Value would suggest the results are likely due to random chance
• Our next slide will cover bar plot Comparing Average MPG by number of cylinders in a car
• What hypothesis would you have about the data in the next slide?

• While not a comprehensive look at P-Values, we were able to use some of the tools of ioslides to create visual aids for our presentation.
• Thank you for engaging with my presentation on P values.