Using StatCrunch Calculators for Continuous Distributions

Introduction

• StatCrunch calculators allow calculation of:
  • Probability given a reference value
  • Reference value associated with a specific probability
• Focus on using the Normal calculator (techniques applicable to other continuous distributions)

Accessing StatCrunch Calculators

• Navigate to the stat menu
• Choose calculators

Types of Continuous Distributions in StatCrunch

• Example used: Normal Distribution
  • Mean: 0
  • Standard deviation: 1 (Standard Normal Distribution)

Modifying Distribution Parameters

• Inputs for mean and standard deviation can be changed
• Found in the first row below the graph

Finding Probability for a Reference Value

• Default display: Area below mean of 0 colored in red
• Probability of standard normal variable ≤ 0 = 0.5
• Example:
  • Reference value: -2.1
  • Compute: Probability ≤ -2.1 ≈ 0.018
  • Interpretation: 1.8% of the area is below -2.1
• Change inequality sign to find probability above a reference value

Finding Reference Value for a Given Probability

• Used in hypothesis tests or confidence intervals
• Example:
  • Probability above value: 0.05
  • Change inequality to ≥
  • Compute: Reference value ≈ 1.64

Finding Probability Between Two Reference Values

• Click between button
• Default: Area between -1 and 1 colored in red, probability ≈ 0.68
• Example:
  • First reference: -0.5
  • Second reference: 2
  • Compute: Probability ≈ 0.67
• Note: First reference value < second reference

Switching Back to Original Calculator

• Click standard button for single reference value calculations

Tips

• Leave one input (reference value or probability) blank when using the calculator to find the other.
• Inputs and probabilities should be between 0 & 1.