Inferential Statistics

• Descriptive Statistics describes data, where as inferential statistics allows us to make predictions (inferences) from that data.
• With inferential statistics we take data from samples and make generalizations about population.
• For example:
  • We might stand in a mall and ask a sample of 100 people if they like shopping at ‘Shoppers Stop’.
  • With Descriptive Statistics
    • We could make a bar chart/pie chart with yes or no aswers
  • With inferential statistics
    • We could use our research to reason that around 65-70% of the population would like shopping at shoppers stop
• Distribution is one of the most important concept to understand in inferential statistics.

Distributions

• When we speak about distributions, we mean probability distributions
• Definitions:
  • A distribution is a function that shows the possible values for a variable and how often they occur.
  • In Probability theory and statistics, a probability distribution is a mathematical function that stated, in simple terms can be thought of as providing the probabilities of occurance of different possible outcomes in an experiment
  • Examples:
    • Normal Distribution
    • Students t-distribution
    • Poisson Distribution
    • Uniform Distribution
    • Binomial Distribution
    • Exponential Distribution
• Example: Lets try to understand the distribution by considering a scenario of rolling one dice
• Activity: Lets try to understand the distribution by considering a scenario of rolling two die’s and we need a distribution of sum of two dies
  • Refer Here for the xlsx containing dice problems solution

Normal Distribution

• The normal distribution is also known as Gaussian distribution or the Bell Curve.
• This is one of the most common distribution due to following reasons:
  • It approximates wide variety of random variables
  • Distribution of sample means with large enought sample sizes could be approximated to normal
  • All computable statistics are elegant
  • Heavily used in regression analysis
  • Good track record
• Examples:
  • Biology
  • IQ tests
  • Stock market information
• This distribution is represented as
• Keeping the standard deviation constant, the graph of a normal distribution with
  • smaller mean would look the same way, but be situated to the left (brown)
  • larger mean would look the same way, but be situated to the right (red)
• Keeping the mean constant, a normal distribution with
  • smaller deviation would be situated in same spot but have a higher peak and thinner tails (red)
  • a larger standard deviation would be situated in the same spot but have lower peak & fatter tails (in brown)