An Introduction to Statistics

What does a statistician do? A statistician makes sense of information collected about the world Analyze effectiveness of drug treatments Determining behavior patterns Analyze spread of West Nile Virus Analyze performance of individuals, businesses, stocks, etc.

What is statistics? Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical/categorical data.

What is statistics? Statistics is a way of reasoning together with collection tools and methods designed to help us to understand data and information about the world.

What are statistics? Calculations made from data.

What are data? Systematically recorded information together with context

Context Tells: Who was measured What was measured Where data was collected When data was collected Why study was performed How data was collected

Data can be... Numbers Dates Words Codes or other labels

What is univariate data? one variable the major purpose of univariate analysis is to describe one variable central tendency: mean, mode, median variability: range, max, min, quartiles, standard deviation graphs: histogram, box-and-whisker plot  

What type of data is it? vs. Qualitative Quantitative Deals with descriptions. Data can be observed but not measured. Colors, textures, smells, tastes, appearance, beauty, etc. Deals with numbers. Data that can be measured. Length, height, area, volume, weight, speed, time, temperature, cost, ages, etc. Go over the Collect student data worksheet and discuss which type of variable each one is.

Qualitative (Categorical) Variable Is a classification or categorization Something that is a name, word, or code Examples: Name of country Type of shoe Class year Area code

Quantitative Variable Is a measurement, amount, or count Can by indicated by words “amount” or “number of” Examples: Height Amount of time spent studying Distance traveled Amounted of money in your wallet

Ordinal Variable Is an ordered rating or ranking Examples: Course grade Class rank Customer service rating

Caution! A thing is not a variable. Shoes are things. The type of shoes is a qualitative variable. The number of shoes is a quantitative variable.

Quantitative Variables Quantitative variables can be discrete or continuous.

Discrete Quantitative Variables A quantitative variable is discrete if the variable involves a count (no decimals/fractions). Examples: Number of students Number of shoes Number of bills in your wallet

Continuous Quantitative Variables A quantitative variable is continuous if the variable involves a measurement. Examples: Height Distance traveled Weight of a box

Caution! Important to consider what values mean and how they are being used Do not treat all numerical data as quantitative The average of qualitative data is meaningless (example: the average zip code)

Example 1: Quantitative or Qualitative? Number of students in a class who turn in a project before it is due. Gender of the next baby born at a hospital. Amount of fluid ounces dispersed by a soda machine. Thickness of the gelatin coating on a pill. Birth order (oldest, middle, youngest) of a student.

Homework Pick 10 items in your home. Describe 5 of these items quantitatively. Provide three different descriptors for each item. Describe the other 5 items qualitatively. Provided three different descriptors for each item. This will be collected for a homework grade tomorrow.