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Introduction to Statistics

Introduction to Statistics. Intro. to Statistics. What is Statistics? “…a set of procedures and rules…for reducing large masses of data to manageable proportions and for allowing us to draw conclusions from those data”. Intro. to Statistics. What can Stats do? Make data more manageable

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Introduction to Statistics

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  1. Introduction to Statistics

  2. Intro. to Statistics • What is Statistics? • “…a set of procedures and rules…for reducing large masses of data to manageable proportions and for allowing us to draw conclusions from those data”

  3. Intro. to Statistics • What can Stats do? • Make data more manageable • Group of numbers: 6, 1, 8, 3, 5, 4, 9 • Average is: 36/7 = 5 1/7 • Graphs:

  4. Intro. to Statistics • What can Stats do? • Allow us to draw conclusions from the data • Variable = Coolness • Group #1: 6, 1, 8, 3, 5, 4, 9 • People who take my stats class • Average is 5 1/7 • Group #2: 8, 3, 4, 2, 7, 1, 4 • People who take other people’s stats classes • Average is 4 ¼ • What can we conclude from these numbers? • Allows us to do this objectively and quantitatively

  5. “Quantitative” Involves measurement Data in numerical form Answers “How much” questions Objective and results in unambiguous conclusions “Qualitative” Describes the nature of something Answers “What” or “Of what kind” questions Often evaluative and ambiguous Intro. to Statistics

  6. Intro. to Statistics • Qualitative Distinctions: • “Good” versus “Bad” • “Right” versus “Wrong” • “A Lot” versus “A Little” • Quantitative Distinctions: • 5 1/7 versus 4 ¼ • 25% versus 50% • 1 hour versus 24 hours

  7. Basic Terminology • Summarizing versus Analyzing • Descriptive Statistics • Inferential Statistics • Inference from sample to population • Inference from statistic to parameter • Factors influencing the accuracy of a sample’s ability to represent a population: • Size • Randomness

  8. Basic Terminology • Size – • Sample of 5 cards from a deck of 52 • 2 of Clubs, 10 of Diamonds, Jack of Hearts, 5 of Clubs, and 7 of Hearts • What could we conclude about the full deck from this sample about what the full deck looks like without any prior knowledge of a deck of cards? • Compare this to a sample of 51/52 cards – What could we conclude from this sample?

  9. Basic Terminology • Randomness – • This time lets use the same 5 card sample, but this time the deck is unshuffled (nonrandom) • 2 of Clubs, 10 of Clubs, Jack of Clubs, 5 of Clubs, and 7 of Clubs • What would we conclude about the characteristics of our population (the deck) this time versus when the sample was more random (shuffled)?

  10. Basic Terminology • Most often, the aim of our research is not to infer characteristics of a population from our sample, but to compare two samples • I.e. To determine if a particular treatment works, we compare two groups or samples, one with the treatment and one without

  11. Basic Terminology • We draw conclusions based on how similar the two groups are • If the treated and untreated groups are very similar, we cannot declare the treatment much of a success • Another way of putting this in terms of samples and populations is determining if our two groups/samples actually come from the same population, or two different ones

  12. Basic Terminology • Group A (Treated) and B (Untreated) are sampled from different populations/treatment worked: Group A Population of Well People Group B Population of Sick People

  13. Basic Terminology • Group A and B are sampled from the same population/treatment didn’t work: Group A Group B Population of Sick People

  14. Basic Terminology • Quantitative Data • Dimensional/Measurement Data versus Categorical/Frequency Count Data • Dimensional • When quantities of something are measured on a continuum • Answers “how much” questions • I.e. scores on a test, measures of weight, etc.

  15. Basic Terminology • Categorical • When numbers of discrete entities have to be counted • Gender is an example of a discrete entity – you can be either male or female, and nothing else – speaking of “degree of maleness” makes little sense • Answers “how many” questions • I.e. number of men and women, percentage of people with a given hair color

  16. Basic Terminology • A dimensional variable can be converted into a categorical one • Convert scores on a test (0-100) into “Low”, “Medium”, and “High” groups – 0-33 = Low; 34-66 = Medium, and 67-100 = High • The groups are discrete categories (hence “categorical”), and you would now count how many people fall into each category

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