Introduction to Statistics

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

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

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

Intro. to Statistics Qualitative Distinctions: Qualitative Distinctions: “Good” versus “Bad”“Good” versus “Bad” “Right” versus “Wrong”“Right” versus “Wrong” “A Lot” versus “A Little”“A Lot” versus “A Little” Quantitative Distinctions: Quantitative Distinctions: 5 1/7 versus 4 ¼5 1/7 versus 4 ¼ 25% versus 50%25% versus 50% 1 hour versus 24 hours1 hour versus 24 hours

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

Basic Terminology Size –Size – Sample of 5 cards from a deck of 52 Sample of 5 cards from a deck of 52 2 of Clubs, 10 of Diamonds, Jack of Hearts, 5 of Clubs, and 7 of Hearts2 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? 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? Compare this to a sample of 51/52 cards – What could we conclude from this sample?

Basic Terminology Randomness –Randomness – This time lets use the same 5 card sample, but this time the deck is unshuffled (nonrandom) 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 Clubs2 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)? What would we conclude about the characteristics of our population (the deck) this time versus when the sample was more random (shuffled)?

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 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 withoutI.e. To determine if a particular treatment works, we compare two groups or samples, one with the treatment and one without

Basic Terminology We draw conclusions based on how similar the two groups areWe 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 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 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

Basic Terminology Group A (Treated) and B (Untreated) are sampled from different populations/treatment worked: 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

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

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

Basic Terminology Categorical Categorical When numbers of discrete entities have to be countedWhen 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 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” questionsAnswers “how many” questions I.e. number of men and women, percentage of people with a given hair colorI.e. number of men and women, percentage of people with a given hair color

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