Introduction to Statistics

1. Introduction to Statistics Basic Concepts

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 • Group of numbers #1: 6, 1, 8, 3, 5, 4, 9 • Average is 5 1/7 • Group of numbers #2: 8, 3, 4, 2, 7, 1, 4 • Average is 4 ¼ • 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 • Smaller/less random samples both poorly represent population of entire deck of cards • Also result in inaccurate inferences about population – poor external validity

11. 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

12. 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

13. 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

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

15. Basic Terminology • What if Group A (who received the Tx) were sicker then Group B (who did not receive Tx), prior to treatment? What would their scores look like after Tx? • The inability to attribute changes in the variable of interest to the manipulation – poor internal validity • I.e. we can’t say for sure if our experiment worked or not

16. 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.

17. 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

18. 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

19. Basic Concepts • Scales of Measurement: • Nominal • labeling/classifying objects • i.e. your last name, names on jerseys, social security number, etc. • not technically a scale of measurement since nothing is measured • Ordinal • labels that imply rank • i.e. place in a race, military rank – 1st > 2nd > 3rd and General > Lieutenant > Private • doesn’t say how much more one is than the other

20. Basic Concepts • Interval • provides labels that imply exactly how much different one label is than another • i.e. temperature - 15° F is 5 ° F more than 10 ° F • lacks true zero point - 0 ° F does not represent the complete absence of heat because we have negative values of °F • Ratio • has all of the above, plus a true zero point • i.e. height, weight, ° Kelvin – 0 lbs represents a true lack of weight • can talk about 16 ° being four times 4 °, which is a proportion /ratio, hence the name of the scale - x = 4y • often very difficult to identify in practice if a true zero point exists

21. Scales of Measurement Nominal Ordinal Interval Ratio Qualitative Quantitative Basic Concepts

22. Basic Concepts • Variables • Discrete versus Continuous Variables • same as Categorical versus Dimensional variables • Not to be confused with “discreet” variables, that people simply do not think should be talked about

23. Basic Concepts Constant Variable Qualitative Quantitative Categorical/ Discrete Dimensional/ Continuous Nominal Ordinal Interval Ratio

24. Basic Concepts • Variables versus Constants • A constant has only one possible value that it can assume • π = 3.1415923536… • A variable can assume many possible values • X = ? • Independent Variables (IV’s) versus Dependent Variables (DV’s) • IV manipulated, DV measured • Whether a variable is a DV or IV depends upon the design of the experiment

25. Basic Concepts • Variables • In true experiments, the effects of one variable (the IV) are manipulated to see the effects on another variable (the DV) • All other factors other than the IV are kept constant so that we can attribute the change to the IV and not to something else • Example: Influence of direct heat on the temperature of water • IV = presence or absence of heat • DV = temperature of water