1. 1 1-1 Overview 1- 2 Types of Data 1- 3 Random Sampling 1- 4 Design of Experiments 1- 5 Abuses of Statistics Chapter 1 Introduction to Statistics

2. 2 Statistics (Definition) A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data 1-1 Overview

3. 3 Definitions  Population The complete collection of all data to be studied.  Census The collection of data from every member of the population.  Sample The collection of data from a subset of the population.

4. 4 Example  Identify the population and sample in the study A quality-control manager randomly selects 50 bottles of Coca-Cola to assess the calibration of the filing machine.

5. 5 Statistics Broken into 2 areas  Descriptive Statistics  Inferencial Statistics Definitions

6. 6  Descriptive Statistics Describes data usually through the use of graphs, charts and pictures. Simple calculations like mean, range, mode, etc., may also be used.  Inferencial Statistics Uses sample data to make inferences (draw conclusions) about an entire population Test Question

7. 7  Parameter vs. Statistic  Variables  Quantitative Data vs. Qualitative Data  Nominal Data vs. Ordinal Data  Discrete Data vs. Continuous Data  Univariate Data vs. Bivariate Data 1-2 Types of Data

8. 8  Parameter a numerical measurement describing some characteristic of a population population parameter Definitions

9. 9  Statistic a numerical measurement describing some characteristic of a sample sample statistic Definitions

10. 10 Examples  Parameter 51% of the entire population of the US is Female  Statistic Based on a sample from the US population is was determined that 35% consider themselves overweight.

11. 11  Variable » characteristics of the individuals (data) being measured or observed » represented as asymbol (x, Y, s, σ, µ, etc.). Definitions

12. 12 We further describe variables by distinguishing between Qualitative and Quantitative data (variables) Definitions Variables Qualitative Quantitative

13. 13 Definitions  Quantitative data Numbers representing counts or measurements  Qualitative (or categorical or attribute) data Can be separated into different categories that are distinguished by some nonnumeric characteristics

14. 14 Examples  Quantitative data x = The number of FLC students with blue eyes  Qualitative (or categorical or attribute) data y = The eye color of FLC students

15. 15 Example  Of the adult U.S. population, 36% has an allergy. A sample of 1200 randomly selected adults resulted in 33.2% reporting an allergy. 1. Describe the variable and give its type 2.Describe the population 3.Describe the sample 4.What is the value of the parameter? 5.What is the value of the statistic? 6. Which statement is descriptive in nature? 7.Which statement is inferential in nature? Quiz Question

16. 16 We further describe qualitative data by distinguishing between Nominal and Ordinal data Definitions Qualitative Data Nominal Ordinal

17. 17  Nominal Nominal data are categorical data where the order of the categories is arbitrary Example: race/ethnicity has values 1=White, 2=Hispanic, 3=American Indian, 4=Black, 5=Other. Note that the order of the categories is arbitrary. Ordinal Ordinal data are categorical data where there is a logical ordering to the categories Example: scale that you see on many surveys: 1=Strongly disagree; 2=Disagree; 3=Neutral; 4=Agree; 5=Strongly agree. Definitions

18. 18 We further describe quantitative data by distinguishing between discrete and continuous data Definitions Quantitative Data Discrete Continuous

19. 19  Discrete data result when the number of possible values is either a finite number or a ‘countable’ number of possible values 0, 1, 2, 3,...  Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale or interval that covers a range of values without gaps, interruptions, or jumps Definitions 2 3

20. 20  Discrete The number of eggs that hens lay; for example, 3 eggs a day.  Continuous The amounts of milk that cows produce; for example, 2.343115 gallons a day. Examples

21. 21  Univariate Data »Involves the use of one variable (X) »Does not deal with causes and relationship  Bivariate Data »Involves the use of two variables (X and Y) »Deals with causes and relationships Definitions

22. 22  Univariate Data How many first year students attend FLC?  Bivariate Data Is there a relationship (association) between then number of females in Computer Programming and their scores in Mathematics? Example

23. 23 1. Center: A representative or average value that indicates where the middle of the data set is located 2. Variation: A measure of the amount that the values vary among themselves or how data is dispersed 3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed) 4. Outliers: Sample values that lie very far away from the vast majority of other sample values 5. Time: Changing characteristics of the data over time Important Characteristics of Data

24. 24 Uses of Statistics  Almost all fields of study benefit from the application of statistical methods  Sociology, Genetics, Insurance, Biology, Polling, Retirement Planning, automobile fatality rates, and many more too numerous to mention.

25. 25 1- 3 Design of Experiments

26. 26 Designing an Experiment  Identify your objective  Collect sample data  Use a random procedure that avoids bias  Analyze the data and form conclusions

27. 27  Observational Study measures the characteristics of a population by studying individuals in a sample, but does not attempt to manipulate or influence variables of interest  Experiment applies treatments to experimental units or subjects and attempts to isolate the effects of the treatments on a response variable Definition

28. 28  Observational Study A poll is conducted in which 500 people are asked whom they plan to vote for in the upcoming election  Experiment To determine the effect of type of fertilizers a farmer might divide 20 tomato plants into two groups. Group 1 received fertilizer 1 and Group 2 receives fertilizer 2. All other factors for the two groups are kept the same (sunlight, water, etc). Examples

29. 29  Define the treatment, experimental unit and response variable in the following experiment. To determine the effect of type of fertilizers a farmer might divide 20 tomato plants into two groups. Group 1 received fertilizer 1 and Group 2 receives fertilizer 2. All other factors for the two groups are kept the same (sunlight, water, etc). i.e., Confounding does not occur Experimental Design

30. 30  Lurking variables: A variable that was not considered in a study but may affect study.  Confounding: Occurs in a study when lurking variables affect the outcome. Confounding

31. 31  Example: F lu shots are associated with a lower risk of being hospitalized or dying from influenza.  Possible Lurking Variables: age health status mobility of the senior Confounding

32. 32  Experiment apply some treatment (Action)  Event (Response) observe its effects on the subject(s) (Observe) Example: Experiment: Toss a coin Event: Observe a tail Probability Experiment

33. 33 1- 4 Sampling

34. 34  Random (type discussed in this class)  Systematic  Convenience  Stratified  Cluster Methods of Sampling

35. 35 TI-83 Calculator Using a random number generator 1.Press Math 2.Cursor over to PRB 3.Press “5” RandInt 4.Enter (low value, high value, sample size) Example: RandInt(1,30,5) will select 5 random numbers between 1 and 30 Note: if you get duplicate numbers you should draw more numbers than you need and ignore the duplicates.

36. 36  Simple Random Sample members of the population are selected in such a way that each has an equal chance of being selected (if not then sample is biased) Definitions

37. 37 Random Sampling - selection so that each has an equal chance of being selected

38. 38 Systematic Sampling Select some starting point and then select every K th element in the population

39. 39 Convenience Sampling use results that are easy to get

40. 40 Stratified Sampling subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

41. 41 Cluster Sampling - divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

42. 42  Sampling Error the difference between a sample result and the true population result; such an error results from chance sample fluctuations.  Nonsampling Error sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly). Errors in Sampling

43. 43  Sampling Error (Example) A recent poll showed potential voters favored the proposition 52% to 48%. The margin of error for the poll was 3%.  Nonsampling Error (Example) During presidential election or 2000, early results from an Florida exit poll were skewed by a programming error. Errors in Sampling

44. 44  Bad Samples  Small Samples  Loaded Questions  Misleading Graphs  Pictographs  Precise Numbers  Distorted Percentages  Partial Pictures  Deliberate Distortions 1-5 Abuses of Statistics

45. 45 Abuses of Statistics  Bad Samples Inappropriate methods to collect data. BIAS (on test) Example: using phone books to sample data.  Small Samples (will have example on exam) We will talk about same size later in the course. Even large samples can be bad samples.  Loaded Questions Survey questions can be worked to elicit a desired response

46. 46  Bad Samples  Small Samples  Loaded Questions  Misleading Graphs  Pictographs  Precise Numbers  Distorted Percentages  Partial Pictures  Deliberate Distortions Abuses of Statistics

47. 47 Bachelor High School Degree Diploma Salaries of People with Bachelor’s Degrees and with High School Diplomas $40,000 30,000 25,000 20,000 $40,500 $24,400 35,000 $40,000 20,000 10,000 0 $40,500 $24,400 30,000 Bachelor High School Degree Diploma (a)(b) (test question)

48. 48 We should analyze the numerical information given in the graph instead of being mislead by its general shape.

49. 49  Bad Samples  Small Samples  Loaded Questions  Misleading Graphs  Pictographs  Precise Numbers  Distorted Percentages  Partial Pictures  Deliberate Distortions Abuses of Statistics

50. 50 Double the length, width, and height of a cube, and the volume increases by a factor of eight What is actually intended here? 2 times or 8 times?

51. 51  Bad Samples  Small Samples  Loaded Questions  Misleading Graphs  Pictographs  Precise Numbers  Distorted Percentages  Partial Pictures  Deliberate Distortions Abuses of Statistics

52. 52  Precise Numbers There are 103,215,027 households in the US. This is actually an estimate and it would be best to say there are about 103 million households.  Distorted Percentages 100% improvement doesn’t mean perfect.  Deliberate Distortions Lies, Lies, all Lies Abuses of Statistics

53. 53  Bad Samples  Small Samples  Loaded Questions  Misleading Graphs  Pictographs  Precise Numbers  Distorted Percentages  Partial Pictures  Deliberate Distortions Abuses of Statistics

54. 54 Abuses of Statistics  Partial Pictures “Ninety percent of all our cars sold in this country in the last 10 years are still on the road.” Problem: What if the 90% were sold in the last 3 years?

55. 55  Factorial Notation 8! = 8x7x6x5x4x3x2x1  Order of Operations 1.( ) 2.POWERS 3.MULT. & DIV. 4.ADD & SUBT. 5.READ LIKE A BOOK  Keep number in calculator as long a possible Using Formulas