Statistics can be found in all aspects of

Statistics can be found in all aspects of life: 1

Statistics can be found in all aspects of life: • Space exploration • Politics • Business • Sciences • Medicine • Sports -- Baseball players 2

What is Statistics? Statistics is the science of: – Collecting and obtaining data and then – Summarizing, organizing, presenting, analysing and finally – Interpreting and drawing conclusions from that data. 3

What is Statistics? Statistics is the science of: – Collecting and obtaining data and then – Summarizing, organizing, presenting, analysing and finally – Interpreting and drawing conclusions from that data. Two types of Statistics: Descriptive and Inferential 4

Descriptive Statistics uses both numerical and graphical methods to summarize and/or describe the characteristics of a known set of data. 5

Descriptive Statistics uses both numerical and graphical methods to summarize and/or describe the characteristics of a known set of data. For example: Let us consider everyone in this room. Each one of us is a source of data. A characteristic of this data may be degree program, age, height, sex, marital status, whether they went to the bar last night 6

Descriptive Statistics For example: Let us consider everyone in this room. Each one of us is a source of data. A characteristic of this data may be degree program, age, height, sex, marital status, whether they went to the bar last night. A descriptive statistics summarizes this data somehow. Think of the average age, a bar graph of people’s heights, a pie chart of their martial status or the proportion of those who went to the bar last night. 7

Inferential Statistics goes beyond the description. It involves the use of sample data to make inferences about a larger set of data from which the sample was chosen. 8

Inferential Statistics goes beyond the description. It involves the use of sample data to make inferences about a larger set of data from which the sample was chosen. For example: If we consider this class as a sample of STFX students and calculated the average of the class. We could then infer that the average of all STFX students is the same as our sample. 9

Bias Selection bias results when a subset of the experimental units in the populations is excluded. 10

Bias Selection bias results when a subset of the experimental units in the populations is excluded. Example: Ask who thinks tuition should be lowered? 11

Bias Selection bias results when a subset of the experimental units in the populations is excluded. Example: Ask who thinks tuition should be lowered? – Student Rally 12

Bias Selection bias results when a subset of the experimental units in the populations is excluded. Example: Ask who thinks tuition should be lowered? – Student Rally – School Administrators 13

Bias Selection bias results when a subset of the experimental units in the populations is excluded. Example: Ask who thinks tuition should be lowered? – Student Rally – School Administrators – Communities 14

Bias Selection bias results when a subset of the experimental units in the populations is excluded. Example: Ask who thinks tuition should be lowered? – Student Rally – School Administrators – Communities – Random Sample 15

Bias Non-Response Bias results when you can not obtain information from some members of your sample. 16

Bias Non-Response Bias results when you can not obtain information from some members of your sample. i. e. Telephone survey Liberal survey, Conservatives refuse to answer 17

Bias Measurement Error: • Inaccuracies in recording data 18

Bias Measurement Error: • Inaccuracies in recording data • Misleading questions 19

Bias Measurement Error: • Inaccuracies in recording data • Misleading questions • Physical errors or limitations 20

Basics of Data Collection 21

Basics of Data Collection (Who? ) • A population is a set (or group) of elements (objects, people, transactions, events) which we wish to study. • A sample is a sub-collection of elements from the population An experimental unit (or just unit or element) is an object (person, object, event) upon which we collect data. • An experimental unit is a particular element upon which we collect data. 22

Basics of Data Collection (Who? ) • A population is a set (or group) of elements (objects, people, transactions, events) which we wish to study. • A sample is a sub-collection of elements from the population An experimental unit (or just unit or element) is an object (person, object, event) upon which we collect data. • An experimental unit is a particular element upon which we collect data. For Example: A typical Angus Reid poll uses a sample of 1000 randomly selected Canadians, the results are then used to make conclusions about the population of 23 30 million Canadians.

Basics of Data Collection (Who? ) • A population is a set (or group) of elements (objects, people, transactions, events) which we wish to study. • A sample is a sub-collection of elements from the population An experimental unit (or just unit or element) is an object (person, object, event) upon which we collect data. • An experimental unit is a particular element upon which we collect data. 24

Basics of Data Collection (Why? ) A parameter is a numerical measurement describing some characteristic of a population. A statistic is a numerical measurement describing some characteristic of a sample. A statistical inference is an estimate or prediction about a population and its parameters based on information obtained through the sample and its sample statistics. 25

Basics of Data Collection (Why? ) A statistical inference is an estimate or prediction about a population and its parameters based on information obtained through the sample and its sample statistics. A measure of reliability is a statement about how certain we are of our inference. 51% ± 2% - confidence interval 26

Basics of Data Collection (What? ) A variable is a characteristic observed on sample data that can vary from unit to unit in the sample. For Example: Consider the class as a sample of STFX students. What are some characteristics that can be observed on each student here? Hair Color, Degree, Height, Shoe Size 27

Classification of Variables 28

Examples of different types of Variables: Classify as Qualitative or Quantitative • The weights of students in this class. • The number of siblings in each of your families. • The marital status of students in this class. (married, common-law, single, divorced) • The number of times a day you brush your teeth. • Your degree program. • Your yearly income. • The number of servings of fruits and vegetables in your daily diet. 29

Basics of Data Collection (When and How? ) Collecting Data: Variable Qualitative Variables classified as belonging to groups or categories. E. g. , Hair colour, Degree program, Political affiliation Quantitative Variables measured using a numerical scale Discrete variables can take only a finite set of values E. g. , Shoe size Continuous variables can take all or any value E. g. , Height, 30

Basics of Data Collection (When and How? ) Collecting Data: – Published source (book, journal, news paper, etc. ) – Designed experiment – Survey • Ask questions • A census is a survey of the entire population – Observational study • Natural environment 31

Basics of Data Collection (When and How? ) To infer about the general population we must have a representative sample. A representative sample exhibits characteristics typical of these in the whole population. (There are other methods such as cluster sampling). 32

Basics of Data Collection (When and How? ) To infer about the general population we must have a representative sample. A representative sample exhibits characteristics typical of these in the whole population. (There are other methods such as cluster sampling). To obtain a representative sample we select a random sample from the population. 33

Basics of Data Collection (When and How? ) To obtain a representative sample we select a random sample from the population. A random sample of n experimental units is a sample selected from the population so that every possible sample has an equal chance to be selected. (Completely Random). 34

Key Elements of a Statistical Problem • • • Describe the population Describe the variable/s of interest Describe the sample Describe the inference Describe sources of possible errors/bias 35

Example (Study 1: page 5 of text) Speed Training Program for High School Football players • Michael Gray and Jessica Sauerbeck researchers at Northern Kentucky University designed and tested a speed training program for a junior-varsity and varsity high school football players Each participant was timed in a 40 -yard sprint prior to the start of the training program and timed again after completing the program. Based on these sprint times, each participant was classified as having an “improved” time, “no change” in time, or a “decrease” in time. In a sample of 15 players selected from different schools in the area, 13 had an “improved” time. The results show that nearly 87% of players who participated in this speed training program improved their sprint times. 36

Overview • Definitions of Statistics, Population, Sample, Inference, Parameter, Statistic, Variable, • Classification of Variables (qualitative, quantitative, discrete and continuous), • Sections 1. 1, 1. 2, 1. 3, 1. 4, 1. 5, 1. 6 in text 37

Homework • Read Sections 1. 1 to 2. 1 • Question 1. 23, 1. 25 • Find SPSS on the STFX network and “play” around with it. 38