1.1 Intro to Statistics

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1 1.1 Intro to Statistics Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions A statistic is a numerical summary based on a sample. A parameter is a numerical summary of a population. Data can be numeric or non-numerical and are used to draw conclusions Height, gender Easy to misuse draw the wrong conclusion Where did the data come from?

2 A survey of 200 adults in the U.S. found that 76% regularly wear seatbelts while driving. True or false: 76% is a parameter. A. True B. False

3 Sample Problem Parameter versus Statistic Suppose the percentage of all students on your campus who have a job is 84.9%. This value represents a parameter because it is a numerical summary of a population. Suppose a sample of 250 students is obtained, and from this sample we find that 86.3% have a job. This value represents a statistic because it is a numerical summary based on a sample.

4 1.1 Intro to Statistics Problems that will be encountered when analyzing data Often times 2 variables are influenced by a third variable - lurking variable that must be accounted for Data vary must be able to describe and understand sources of variation

5 Intro to Stats The entire group of individuals to be studied is called the population. An individual is a person or object that is a member of the population being studied. A sample is a subset of the population that is being studied.

6 The Process of Statistics 1. Identify the objective what question do you want answered? 2. Collect information 3. Organize and summarize the information a. Descriptive statistics is used to describe the information collected through numerical measurements, charts, graphs and tables. 4. Draw conclusions from the information a. Inferential statistics uses methods that take results gathered from a sample and extends them to the population and then measures the reliability of the results

7 Variables Qualitative or categorical variables allow for classification of individuals based on some attribute or characteristic Arithmetic operations CANNOT be performed Quantitative variables provide numerical measures of individuals Arithmetic operations CAN be performed

8 True or false: The checking account numbers of customers at a bank represent quantitative data. A. True B. False

9 Variable Examples Researcher Elisabeth Kvaavik and others studied factors that affect the eating habits of adults in their mid-thirties. (Source: Kvaavik E, et. al. Psychological explanatorys of eating habits among adults in their mid-30 s (2005) International Journal of Behavioral Nutrition and Physical Activity (2)9.) Classify each of the following variables considered in the study as qualitative or quantitative. a. Nationality b. Number of children c. Household income in the previous year d. Level of education e. Daily intake of whole grains (measured in grams per day)

10 Ask: How do you know if a variable is categorical or quantitative? What are the n individuals/units in the sample (of size n )? What is being recorded about those n individuals/units? Is that a number ( quantitative) or a statement ( categorical)? Categorical Each individual is assigned to one of several categories. Quantitative Each individual is attributed a numerical value. Individuals in sample DIAGNOSIS AGE AT DEATH Patient A Heart disease 56 Patient B Stroke 70 Patient C Stroke 75 Patient D Lung cancer 60 Patient E Heart disease 80 Patient F Accident 73 Patient G Diabetes 69

11 Quantitative Variables A discrete variable has either finite number of possible values or a countable number of possible values The number of heads obtained after flipping a coin ten times A continuous variable has an infinite number of possible values that are not countable (think measurable) The distance a 2006 Ford Focus can travel in the city with a full tank of gas

12 Determine whether the quantitative variable is continuous or discrete. The time (in minutes) required for a student to complete a quiz. A. Continuous B. Discrete Copyright 2010 Pearson Education, Inc. Slide 1-12

13 Sample Problem - Qualitative and Quantitative Variables Researcher Elisabeth Kvaavik and others studied factors that affect the eating habits of adults in their mid-thirties. (Source: Kvaavik E, et. al. Psychological explanatorys of eating habits among adults in their mid-30 s (2005) International Journal of Behavioral Nutrition and Physical Activity (2)9.) Classify each of the following quantitative variables considered in the study as discrete or continuous. a. Number of children b. Household income in the previous year c. Daily intake of whole grains (measured in grams per day)

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