STATISTICS 200 Lecture #2Thursday, August 25, 2016 Distinguish between: - A statistic and a parameter - A categorical and a quantitative variable - A response and an explanatory variable Identify: - When a categorical variable is ordinal - When a quantitative variable is continuous - Appropriate numerical & visual summaries for categorical variables Objectives:

What do data look like? Usually, a spreadsheet, and sometimes it’s messy! Ideally, a dataset will provide all of the values for each observation. Sometimes there is missing data. This type of data is called raw data. It’s very hard to see patterns in raw data.

A variable is a characteristic that can differ from one individual to the next. An observational unit is a single individual who participates in a study. Also called an observation. The sample size is the total number of observations. Key terms: variable and observation

Key terms: Parameters and Statistics Population Sample A parameter is a summary measure for the entire population. Example: Proportion of all PSU students that live in a dorm A statistic is a summary measure for a sample. Example: Proportion of students in this classroom that live in a dorm

Section 2.2: Types of variables A categorical variable consists of group or category names. Example: - Living situation - Eye Color A quantitative variable consists of numerical measures or counts. Example: - Height - GPA

Ordinal Special types of variables Categorical A categorical variable whose categories have a logical ordering Examples: Agreement with the statement: “I depend on my smartphone” Response: strongly disagree, disagree, neutral, agree, strongly agree How many drinks did you have during finals week? Response: 0, 1 to 3, 4 to 7, 8 or more

Special types of variables A quantitative variable that can take on any value within some interval. Continuous Numerical Examples: Weight, measured in pounds Time to run a 5k, measured in minutes Length of stride, measured in inches Numerical but not continuous: discrete (more on this in Chapter 8)

Explanatory vs Response Variables An explanatory variable is one which is thought to (partially) explain a difference in the response variable. Examples: Height and Weight Sex and Height Age and Reading distance Education level and income

2.3: Summarizing one or two categorical variables Numerical Summaries Graphical Summaries Tables of counts and percentages Pie Charts Bar Graphs

2.3: Numerical Summary Use a table to display how many observations are in each category. Counts

2.3: Numerical Summary Use a table to display how many observations are in each category. Counts Percent of observations in each category also displayed. Percent = Count / Total

Two-way tables With one variable, we use a one-way table. With two variables, we use a two-way table. Each cell shows the count and row percent for the corresponding variable categories 106: Number of observations who answered ‘female’ and ‘Yes’ 18.56: Percent of females that answered ‘Yes’.

Statistical picture for one categorical variable However, pie charts are a very bad way of displaying information. The eye is good at judging linear measures and bad at judging relative areas. A bar graph works too.

Statistical picture for one measurement variable Note: “Measurement” = “Quantitative” = “Numerical” Either a histogram or a boxplot could work here

Statistical picture for two categorical variables This bar graph, or bar chart, shows counts for subgroups defined by both sex and eye color.

Statistical picture for two measurement variables In this scatterplot, the diagonal line shows actual=ideal. Note: “Measurement” = “Quantitative” = “Numerical”

March 2005 poll: Do you agree with the court decision to remove Terry Schiavo’s feeding tube? Source:

CNN.com updated its graphic a few days later: Old graph: Source:

Review: If you understood today’s lecture, you should be able to solve 2.1, 2.3, 2.13, 2.15, 2.19, 2.21, 2.29, 2.27, 2.30, 2.31 Distinguish between: - A statistic and a parameter - A categorical and a quantitative variable - A response and an explanatory variable Identify: - When a categorical variable is ordinal - When a quantitative variable is continuous - Appropriate numerical & visual summaries for categorical variables Review of Objectives: