Statistics 270 Lecture 1

Today Course outline Introductory to statistics Some Definitions Descriptive statistics

Introduction What is statistics? Discipline which deals with the collection, organization and interpretation of data. Done to answer questions of interest.

Example (Pain Reduction and Reiki) Is Reiki an effective pain management tool? Reiki treatment is touch therapy used as an alternative to pain medication. A pilot study involving 20 volunteers experiencing pain was conducted. All treatments were provided by a certified Reiki therapist. Pain was measured using before and after the Reiki treatment. If study was repeated, would we see the same results?

Example (Saving for Retirement) What are the attitudes of low wage earners about saving for retirement? Americans earning $35,000 or less were asked how they are likely to accumulate enough money to retire. What are the data?

Some Definitions Interested in something about a population. Population is a collection of individuals. Describe individuals with data. Data sets contain information/facts relating to individuals. A variables are attributes of an individual (e.g., hair color, pain severity,...). Distribution of a variable gives the values the variable can take and how often it takes on each value

Some Definitions Can measure individuals a single time (e.g., weight) to get a univariate data set Can measure several variables per individual – multi-variate data Would like to measure a sample of indivuduals to make inference about the population – inferential statistics

Types of Variables Two types of variable: Quantitative Variables take on numeric values for which addition and averaging make sense (height, weight, income,…). Qualitative Variables: each individual falls into a category (ethnicity, machine works or does not, …). Hair color: Color preference (red=1, blue=2, green=3): Length of time slept:

Will first focus on descriptive statistics (graphical and numeric). Will move on to inferential statistics (test hypotheses). In either case, statistical tools are used to describe data and help answer scientific questions.

Descriptive Statistics Want to describe or summarize data in a clear and concise way. Two basic methods: graphical and numerical.

Graphical Descriptions of Data Often, pictures tells entire story of data. Have different plots for the different sorts of variables. For Qualitative variables, will use bar-plots and pie charts.

Bar Charts Variable values are the category labels (typically placed along the x- axis) Heights of bar is the count (percentage) of values falling in that category. Note bars are the same width!

Example(retirement savings) A USA Today (Jan. 4, 2000) poll asked Americans who earn $35,000 or less how they expected to accumulate a $500,000 retirement nest- egg. The results are summarized in the frequency table below:

Pie Charts Variable values are the category labels Each category must appear on the plot Percentage of area of pie covered by pie is relative frequency or percent) of values falling in that category. Can easily see percentage for each category Note Less flexible than bar chart