Chapter 1 Getting Started 1.1 What is Statistics?
What is Statistics? • The science that deals with the collection, organization, and interpretation of data.
Individuals vs. Variables Individuals Variables Characteristic of the individual to be measured or observed • People or objects included in the study
Quantitative vs. Qualitative Quantitative Variables Qualitative/CategoricaVariables Describes an individual by placing the individual into a category or group, such as male or female • Have value or numerical measurement for which operations such as addition or averaging make sense
Population vs. Sample Population Data Sample Data The data are from only some of the individuals of interest Sample Statistics are numerical measures that describe an aspect of a sample • Data is from every individual of interest • Population Parameters are numerical measures that describe an aspect of a population
Levels of Measurement • Nominal – Names, Labels, Categories • Ordinal – Arranged in meaningful mathematical order • Interval – Differences are meaningful • Ratio – Division or percentage comparisons make sense; zero point
Another Version • http://www.youtube.com/watch?v=hZxnzfnt5v8
An Example: What is the individual and what are the variables in this study? What variables are qualitative? What variables are quantitative? Classify each variable by its highest level of measurement. • Student Data Sheet: • Height: 58 inches • Weight: 145 lbs • Date of Birth: 11/12/1999 • Grade in Last Course: B+ • Declaration of Major: Physics • Time of First Class: 9:05 A.M. • Rating of Last Professor: Above Average
Do Now – Drug Testing • On the back of the sheet you picked up on the way into the classroom, create a detailed plan to drug test 25 members of the senior class.
Chapter 1 Getting Started 1.2 Random Samples
Activity • How can we use a Random Number Table (R.N.T.) to decide which 5 student homes or TL buildings could meet a celebrity who came to campus? • Note there are a total of 68 student homes and TL buildings.
Simple Random Sample (SRS) • A simple random sample of n measurements from a population is a subset of the population selected in such a manner that every sample of size n from the population has an equal chance of being selected.
Random Number Tables (RNT) • Used to help secure a SRS • Steps: • Number all members of the population sequentially (each must have the same number of digits) • Drop a pin on the RNT to pick a starting point • Pull digits n at a time, discarding non-used numbers • Repetition?
Do Now • A local Sheetz expects 7,225 customers per day. On a piece of paper: • Explain how a RNT or RNG could be used to secure a sample of 25 customers who could receive a gift card for their participation in a customer service survey. • Find the identification numbers of your 25 sampled customers.
Other Methods to Secure a Sample • Systematic • Stratified • Cluster • Multistage • Convenience
Do Now • Describe a way to secure a sample of 25 students from the 200 students at first lunch using each of the 5 sampling techniques. • SRS • Convenience • Systematic • Stratified • Cluster
Systematic Sampling • Population is numbered • Select a starting point at random and pick every kth member
Convenience Sampling • Create sample by selecting population members which are easily available
Stratified Sampling • Divide population into distinct subgroups based on specific characteristics • Draw random samples from each strata
Cluster Sampling • Divide population into pre-existing segments or clusters (often geographic). • Make a random selection of clusters. • All members of cluster are chosen.
Multistage Sampling • Use a variety of sampling methods to create successively smaller groups at each stage. • Final sample is made of clusters.
Do Now • Copy the Blue Box from page 21 into your notebooks. This is the beginning of Section 1.3 “Introduction to Experimental Design”
Chapter 1 – Getting Started 1.3 Introduction to Experimental Design • Introductory Youtube Clip
Census vs. Sample • Census – measurements from observations from the entire population are used. • Sample – measurements from observations from part of the population are used
Observational Study vs. Experiment • Observational Study – observations and measurements of individuals are conducted in a way that doesn’t change the response or the variable being measured • Experiment – a treatment is deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured
Within Experiments: • Placebo Effect – occurs when a subject receives no treatment but (incorrectly) believes he or she is in fact receiving treatment and responds favorably • Control Group – those who receive the placebo treatment • Treatment Group – those who receive the actual treatment • Completely Randomized Experiment – one in which a random process is used to assign each individual to one of the treatments
Completely Randomized Experiment • C.R.E. – is one in which a random process is used to assign each individual to one of the treatments
Characteristics of a Well-Designed Experiment • Block – a group of individuals sharing some common features that might affect the treatment • Randomized Block Experiment – individuals are first sorted into blocks, and then a random process is used to assign each individual in the block to one of the treatments
Characteristics of a Well-Designed Experiment • Control Groups – used to account for the influence of other known or unknown variables that might be an underlying cause of change in response in the experimental group. • Lurking or Confounding Variables – such variables
Characteristics of a Well-Designed Experiment • Randomization – used to assign individuals to the two treatment groups. Helps to prevent bias in selecting members to the groups • Replication – on many patients reduces the possibility that the differences in occurred by chance alone.
Potential Pitfalls of Surveys • Nonresponse • Truthfulness of Response • Faulty Recall • Hidden Bias • Vague Wording • Interview Influence • Voluntary Response
Data Collection Techniques (Summary) • Census • Samples • Observational Studies • Experiments • Surveys • Simulations (previously)
Do Now • Open Textbook to page 28. • Create a list (using Excel) of 23 random numbers between 1 and 365.
The Birthday Paradox States… • In a room full of 23 randomly selected people, the probability that at least two share a birthday is around 50%...
Believe it or not… • The probability is very close to 99% if there are 57 people in the room.
Do Now • On the blank sheet of paper (and using your notes): • List the four levels of measurement (with one word definitions) • List five sampling methods (with slightly longer definitions)