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## Chapter 1 Getting Started

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**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)