Statistics Mr. zboril | Milford PEP

Chapter 1 Section 1.1 Getting Started I am happy you are in my class. You are important to me – don’t ever think otherwise! This Photo by Unknown Author is licensed under CC BY-SA

Section 1.1 What is Statistics? Focus points for Section 1.1 Identify variables in statistical study. Difference between quantitative and qualitative variables. Identify populations and samples Distinguish between parameters and statistics Determine the level of measurement Compare differential and inferential statistics

Section 1.1 Getting Started I want to perform a study on all the people who have climbed Mt. Everest. The people who have climbed Mt. Everest are the individuals in the study. (If we were studying inanimate things – like items left behind by climbers on Mt. Everest - ‘individuals’ would be replaced by ‘objects’.) We might classify the individuals according to nationality, height, gender, or age. These are called variables.

Section 1.1 Variables Is age a value? Yes – it is a quantitative variable. Is gender a value? No – it is a qualitative variable. Other quantitative variables would be height and weight. Other qualitative variables would be nationality, race, or religion.

Chapter 1 Population Data vs. Sample Data Does the data comprise information from all the climbers, or just some of the climbers? ALL of the climbers population data SOME of the climbers sample data This Photo by Unknown Author is licensed under CC BY This Photo by Unknown Author is licensed under CC BY

Chapter 1 Parameter vs. Statistic A population parameter is a numerical measure that describes an aspect of the population. Proportion of males in the population of all the climbers. A sample statistic is a numerical measure that describes an aspect of a sample. Proportion of male climbers in the sample. This may vary from sample to sample.

Chapter 1 Pineapples on Page 6 The Hawaii Department of Tropical Agriculture is conducting a study of ready-to-harvest pineapples. Are the pineapples considered ‘individuals’ or ‘objects?’ Researchers wish to classify the pineapple by weight – is this a qualitative or quantitative variable? The average weight is called a parameter.

Chapter 1 Pineapples on Page 6 The researchers also wish to classify the pineapples by taste and employ a panel to taste some of the objects and label them “poor”, “acceptable”, or “good”. Would the taste results represent population data or sample data? Taste is a variable. Is this a quantitative or qualitative variable? Would the proportion of “good” pineapples be a parameter or a statistic? GUIDED EXERCISE #1 Page 6 Bottom

Chapter 1 Levels of Measurement Nominal Level – names, labels or categories Ordinal Level – data that can be arranged in order Interval Level – data that can be arranged in order with meaningful differences Ratio Level – ratio of data also meaningful. Data has a true zero.

Chapter 1 Levels of Measurement Example 2 Levels of Measurement Page 7 Identify the Type of Data Taos, Acoma, Zuni, Cochiti – nominal level High School Class – Jim ranked 25th, June ranked 19th, Walter ranked 10th, Julia ranked 4th. Ordinal Level – we can arrange the data in order, however there is no way to measure the difference between the ranks.

Chapter 1 Levels of Measurement Body Temperatures of Trout in Yellowstone River Interval Level – the data can be arranged in order and meaningful differences can be calculated. However, there is no “zero” point since 0 deg. (C or F) does not indicate “no heat”

Chapter 1 Levels of Measurement Length of Trout Swimming in Yellowstone River Ratio Level – an 18in trout is 3x longer than a 6in trout. There is a “zero point”.

Chapter 1 Levels of Measurement & Statistics Let’s do the Guided Exercise #2 on pg. 8 So….what is Statistics? It is the study of how to collect, organize, analyze, and interpret numerical information from data

Chapter 1 Descriptive vs. Inferential Statistics There are two methods to employing statistics: Descriptive Statistics - methods of organizing, picturing, and summarizing information from samples or populations Inferential Statistics – involves methods of using information from a sample to draw conclusions regarding the population

Mr. Zboril Contact Information brian44212@gmail.com cell: 513-375-7552 Class Time 1pm Tues & Thurs www.brianzboril.weebly.com

Section 1.2 Random Samples Mr. zboril | Milford PEP

Section 1.2 Random Samples I am still happy you are in my class.

Section 1.2 Random Samples Focus points for Section 1.2 Explain the importance of random samples Construct a simple random sample using random numbers Simulate a random process Describe stratified sampling, cluster sampling, systematic sampling, multistage sampling, and convenience sampling

Section 1.2 Random Samples Coyote story on pg. 12. What is the lesson – learned? 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. We have a population of 100 individuals and randomly divide them into group of 20 (for 5 groups total). Then we are going to choose one group of 20 to gather information. Each group has an equal chance of being selected and each individual has an equal chance of being selected.

Section 1.2 Random-Number Table Let’s go through Guided Exercise 3 on pg. 13. Let’s do another exercise…. We need to sample some vehicles from a shipment of 500 Toyotas. A random selection of 30 vehicles will be needed. How will we randomly select thirty vehicles? We could do a couple things…. One method is to number the cars 1 – 500, write the number on a set of 500 cards, mix the cards, then randomly select 30 numbers. An easier way is to use a random-number table.

Section 1.2 Random-Number Table You can create your own random-number table by writing the numbers 0 through 9 on separate cards. Draw a card Write down the numbers Return the card Mix up the cards. Table 1 in the Appendix is a ready-made random-number table. It has 50 rows and 10 blocks of 5 digits each.

Section 1.2 Random-Number Table Start anywhere on the table – the book starts at row 15, block 5, and lists the remaining numbers for that row. 99281 59640 15221 96079 09961 05371 The highest number assigned is 500. Since this has 3 digits, regroup the numbers into groups of three. 992 815 964 015 221 960 790 996 105 371

Section 1.2 Random-Number Table 992 815 964 015 221 960 790 996 105 371 That gives us four vehicles. Continue with the next row of numbers and repeat until we have 30 numbers. If we encounter a number we’ve already used, skip it. Alright!.....we now have a procedure…..

Section 1.2 Procedure How to Draw a Random Sample (pg.14) Number all members of the population sequentially. Use a table, calculator, or computer to select random numbers [from the numbers assigned to the population members]. Create the population sample using population members with numbers corresponding to those randomly selected.

Section 1.2 Other Sampling Techniques Stratified Sampling : divide population into subgroups (called “strata”) based on specific characteristics such as age, income, etc. Draw random samples from each stratum.

Section 1.2 Stratified Sampling The groups or classes inside a population that share a common characteristic are called ‘strata’ – plural of ‘stratum’. In a high school or college, an example of strata would be freshmen, sophomores, juniors, or seniors. Other examples could be men or women or in-state students and out-of-state students. The groups or strata are often sampled in proportion to their percentage of the overall population.

Section 1.2 Other Sampling Techniques Systemic Sampling : Number all members of the population sequentially. Then, from a starting point selected at random, include every kth member of the population in the sample. This Photo by Unknown Author is licensed under CC BY-NC-SA

Section 1.2 Systemic Sampling Advantage of systematic sampling is the information is easy to get. The disadvantage of this sampling method is it cannot be used if the population is repetitive or cyclic in nature. Consider a manufacturing process that produces a flaw every 13th item. If every 15th item is selected for quality-assurance testing, it will be difficult to determine the frequency of flaws.

Section 1.2 Other Sampling Techniques Cluster Sampling : Divide the entire population into pre-existing segments or clusters. Make a random selection of clusters and include every member of the cluster. This Photo by Unknown Author is licensed under CC BY-SA

Section 1.2 Cluster Sampling An example of cluster sampling would be conducting a survey of technical employees in a city. You would randomly select five companies that employ a similar number of people and survey the employees at each location. This Photo by Unknown Author is licensed under CC BY-SA

Section 1.2 Other Sampling Techniques Convenience sampling uses results and data that is easily and readily obtained. Runs the risk of being severely biased. This Photo by Unknown Author is licensed under CC BY-SA

I can stay afterwards for extra help Mr. Zboril Contact Information brian44212@gmail.com cell: 513-375-7552 Class Time 2pm Tues & Thurs I can stay afterwards for extra help www.brianzboril.weebly.com