CHAPTER 1 Defining and Collecting Data

Transcription

1 CHAPTER 1 Defining and Collecting Data In this book we will use Define the variables for which you want to reach conclusions Collect the data from appropriate sources Organize the data collected by developing tables Visualize the data by developing charts Analyze the data by examining the appropriate tables and charts (and in later chapters by using other statistical methods) to reach conclusions Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 1

2 Types of Variables Categorical (qualitative) variables have values that can only be placed into categories, such as yes and no. Numerical (quantitative) variables have values that represent a counted or measured quantity. Discrete variables arise from a counting process Continuous variables arise from a measuring process Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 2

3 Operational Definitions Of Terms VARIABLE A characteristic of an item or individual. DATA The set of individual values associated with a variable. STATISTICS The methods that help transform data into useful information for decision makers. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 3

4 Types of Variables Variables Categorical Numerical Examples: Marital Status Political Party Eye Color (Defined categories) Discrete Examples: Number of Children Defects per hour (Counted items) Continuous Examples: Weight Voltage (Measured characteristics) Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 4

5 Levels of Measurement A nominal scale classifies data into distinct categories in which no ranking is implied. Categorical Variables Categories Do you have a Facebook profile? Type of investment Cellular Provider Yes, No Growth, Value, Other AT&T, Sprint, Verizon, Other, None Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 5

6 Levels of Measurement (con t.) An ordinal scale classifies data into distinct categories in which ranking is implied Categorical Variable Ordered Categories Student class designation Product satisfaction Faculty rank Standard & Poor s bond ratings Student Grades Freshman, Sophomore, Junior, Senior Very unsatisfied, Fairly unsatisfied, Neutral, Fairly satisfied, Very satisfied Professor, Associate Professor, Assistant Professor, Instructor AAA, AA, A, BBB, BB, B, CCC, CC, C, DDD, DD, D A, B, C, D, F Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 6

7 Levels of Measurement (con t.) An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity but the measurements do not have a true zero point. A ratio scale is an ordered scale in which the difference between the measurements is a meaningful quantity and the measurements have a true zero point. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 7

8 Interval and Ratio Scales Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 8

9 Collecting Data Correctly Is A Critical Task Need to avoid data flawed by biases, ambiguities, or other types of errors. Results from flawed data will be suspect or in error. Even the most sophisticated statistical methods are not very useful when the data is flawed. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 9

10 Sources of Data Primary Sources: The data collector is the one using the data for analysis Data from a political survey Data collected from an experiment Observed data Secondary Sources: The person performing data analysis is not the data collector Analyzing census data Examining data from print journals or data published on the internet. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 10

11 Sources of data fall into five categories Data distributed by an organization or an individual The outcomes of a designed experiment The responses from a survey The results of conducting an observational study Data collected by ongoing business activities Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 11

12 Data Is Collected From Either A Population or A Sample POPULATION A population consists of all the items or individuals about which you want to draw a conclusion. The population is the large group. When you analyze data from a population you compute parameters. SAMPLE A sample is the portion of a population selected for analysis. The sample is the small group. When you analyze data from a sample you compute statistics. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 12

13 Population vs. Sample Population Sample All the items or individuals about which you want to draw conclusion(s) A portion of the population of items or individuals Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 13

14 Collecting Data Via Sampling Is Used When Selecting A Sample Is Less time consuming than selecting every item in the population. Less costly than selecting every item in the population. Less cumbersome and more practical than analyzing the entire population. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 14

15 Things To Consider / Deal With In Potential Sources Of Data Is the source of data structured or unstructured? How is electronic data formatted? How is data encoded? Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 15

16 Structured Data Follows An Organizing Principle & Unstructured Data Does Not A Stock Ticker Provides Structured Data: The stock ticker repeatedly reports a company name, the number of shares last traded, the bid price, and the percent change in the stock price. Due to their inherent structure, data from tables and forms are structured data. s from five people concerning stock trades is an example of unstructured data. In these s you cannot count on the information being shared in a specific order or format. This book will deal almost exclusively with structured data Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 16

17 Data Can Be Formatted and / or Encoded In More Than One Way Some electronic formats are more readily usable than others. Different encodings can impact the precision of numerical variables and can also impact data compatibility. As you identify and choose sources of data you need to consider / deal with these issues Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 17

18 Data Cleaning Is Often A Necessary Activity When Collecting Data Often find irregularities in the data Typographical or data entry errors Values that are impossible or undefined Missing values Outliers When found these irregularities should be reviewed / addressed Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 18

19 A Sampling Process Begins With A Sampling Frame The sampling frame is a listing of items that make up the population Frames are data sources such as population lists, directories, or maps Inaccurate or biased results can result if a frame excludes certain portions of the population Using different frames to generate data can lead to dissimilar conclusions Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 19

20 Types of Samples Samples Non-Probability Samples Probability Samples Judgment Convenience Simple Random Stratified Systematic Cluster Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 20

21 Types of Samples: Nonprobability Sample In a nonprobability sample, items included are chosen without regard to their probability of occurrence. In convenience sampling, items are selected based only on the fact that they are easy, inexpensive, or convenient to sample. In a judgment sample, you get the opinions of preselected experts in the subject matter. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 21

22 Types of Samples: Probability Sample In a probability sample, items in the sample are chosen on the basis of known probabilities. Probability Samples Simple Random Systematic Stratified Cluster Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 22

23 Probability Sample: Simple Random Sample Every individual or item from the frame has an equal chance of being selected Selection may be with replacement (selected individual is returned to frame for possible reselection) or without replacement (selected individual isn t returned to the frame). Samples obtained from table of random numbers or computer random number generators. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 23

24 Selecting a Simple Random Sample Using A Random Number Table Sampling Frame For Population With 850 Items Item Name Item # Bev R. 001 Ulan X Joann P. 849 Paul F. 850 Portion Of A Random Number Table The First 5 Items in a simple random sample Item # 492 Item # 808 Item # does not exist so ignore Item # 435 Item # 779 Item # 002 Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 24

25 Probability Sample: Systematic Sample Decide on sample size: n Divide frame of N individuals into groups of k individuals: k = N / n Randomly select one individual from the 1 st group Select every k th individual thereafter N = 40 n = 4 k = 10 First Group Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 25

26 Probability Sample: Stratified Sample Divide population into two or more subgroups (called strata) according to some common characteristic A simple random sample is selected from each subgroup, with sample sizes proportional to strata sizes Samples from subgroups are combined into one This is a common technique when sampling population of voters, stratifying across racial or socio-economic lines. Population Divided into 4 strata Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 26

27 Probability Sample: Cluster Sample Population is divided into several clusters, each representative of the population A simple random sample of clusters is selected All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique A common application of cluster sampling involves election exit polls, where certain election districts are selected and sampled. Population divided into 16 clusters. Randomly selected clusters for sample Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 27

28 Evaluating Survey Worthiness What is the purpose of the survey? Is the survey based on a probability sample? Coverage error appropriate frame? Nonresponse error follow up Measurement error good questions elicit good responses Sampling error always exists Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 28

29 Types of Survey Errors (1) Coverage error or selection bias Exists if some groups are excluded from the frame and have no chance of being selected Nonresponse error or bias People who do not respond may be different from those who do respond Sampling error Variation from sample to sample will always exist Measurement error Due to weaknesses in question design and / or respondent error Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 29

30 Types of Survey Errors (2) Coverage error Nonresponse error Sampling error Measurement error Excluded from frame Follow up on nonresponses Random differences from sample to sample Bad or leading question Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 1, Slide 30