Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 1 Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter One Getting Started

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 2 Statistics is The study of how to: collect organize analyze interpret numerical information from data

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 3 Individuals and Variables Individual: a person or object included in a study Variable: a characteristic of the individual to be measured or observed

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 4 Quantitative and Qualitative Data Quantitative variable has a value or numerical measurement –example: number of siblings Qualitative variable places an individual in a category or group –example: brand of computer

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 5 Population Variable is taken from every individual of interest Example: incomes of all residents of a county

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 6 Sample Variable is taken from only some of the indiviuals Example: incomes of selected residents

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 7 Levels of Measurement Nominal Ordinal Interval Ratio

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 8 Nominal Measurement Data is put into categories only. Example: eye color

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 9 Ordinal Measurement Data can be ordered. Differences cannot be calculated or interpreted. Example: class rank

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 10 Interval Measurement Data can be ordered. Differences between data values can be compared. Example: temperature

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 11 Ratio Measurement Data can be ordered. Differences and ratios between data values can be compared. Example: time

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 12 Branches of Statistics Descriptive: methods of organizing, picturing, and summarizing information Inferential: methods of using information from a sample to draw conclusions regarding the population

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 13 Methods of Producing Data Sampling: drawing subsets from the population Experimentation: impose a change and measure the result Simulation: numerical facsimile of real-world phenomena Census: using measurements from entire population Survey:asking questions

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 14 Simple Random Sample of n measurements: every sample of size n has equal chance of being selected every item in the population has equal chance of being included

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 15 Not random sampling: asking for volunteers to respond to a survey choosing the first five customers in a store

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 16 Random sampling: drawing names “from a hat” using a random number table to select sample using a random number generator

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 17 Simulation Provides arithmetic imitation of “real” phenomenon Random number table may be used

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 18 Sampling with replacement The same number may be selected for a sample more than one time.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 19 Other sampling techniques Stratified Sampling Systematic Sampling Cluster Sampling Convenience Sampling

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 20 Stratified Sampling Population is divided into groups (“strata”) Random samples are drawn from each group

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 21 Systematic Sampling Population is arranged in sequential order. Select a random starting point. Select every “kth” item.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 22 Cluster Sampling Population is divided into sections Some sections are randomly selected Every item in selected sections is included in sample

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 23 Convenience Sampling Use whatever data is readily available. Risk severe bias.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 24 Which sampling technique is described? College students are waiting in line for registration. Every eighth person in line is surveyed. Systematic sampling

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 25 Which sampling technique is described? College students are waiting in line for registration. Students are asked to volunteer to respond to a survey. Convenience sampling

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 26 Which sampling technique is described? In a large high school, students from every homeroom are randomly selected to participate in a survey Stratified sampling

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 27 Which sampling technique is described? An accountant uses a random number generator to select ten accounts for audit. Simple random sampling

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 28 Which sampling technique is described? To determine students’ opinions of a new registration method, a college randomly selects five majors. All students in the selected majors are surveyed. Cluster sampling

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 29 Experimental Design Statistical studies are used to obtain reliable information.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 30 Planning a Statistical Study Identify individuals or object of interest Specify variables and protocols for observations Decide whether to use a census or a sample and determine viable sampling method Collect data Make decisions List concerns and recommendations

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 31 Census Measurements or observations from entire populations are used.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 32 Sample Measurements or observations from a representative part of the population are used.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 33 Simulation A numerical facsimile of real-world phenomena

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 34 Experiments and Observation Observational Study: no change is made in the responses or variable being studied Experiment: a treatment is imposed in order to observe a possible change in the response or variable being measured

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 35 Randomized two-treatment experiment Subjects are randomly assigned to one of two groups One group receives treatment under study Control group receives placebo Results are compared Randomization prevents bias Replication on many subjects assures changes not caused by random chance

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 36 Surveys Data is gathered by asking people questions.

Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 37 Problems with data collection Some individuals do not respond. People with strong opinions may be over- represented in voluntary response samples. There may be a hidden bias in the data collection process. There may be hidden effects of other variables. There is no guarantee that results can be generalized.