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## Chapter 1 The Where, Why, and How of Data Collection

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What is Statistics?

- Statistics is the development and application of methods to collect, analyze and interpret data.
- Modern statistical methods involve the design and analysis of experiments and surveys, the quantification of biological, social and scientific phenomenon and the application of statistical principles to understand more about the world around us.
- Statistics is a discipline which is concerned with:
- designing experiments and other data collection,
- summarizing information to aid understanding,
- drawing conclusions from data, and
- estimating the present or predicting the future.

Population vs. Sample

Population

Sample

a b c d

ef gh i jk l m n

o p q rs t u v w

x y z

b c

g i n

o r u

y

Populations and Samples

- A Population is the set of all items or individuals of interest
- Examples: All likely voters in the next election

All parts produced today

All sales receipts for November

- A Sample is a subset of the population
- Examples: 1000 voters selected at random for interview

A few parts selected for destructive testing

Every 100th receipt selected for audit

Why Sample?

- Less time consuming than a census
- Less costly to administer than a census
- It is possible to obtain statistical results of a sufficiently high precision based on samples.

Sampling Techniques

Sampling Techniques

Nonstatistical Sampling

Statistical Sampling

Simple

Random

Convenience

Systematic

Judgment

Cluster

Stratified

Not interested in……

Statistical Sampling

- Items of the sample are chosen based on known or calculable probabilities

Statistical Sampling

(Probability Sampling)

Simple Random

Stratified

Systematic

Cluster

Video Clip

Please read the book

Example of Random Sampling

- Suggesting how the statistical sampling techniques can be used to gather data on employees' preferences for scheduling vacation times.
- Simple random sampling could be used by assigning each employee a number and then using a random number generator to select employees.
- Table and Excel Toolpak

Simple Random Sampling

- Every possible sample of a given size has an equal chance of being selected
- Selection may be with replacement or without replacement
- The sample can be obtained using a table of random numbers or computer random number generator

Typeof Statistics

- Descriptive statistics
- Mathematical methods (such as mean, median, standard deviation) that summarize and interpret some of the properties of a set of data (sample) but do not infer the properties of the population from which the sample was drawn.
- Inferential statistics
- Mathematical methods (such as hypothesis development) that employ probability theory for deducing (inferring) the properties of a population from the analysis of the properties of a set of data (sample) drawn from it. It is concerned also with the precision and reliability of the inferences it helps draw.

Descriptive Statistics

- Collect data
- e.g., Survey, Observation,

Experiments

- Present data
- e.g., Charts and graphs
- Characterize data
- e.g., Sample mean =

Inferential Statistics

- Making statements about a population by examining sample results

Sample statisticsPopulation parameters

(known) Inference(unknown, but can

be estimated from

sample evidence)

Inferential Statistics

Drawing conclusions and/or making decisions concerning a populationbased on sample results.

- Estimation
- e.g., Estimate the population mean weight using the sample mean weight
- Hypothesis Testing
- e.g., Use sample evidence to test the claim that the population mean weight is 120 pounds

Tools for Collecting Data

Data Collection Methods

Experiments

Written questionnaires

Direct observation and personal interview

Telephone surveys

Survey Design Steps

- Define the issue
- what are the purpose and objectives of the survey?
- Define the population of interest
- Develop survey questions
- make questions clear and unambiguous
- use universally-accepted definitions
- limit the number of questions

Survey Design Steps

(continued)

- Pre-test the survey
- pilot test with a small group of participants
- assess clarity and length
- Determine the sample size and sampling method
- Select sample and administer the survey

Types of Questions

- Closed-end Questions
- Select from a short list of defined choices

Example: Major: __business __liberal arts

__science __other

- Open-end Questions
- Respondents are free to respond with any value, words, or statement

Example: What did you like best about this course?

- Demographic Questions
- Questions about the respondents’ personal characteristics

Example: Gender: __Female __ Male

Data (variable) Types

- Examples:
- Marital Status
- Political Party
- Eye Color
- (Defined categories)

- Examples:
- Number of Children
- Defects per hour
- (Counted items)

- Examples:
- Weight
- Voltage
- (Measured characteristics)

Qualitative vs. Quantitative Variables (Data)

- Qualitative variables (data) take on values that are names or labels.
- Example: the color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier)
- Quantitative variables are numerical. They represent a measurable quantity.
- Example: # of students in CSUB or # of people in Bakersfield

Discrete vs. Continuous Variables (Data)

- Quantitative variables can be further classified as discrete or continuous.
- If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable.
- Example: The fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.

Discrete vs. Continuous Variables (Data)

- Example: If we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. That is, we could not, for example, get 2.3 heads. Therefore, the number of heads must be a discrete variable.

Data Measurement Levels

Highest Level

Complete Analysis

Measurements

Ratio/Interval Data

Rankings

Ordered Categories

Higher Level

Mid-level Analysis

Ordinal Data

Categorical Codes ID Numbers Category Names

Lowest Level

Basic Analysis

Nominal Data

Nominal

- Nominal basically refers to categorically discrete data such as name of your school, type of car you drive or name of a book. This one is easy to remember because nominal sounds like name (they have the same Latin root).

Ordinal

- Ordinal refers to quantities that have a natural ordering. The ranking of favorite sports, the order of people's place in a line, the order of runners finishing a race or more often the choice on a rating scale from 1 to 5. With ordinal data you cannot state with certainty whether the intervals between each value are equal. For example, we often using rating scales (Likert-Scale questions). On a 10 point scale, the difference between a 9 and a 10 is not necessarily the same difference as the difference between a 6 and a 7. This is also an easy one to remember, ordinal sounds like order.

Interval

- Interval data is like ordinal except we can say the intervals between each value are equally split. The most common example is temperature in degrees Fahrenheit. The difference between 29 and 30 degrees is the same magnitude as the difference between 78 and 79 (although I know I prefer the latter). With attitudinal scales and the Likert questions you usually see on a survey, these are rarely interval, although many points on the scale likely are of equal intervals.

Ratio

- Ratio data is interval data with a natural zero point. For example, time is ratio since 0 time is meaningful. Degrees Kelvin has a 0 point (absolute 0) and the steps in both these scales have the same degree of magnitude.

Data Types

- Time Series Data
- Ordered data values observed over time
- Cross Section Data
- Data values observed at a fixed point in time

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