Statistics Chapter 1

Statistics

(1.1)

the science of collecting, organizing, analyzing, and summerizing , information to draw conclusions or answer questions

Data

(1.1)

• fact or proposition used to draw a conclusion

• describes characteristics

Population

(1.1)

an entire group

Individual

(1.1)

person or object that is a member

Sample

(1.1)

part of the population that is being studied

Statistic

(1.1)

numerical summary based on a sample

Descriptive Statistic

(1.1)

organizes/summerizes data

Inferential Statistic

(1.1)

takes results from samples and extends them to the whole population; measures reliability

Parameter

(1.1)

Numerical summary of a population

What are the steps in the process of statistics

(1.1)

1) Identify the research objective

2)collect the data needed to answer the question posed

3) describe the data

4)create an inference

Variables

(1.1)

characteristics of the individuals within the population

Qualitative/Categorical Variables

(1.1)

classification based on attributes/characteristics

Quantitative Variables

(1.1)

• Numerical measures of individuals

• can be added or subtracted and provide meaningful results

Discrete Variable

(1.1)

• quantitative

• finite number of possible values

• countable number of possible values

Continuous Variable

(1.1)

• quantitative

• Infinite number of possible values

• i.e decimals or fractions

Data

(1.1)

list of observations a variable assumes

Qualitative Data

(1.1)

observing qualities

Quantitative data

(1.1)

observations based on a numerical variable

+Nominal

(1.1)

can not be ranked in any specific order

+Ordinal

(1.1)

Can be ranked in a specific order

Interval Level of Measurement

(1.1)

• zero doesnt really mean zero

• addition and subtraction can be formed

Ratio Level of Measurement

(1.1)

• Zero means absolute zero

• multiplication and division can occur

Response Variable

(1.2)

what is the result?

Explanatory Variables

(1.2)

what you manipulate or observe changes in

Observational Study

(1.2)

measures the value of the response variable without influence

Designed experiment

(1.2)

• intentionally changing the value of the explanatory variable

• records the value of the response variable for each group

Confounding Variable

(1.2)

• a third variable that influences both the independent and dependent variable

• is considered in a study.

• The effect cannot be distinguished from a second explanatory variable.

Lurking Variables

(1.2)

• explanatory variable

• not considered in a study

• affects the value of the response variable

Census

(1.2)

list of all people in a population and certain characteristics of each individual

Web Scrapping/ Data Mining

(1.2)

process of extracting data from the internet

Random Sampling

(1.3)

Process of using pure chance to select individuals from a population to be included in a sample

‘n’

(1.3)

sample coming from a population

‘N’

(1.3)

sample obtained through simple random sampling

Simple Random Sampling

(1.3)

Each member of the population has an equal chance of being selected

What are the steps to obtain a simple random sample?

(1.3)

• list all the individuals in the population

• number the individuals

• use a software to generate numbers

Stratified Sample

(1.4)

obtained by seperating the population into strata

Strata

(1.4)

non-overlapping groups

Systematic Sample

(1.4)

• researchers select members of the population at a regular interval

• for example, by selecting every 15th

Cluster Sample

(1.4)

• selecting all individuals within a random collection or group

Convenience Sample

(1.4)

• the sample group is easily assembled

• generally have unreliable results

Sampling Bias

(1.5)

• The subject selection process favors part of a population over another

• results from undercoverage

Undercoverage

(1.5)

• one part of the population is more represented than the other

• results in sampling bias

Nonresponse Bias

(1.5)

• Selected study participants who have a minority opinion do not respond to the survey

• can potentially be improved through callbacks, rewards, or incentives

Response Bias

(1.5)

Survey data does not reflect the subject’s true feelings

Data-Entry Error

(1.5)

• subject could report incorrect data

• data could be entered into a computer incorrectly

• leads to results that are not representative of of the population

Nonsampling Error

(1.5)

errors as a result of:

• sampling bias

• nonresponse bias

• response bias

• data entry error

• the population census itself

Sampling Error

(1.5)

errors as a result of:

• using a sample to estimate population info

raw data

Data that is not organized

Ways to Organize Data

• Tables
• Graphs
• Numerical Summaries- mean, median, mode

+++Frequency Distribution

lists each category of data and the
number of occurrences for each

Frequency Table

relative frequency

percent of
observations within a category

relative frequency distribution

lists each category of data with the
relative frequency

bar graph

-constructed by labeling each category of data
on either the horizontal or vertical axis

-frequency or
relative frequency of the category on the other axis

-Rectangles of equal width are drawn for each category

-height of each rectangle represents the category’s frequency/relative frequency.

Frequency Chart

Relative Frequency Chart

Pareto chart

-bar graph

-bars are drawn in
decreasing order of frequency or relative frequency