Chapter 1: Introduction to Statistics, Organizing and Visualizing Data
Definition
- Variable:
o A characteristic or property of an item or individual.
o A description that can take more than one values.
- Data:
o The set of values associated with one or more variable.
- Statistic:
o A value that summarizes the data of a particular variable, such as, mean, mode, median… (which in
turn are used to estimate a parameter of the corresponding population)
Descriptive and Inferential Statistics
Descriptive Statistics Inferential Statistics
The methods that primarily help summarize Methods that use data collected from a small
and present data. (describe something) group to reach conclusions about a larger
group. (conclude something)
consists of: consists of
- Collecting data - Making conclusion on a population from a
- Organizing data sample of it
- Presenting data (by drawing graphs, - Estimating something
charts, tables…) - Finding probability of an event (is an
- Summarizing data (using mean, median, assumption)
variance…) - Finding relationship among variables
- Making predictions
For example: For example:
- In the last semester, a total of 417 - In the coming semester, we expect 500
students registered for MF004. students taking MF004.
- From 200 students in UCSI, it was found - The probability of finding a student
that 74 of them wear glasses. wearing glasses in UCSI is calculated as
- From 100 students in UCSI, this is what 0.37.
we have found: - From 100 students in UCSI, we conclude
obese normal that eating burger causes obesity.
eat burger 36 24
don’t eat burger 19 21
Types of Variables
Variable
Categorical (qualitative) Numerical (quantitative)
Discrete Continuous
- Categorial: not number
- Numerical, discrete: counting number
- Numerical, continuous: measuring number
Levels of Measurement
distinct ranking is has a meaningful have a true Level of
Example
categories? applied? quantity? zero point? measurement
Gender of a student O X Nominal
Size of a brand of shirt O O X Ordinal
Temperature of a city in °C O O O X Interval
Height of a student O O O O Ratio
,Population vs Sample
- Population: contains all of the items or individuals of interest that you seek to study. All subject of
interest.
o Population parameter: summarize the value of a specific variable for a population.
o To describe population data.
- Sample: contains only a portion of a population of interest. A group of subjects selected from the
population.
o Sample statistic: summarize the value of a specific variable for sample data.
o To describe sample data.
o Used to estimate population parameters
Sources of Data
- Primary sources: the data collector is the one using the data for analysis.
- Secondary sources: the person performing data analysis is not the data collector.
Types of Samples
- Nonprobability sample
o Items included are chosen without regard to their probability of occurrence.
o Chance for an item being selected is not equal.
o Two types:
o Convenience sampling
o Item are selected based only on the fact that they are easy, inexpensive, or
convenient to sample.
o Judgment sample
o Get the opinions of pre-selected experts on the subject matter.
- Probability sample
o Simple random sample
o Every item has an equal chance of being selected.
o Exp: random choose 400 students across all universities in M’sia.
o Systematic sample
o Decide on sample size, n.
o K = N/n, select every kth individual.
o Exp: select every 100th student in the name list from all universities in M’sia.
o Stratified sample
o Divide population into subgroups according to common characteristic.
o A simple random sample is selected from each subgroup.
o Exp: randomly choose 10 students from each university in M’sia.
o Cluster sample
o Divide population into clusters without caring about the characteristic.
o A simple random sample of clusters is selected. (simple select the whole clusters)
o Exp: choose all students from Uni A and Uni B only.
- Types of survey errors
o Coverage error: excluded from frame
o Nonresponse error: follow up on nonresponses
o Sampling error: random differences from sample to sample
o Measurement error: bad or leading question
, Table and Visualizations
- Categorical (qualitative) data
o Tables:
o Summary table (for one variable)
Devices Used to Watch Movies Percent
Television Set 49%
Tablet 9%
Smartphone 47%
o Contingency table (for two variables)
Overall Total Row Total Column Total
No Yes Total No Yes Total No Yes Total
Small 42% 5% 47% Small 90% 10% 100% Small 51% 31% 48%
Medium 25% 10% 35% Medium 71% 29% 100% Medium 30% 62% 35%
Large 16% 2% 18% Large 93% 7% 100% Large 19% 7% 15%
Total 83% 17% 100% Total 84% 16% 100% Total 100% 100% 100%
o Visualizations:
o For one variable
o Bar chart
o Pie or doughnut chart
o Pareto chart
o For two or more variables
o Side-by-side bar chart
o Doughnut chart
- Categorical (qualitative) data
o Tables
o Ordered array (from smallest value to largest value)
Age of Day Students
Surveyed 15 16 18 19 27 30
Night Students
Definition
- Variable:
o A characteristic or property of an item or individual.
o A description that can take more than one values.
- Data:
o The set of values associated with one or more variable.
- Statistic:
o A value that summarizes the data of a particular variable, such as, mean, mode, median… (which in
turn are used to estimate a parameter of the corresponding population)
Descriptive and Inferential Statistics
Descriptive Statistics Inferential Statistics
The methods that primarily help summarize Methods that use data collected from a small
and present data. (describe something) group to reach conclusions about a larger
group. (conclude something)
consists of: consists of
- Collecting data - Making conclusion on a population from a
- Organizing data sample of it
- Presenting data (by drawing graphs, - Estimating something
charts, tables…) - Finding probability of an event (is an
- Summarizing data (using mean, median, assumption)
variance…) - Finding relationship among variables
- Making predictions
For example: For example:
- In the last semester, a total of 417 - In the coming semester, we expect 500
students registered for MF004. students taking MF004.
- From 200 students in UCSI, it was found - The probability of finding a student
that 74 of them wear glasses. wearing glasses in UCSI is calculated as
- From 100 students in UCSI, this is what 0.37.
we have found: - From 100 students in UCSI, we conclude
obese normal that eating burger causes obesity.
eat burger 36 24
don’t eat burger 19 21
Types of Variables
Variable
Categorical (qualitative) Numerical (quantitative)
Discrete Continuous
- Categorial: not number
- Numerical, discrete: counting number
- Numerical, continuous: measuring number
Levels of Measurement
distinct ranking is has a meaningful have a true Level of
Example
categories? applied? quantity? zero point? measurement
Gender of a student O X Nominal
Size of a brand of shirt O O X Ordinal
Temperature of a city in °C O O O X Interval
Height of a student O O O O Ratio
,Population vs Sample
- Population: contains all of the items or individuals of interest that you seek to study. All subject of
interest.
o Population parameter: summarize the value of a specific variable for a population.
o To describe population data.
- Sample: contains only a portion of a population of interest. A group of subjects selected from the
population.
o Sample statistic: summarize the value of a specific variable for sample data.
o To describe sample data.
o Used to estimate population parameters
Sources of Data
- Primary sources: the data collector is the one using the data for analysis.
- Secondary sources: the person performing data analysis is not the data collector.
Types of Samples
- Nonprobability sample
o Items included are chosen without regard to their probability of occurrence.
o Chance for an item being selected is not equal.
o Two types:
o Convenience sampling
o Item are selected based only on the fact that they are easy, inexpensive, or
convenient to sample.
o Judgment sample
o Get the opinions of pre-selected experts on the subject matter.
- Probability sample
o Simple random sample
o Every item has an equal chance of being selected.
o Exp: random choose 400 students across all universities in M’sia.
o Systematic sample
o Decide on sample size, n.
o K = N/n, select every kth individual.
o Exp: select every 100th student in the name list from all universities in M’sia.
o Stratified sample
o Divide population into subgroups according to common characteristic.
o A simple random sample is selected from each subgroup.
o Exp: randomly choose 10 students from each university in M’sia.
o Cluster sample
o Divide population into clusters without caring about the characteristic.
o A simple random sample of clusters is selected. (simple select the whole clusters)
o Exp: choose all students from Uni A and Uni B only.
- Types of survey errors
o Coverage error: excluded from frame
o Nonresponse error: follow up on nonresponses
o Sampling error: random differences from sample to sample
o Measurement error: bad or leading question
, Table and Visualizations
- Categorical (qualitative) data
o Tables:
o Summary table (for one variable)
Devices Used to Watch Movies Percent
Television Set 49%
Tablet 9%
Smartphone 47%
o Contingency table (for two variables)
Overall Total Row Total Column Total
No Yes Total No Yes Total No Yes Total
Small 42% 5% 47% Small 90% 10% 100% Small 51% 31% 48%
Medium 25% 10% 35% Medium 71% 29% 100% Medium 30% 62% 35%
Large 16% 2% 18% Large 93% 7% 100% Large 19% 7% 15%
Total 83% 17% 100% Total 84% 16% 100% Total 100% 100% 100%
o Visualizations:
o For one variable
o Bar chart
o Pie or doughnut chart
o Pareto chart
o For two or more variables
o Side-by-side bar chart
o Doughnut chart
- Categorical (qualitative) data
o Tables
o Ordered array (from smallest value to largest value)
Age of Day Students
Surveyed 15 16 18 19 27 30
Night Students
