Introduction to Statistics

• Introduction to Statistics from La Salle College Antipolo

Learning Targets

• Define Statistics
• Differentiate types of statistics
• Define the basic terms in statistics
• Learn about Population and Sample, Parameters and Statistic, Data and Variable
• Learn about Qualitative and Quantitative Variables
• Study continuous and discrete Variables
• Identify and differentiate four levels of measurement
• Give examples for each level of measurement

Statistics Definition

• Statistics involves planning studies and experiments to obtain data, and organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions
• Two Types of statistics include Descriptive and Inferential

Population

• The population is a complete collection or set the properties of which are analyzed
• It consists of all subjects being studied

Sample

• A sample is a sub-collection of members selected from a larger population
• It is a group of subjects selected from a population for study

Population vs. Sample

• Population example: all Filipino households when surveying computer ownership
• Sample example: the 1,353 Filipino households surveyed

Parameter

• A parameter is a numerical value summarizing all the data of an entire population

Statistic

• A statistic is a numerical value summarizing the sample data

Parameter vs. Statistic

• Population Mean is denoted by μ, Sample Mean is denoted by x bar
• Population Variance is denoted by σ^2, Sample Variance is denoted by s^2
• Population Standard Deviation is denoted by σ, Sample Standard Deviation is denoted by s

Descriptive Statistics

• Descriptive statistics are informational coefficients summarizing a data set
• The data set can be a representation of the entire population, or just a sample
• This type of statistics measures central tendency and measures of variability, or spread

Inferential Statistics

• Statisticians use inferential statistics to draw conclusions about population characteristics from a sample
• It helps determine the certainty/reliability of these conclusions
• This type of statistics is used to make generalizations about large groups
• Examples of the use of this type of statistics include estimating average product demand by surveying consumers, or predicting future events

Descriptive vs. Inferential Examples

• Bowler: Descriptive statistics determine a bowling average for the past 12 months, while inferential statistics estimate the chance of winning based on current season averages
• Housewife: Descriptive statistics determine the average weekly spending on groceries in the past 3 months, while inferential statistics predict the average weekly spending on groceries for this year based on last year's bills
• Politician: Descriptive statistics provides the exact number of votes received in the last election, while inferential statistics estimate the chance of winning the upcoming election based on opinion polls

Data

• Data is the value of a variable associated with one element of a population or sample
• Data may be a number or a word
• Measurements, genders, and survey responses are examples of data

Variable

• A variable is any measurable or countable characteristic, number, or quantity about a population or a sample

Variable Examples:

• Age
• Gender
• Business income and expenses
• Capital Expenditure
• Class grades
• Eye color
• Vehicle

Qualitative Variables

• Qualitative variables have distinct categories based on characteristics or attributes
• Examples of types of qualitative variables are gender, religious preference, and geographic location

Quantitative Variables

• Quantitative variables are also known as numerical variables
• These variables can be counted or measured
• Examples of types of quantitative variables include age, height, weight, and body temperature

Quantitative Variable Types

• Discrete variables can only assume values that can be counted and are exact numbers. An example of a discrete variable would be number of children in a family
• Continuous variables can assume an infinite number of values between any two specific values. Temperature, height, and weight are examples of continuous variables

Discrete vs. Continuous Variables

• Discrete variables are exact and countable
• Continuous variables include numbers between numbers and are measurable

Four Levels of Measurement:

• Nominal
• Ordinal
• Interval
• Ratio

Nominal Level of Measurement:

• Data consists of names, labels, or categories. It cannot be arranged in an ordering scheme
• Calculations performed on these variables will be futile, as there is no numerical value to the options
• Examples include:
  • Teachers classified by subject
  • Classifying residents according to zip code
  • Political party (Democratic, Republican, etc.)
  • Religion (Christianity, Judaism, Islam, etc.)
  • Martial status (single, married, etc.)

Ordinal Level of Measurement:

• Data can be arranged in some order, but differences between data values either cannot be determined or are meaningless
• There is no fixed start or true zero
• Data is classified into categories that can be ranked, however, precise differences between the ranks do not exist
• Examples include:
  • Ranking a guest speaker as superior, average, or poor
  • Ranking floats in a parade
  • Size of shirt (S, M, L, XL)

Interval Level of Measurement:

• This is like the ordinal level, with the additional property that the difference between any two data values is meaningful
• "Interval" indicates 'distance between two entities,' which is what this scale helps achieve
• There is no pre-decided starting point or a true zero value
• Data is ranked, and there are precise differences between units of measure; however, there is no meaningful zero
• Examples include:
  • IQ tests, despite not measuring people with no intelligence, still show a meaningful difference between scores
  • Temperature in Fahrenheit/Celsius doesn't really show a "true zero" or lack of heat

Ratio Level of Measurement:

• This is an interval level with a natural zero starting point
• Differences and ratios are both meaningful
• There are no negative values due to the existence of true zero value
• Examples include:
  • Height
  • Weight
  • Time
  • Salary
  • Age

Four Levels of Measurement Charts

  Nominal                  Ordinal                  Interval                Ratio

data can only data can be data can be data can be be categorized categorized and categorized, categorized, ranked ranked, and evenly ranked, evenly spaced spaced, and has a natural zero. City of birth Gender Top 5 Olympic Test scores (e.g., Height Ethnicity medallists IQ or exams) Age Car brands Language ability Personality Weight Marital status (e.g., beginner, inventories Temperature in intermediate,