Statistics

We welcome any student needing to use statistics in their studies, and where students need to use R, SPSS or Excel in any of the following areas:

• Diagrams and tables

• Measures of location

• Measures of dispersion and skewness

• Random Variables and Their Probability Distribution

• Some Standard Discrete and Continuous Probability Distributions

• Approximations to the Binomial and Poisson Distributions

• Linear Functions of Random Variables and Joining Distributions

• Sample Populations and Point Estimation

• Interval Estimation

• Hypothesis Tests for the Mean and Variance of Normal Distributions

• Hypothesis Tests for the Binomial Parameter  

• Hypothesis Tests for Independence and Goodness-of-Fit

• Non-Parametric Hypothesis Tests

• Correlation

• Regression

• Elements of Experimental Design and Analysis

• Quality Control Charts and Acceptance Sampling 

Statistics: It is a science of planning studies and experiments, obtaining data and organizing, summarizing, presenting, analysing, interpreting, and drawing conclusions about the collected data.

Goal of Statistics: To learn about a large group by examining data from some of its members

Data: Observations that are collected (genders, measurements, etc…)

Population: Complete collection of all elements (individuals) that are considered (scores, people, measurements etc…)

Census: Collection of data from every member of the population

Sample: Sub-collection of members selected from a population

Parameter: A numerical measurement describing some characteristic of a POPULATION

Statistic: A numerical measurement describing some characteristic of a SAMPLE

Example:

You want to know the average height of all adult women in a country.

• Population: All adult women in the country.

• Parameter: The true average height of all adult women in that country (e.g., μ = 162.5 cm).

Since it’s hard to measure every single woman in the country, researchers usually collect data from a sample and calculate a statistic (like the sample mean), which is then used to estimate the population parameter.

Result:

1. Nominal

• Definition: Categories with no inherent order. Used for labeling or naming.

• Key Traits: No ranking, no numerical meaning, can't do math with them.

• Examples:

  • Gender: Male, Female, Non-binary

  • Blood type: A, B, AB, O

  • Marital status: Single, Married, Divorced

2. Ordinal

• Definition: Categories with a meaningful order, but unequal intervals between them.

• Key Traits: Ordered, but the differences between ranks aren’t measurable.

• Examples:

  • Education level: High School < Bachelor's < Master's < PhD

  • Satisfaction: Very Unsatisfied < Unsatisfied < Neutral < Satisfied < Very Satisfied

  • Class rank: 1st, 2nd, 3rd, etc.

3. Interval

• Definition: Numerical data with equal intervals between values, but no true zero.

• Key Traits: Can do addition/subtraction, but ratios are meaningless.

• Examples:

  • Temperature in Celsius or Fahrenheit (0°C doesn’t mean “no temperature”)

  • IQ scores

  • Dates on a calendar

4. Ratio

• Definition: Numerical data with equal intervals and a true zero point.

• Key Traits: All arithmetic operations are valid (add, subtract, multiply, divide).

• Examples:

  • Height (0 cm = no height)

  • Weight (0 kg = no weight)

  • Age (0 years = birth)