Introduction to Statistics

• Statistics: The science of collecting, organizing, analyzing, interpreting, and presenting data.
• Data: Facts or observations used to draw conclusions or make decisions, including results from surveys, experiments, measurements, and responses.

Uses of Statistics

• Statistics is a powerful tool for making informed decisions based on data.
• Statistical methods help understand trends, make predictions, and solve problems in everyday life.
• A strong understanding of statistics is essential for students in science, economics, engineering, and social sciences.

Why Study Statistics

• Numerical data is used in decision-making and problem-solving across various fields.
• News articles use polling data and public opinion statistics.
• Business reports use market analysis and sales forecasting.
• Healthcare uses clinical trials and epidemiology, while government uses census data and economic indicators.
• Sports uses player performance analysis and team strategy.
• Statistical methods have a direct impact on daily lives.

Who Uses Statistics

• Marketing professionals analyze customer behavior and trends.
• Accountants manage financial data and budgets.
• Quality control specialists monitor product quality and consistency.
• Consumers make informed choices by comparing prices and products.
• Administrators manage resources and make data-driven decisions.
• Physicians evaluate treatment effectiveness and patient outcomes.

Descriptive Statistics

• Focus: Organizing, summarizing, and presenting data clearly.
• Includes frequency distributions, graphs (bar charts, histograms, pie charts, box plots), and measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation).
• The U.S. Census collects and organizes population data such as age, income, and employment status.
• Survey of 500 households: 60% prefer online shopping.
• Study of 1,000 students: Average math test score of 85/100, with a standard deviation of 5.

Inferential Statistics

• Uses data from a sample to draw conclusions about a larger population, while assessing the reliability of the conclusions.
• Involves predictions, estimates, and generalizations based on sample data.
• Assesses confidence levels in the results.
• Medical Research: Clinical trials use patient samples to infer the effectiveness of new drugs for larger populations.
• Market Research: Companies use sample data to predict customer preferences and product popularity.
• Probability and Gambling: Inferential statistics uses probability theory
• Quality Control: Manufacturing tests product samples to infer the quality of an entire manufacturing lot.

Population

• Refers to the entire set of individuals, objects, or measurements of interest in a study.
• Includes every member of the group being analyzed.
• Example: Studying the income levels of all working adults in the U.S. includes every working adult in the country.

Sample

• A subset of the population selected for analysis.
• Used when studying the entire population is impractical.
• A survey of 1,000 working adults estimates income levels for all working adults in the U.S.

Types of Population

• Limited Population: Can be counted.
• Example: The number of students in a classroom.
• Unlimited Population: Cannot be precisely counted.
• Example: The number of fish in the Arabian Gulf.

Data Sources

• Indirect Source: Data already collected and published, or historical data.
• Direct Source: Data collected directly through tests, questionnaires, interviews, or observations.

Collection Methods

• Experiment: A controlled study manipulating variables under controlled conditions.
• Example: A clinical trial tests the effect of a new drug on blood pressure.
• Surveys: Collect information via questionnaires or interviews.
• Example: A nationwide poll asking about voting preferences.
• Observational Study: Researchers observe and record data. Can be structured or unstructured.
• Example: Observing students in a classroom without interfering.
• Case Study: A detailed investigation of a single subject.
• Focus Groups: A qualitative data collection method in which a small group of people are interviewed.

Why Take a Sample

• Effort: Collecting data from a large population is complex and resource-intensive.
• Time: Gathering data from an entire population is time-consuming.
• Funds: Collecting data from an entire population requires substantial financial resources.
• Risk: Gathering data can expose individuals to potential risks, such as financial loss or health issues.

Experimental Unit

• The individual or object on which a variable is measured.
• A single data value or measurement is obtained for each experimental unit.
• If the variable is the gender of students, the experimental unit is each student.

Variable

• A characteristic or property that can change or vary across individuals within a population over time.
• Measured on each experimental unit.
• If you are measuring the gender of students, then gender is the variable.

Types of Data

• Univariate Data: Data collected from a single variable.
• Bivariate Data: Data collected from two variables.
• Multivariate Data: Data involving measurement of more than two variables.

Experimental Study

• A study in which one of the variables is manipulated to determine how the manipulation influences other variables

Qualitative Variables

• Represent non-numeric characteristics and describe qualities or categories.
• Examples: Gender, religious affiliation, type of automobile owned, state of birth, eye color.

Quantitative Variables

• Represent measurable quantities reported numerically.
• Examples: Balance in a checking account, minutes remaining in class, number of children in a family.

Discrete Variables

• Take specific, distinct values with gaps between them; typically countable and finite.
• Examples: Number of bedrooms in a house, number of hammers sold at a store (e.g., 1, 2, 3...).

Continuous Variables

• Can take any value within a given range with great precision.
• Examples: Pressure in a tire, weight of a lamb chop, height of students in a class.

Nominal Level

• Data classified into categories without inherent order or ranking.
• Examples: Eye color, gender, religious affiliation.
• Observations of a qualitative variable are classified and counted but have no inherent order.

Ordinal Level

• Data classified and ranked in a meaningful order, but differences between ranks may not be uniform.
• Surveyed satisfaction on a scale of 1 to 5; gold, silver, and bronze rankings.

Interval Level

• Similar to ordinal level with meaningful differences, but no true zero point.
• Temperature in Fahrenheit.
• IQ scores.
• Time of day on a 12-hour clock.

Ratio Level

• The interval level with an inherent zero starting point.
• Includes weight ,age and monthly income.

Types of Measurement

• Practically all quantitative data is recorded on the ratio level.
• The ratio level is the "highest" level because of meaningful zero points and ratios.
• The level of measurement determines what calculations can summarize and analyze the data.
• The level of measurement also informs the selection of statistical tests.

Simple Random Sampling

• Each person or item has an equal chance of being selected.
• Disadvantages: Expensive, large populations make it harder to manage.

Systematic Random Sampling

• Select a random starting point, then choose every kth member, where k = N / n (N = population size, n = sample size).
• Limitations: Before using systematic sampling, check the order of the population carefully. If the order is related to the characteristic being studied, the sample could be biased. To avoid bias, consider stratified or cluster sampling instead

Stratified Random Sampling

• The population is divided into subgroups (strata) based on a characteristic, and a sample is randomly selected from each subgroup. 9th (25 students), 10th (30 students), 11th (25 students), and 12th (20 students).

Cluster Sampling

• The population is divided into clusters, and then some clusters and individuals are randomly chosen from those selected clusters. Suppose you want to survey residents in the northern area of KSA about services and environmental policies.