Introduction to Statistics

Introduction to Statistics

• Statistics involves the methods to collect, organise, analyze, and interpret numerical information from data.
• Decision-making by various economic actors relies on available information.
• Statistics helps in making decisions amid uncertainties, such as assessing treatment efficacy.
• Statistical methods can provide information from a small group to make inferences about a larger population

The Statistical Decision-Making Process

• Data acts as the input, which consists of raw values.
• Statistical analysis acts as the transformation process that converts the data into information.
• Information is the output, including statistical summaries, relationships, patterns, and trends.
• The ultimate benefit is improved decision-making.

Key Statistical Concepts

• Data includes the facts and figures (measurements or observations) collected, analyzed, and summarized for presentation and interpretation.
• A data set refers to all data collected in a particular study.
• Elements are the entities on which data is collected.
• A variable is a characteristic of interest for the elements.
• Data are measurements or observations collected on each variable for every element in a study.
• A population is the entire group of people or objects of interest.
• A sample is a smaller group selected from a population.
• A parameter is a numerical measure that describes an aspect of a population
• A statistic is a numerical measure that describes an aspect of a sample.

Qualitative vs. Quantitative Data

• Data is classified as either qualitative or quantitative.
• Qualitative data includes labels or names which identify attributes and yield categorical (non-numeric) responses.
• Quantitative data requires numeric values indicating quantity.
• Discrete data are numeric, consisting of whole numbers like the number of cars sold in a month.
• Continuous data any numeric value occurring on an interval, like assembly time for a part or the mass of passenger luggage.

Levels of Measurement

• Nominal measurement categorizes qualitative data with categories of equal importance, such as gender or marital status.
• Ordinal measurement ranks data, such as in customer satisfaction rates or hotel class, but the differences between categories cannot be measured.
• Interval scales are quantitative, possessing order and distance properties, with meaningful and equal intervals, but an arbitrary zero, like temperature or calendar dates.
• Ratio scales are quantitative with a zero origin indicating the absence of what is measured, such as age, income, or prices.

Data Sources

• Internal sources are sources from within an organization or entity.
• External sources are sources outside an organization or entity.
• Primary data is data recorded for the first time at the source for a specific purpose, potentially internal or external.
  • Primary data has improved quality because of data collection control.
  • Primary data collection can be time-consuming and costly
• Secondary data already exists in a processed format, also potentially internal or external.
  • Secondary data has relatively short access time and is less costly.
  • Secondary data may lack relevance to the data requirement and be outdated.

Data Collection Methods

• Observation involves collecting primary data by watching a respondent or process, like conducting vehicle traffic surveys.
  • Observation reduces bias because respondents behave naturally when unaware of being watched.
  • Observation is a passive approach that does not provide underlying reasoning or motivate factors.
• Surveys collect primary data through direct questioning using questionnaires, commonly done through interviews, phone calls, or e-surveys.
• Experimentation collects primary data through controlled conditions to control the effects of influencing factors.
  • Experimentation usually delivers high-quality, reliable findings.
  • Experimentation can be costly, time-consuming, and difficult to control confounding variables.

Sampling Methods: Probability and Non-Probability

• Two basic methods for statistical sampling are using probability and non-probability

Sampling Methods: Non-Probability Techniques

• Convenience Sampling is drawing a sample based on the researcher's convenience, like interviewing one textile industry.
• Judgment Sampling applies when researchers select the best sampling units based on their judgment, like interviewing only professional football players.
• Quota Sampling sets quotas for sampling units from specific subgroups; selection bias is introduced when the subgroup quota are met. i.e. interviewing 40 males and 70 females.
• Snowball Sampling helps when identifying members of a target population is difficult due to sensitivity, like in studies on HIV/AIDS or drug addiction.

Disadvantages of Non-Probability Sampling

• Samples may be unrepresentative of their target population, introducing bias.
• Sampling error is impossible to measure, which makes statistical inferences from sample data invalid.

Probability Random Sampling

• This is a selection method where population members have an equal chance of being selected
• Simple Random Sampling gives each population member an equal chance of selection, assuming a homogenous population where any member should be identical.
• Systematic Random Sampling is applied when a sampling frame exists, starting with a random selection of the first unit, followed by uniform interval selections.
• Stratified Random Sampling applies to heterogeneous populations, divided into homogeneous strata from which simple random samples are drawn.
• Cluster Random Sampling applies when the target population naturally divides into similar clusters; clusters are selected randomly for sampling.

Advantages of Random Sampling

• This reduces selection bias so sample statistics better estimate population parameters.
• Sampling error is calculable so inferential analysis is valid.

Statistical Methods and Valid Analyses

• Non-random methods like convenience, judgment, quota, and snowball utilize exploratory descriptive statistics.
• Random methods like simple, systematic, stratified, and cluster utilize descriptive and inferential statistics.

Sampling and Non-Sampling Errors

• Even with a matching frame, a sample may not perfectly represent a population; any mismatch results in sampling error.
• Sampling error is the difference between sample measurements and corresponding population measurements, a consequence of using samples instead of populations.
• Non-sampling error results from poor sample design, sloppy data collection, faulty instruments, and questionnaire bias.