Summary
Highlights
Data is fundamental to statistical analysis. Observations are the individual entities from which data is collected (e.g., people, businesses), and variables record the specific measurements or characteristics of interest (e.g., age, sex, chocolate preference). In spreadsheets, each row represents an observation, and each column represents a variable.
The nominal level, also known as categorical or qualitative, is the most basic. Examples include sex or preferred chocolate type, which are labels without inherent order. Nominal data can be stored as text or numerical codes, but the numbers do not imply order. It's summarized using frequencies or percentages, and a mean cannot be calculated.
Ordinal variables have a meaningful order, but the intervals between values may not be equal (e.g., satisfaction levels, ranks). While frequencies are appropriate, calculating a mean for ordinal data is common in some research, but requires careful justification due to the unequal intervals.
The most precise level, interval/ratio data (also called scale, quantitative, or parametric), includes measurable quantities like age, weight, or number of customers. This data can be discrete (whole numbers) or continuous (fractional numbers) and is mathematically versatile. Common summary measures include the mean, median, and standard deviation.
The choice of graph depends on the level of measurement. Nominal data is best displayed with column or bar charts, and can also be shown in pie charts. Ordinal data should use column or bar charts, avoiding pie charts. Interval/ratio data is best represented by bar charts or histograms, often with data grouped, and line charts are suitable for time-series data.
A case study involving a questionnaire about 'choconutties' illustrates the concepts. Customer age, sex, spending, chocolate bar purchases, and satisfaction levels are analyzed. Chocolate preference is nominal, satisfaction/likelihood are ordinal, and age, spending, and chocolate bar purchases are interval/ratio, each requiring different summary and visualization techniques.
The appropriate statistical analysis for a given dataset is determined by its level of measurement. Understanding these levels is crucial for choosing sensible summary statistics, graphs, and analytical methods.