Statistical Analysis with Software Applications - Handout 01

Vocabulary flashcards covering core concepts in introductory statistics, data collection methods, sampling techniques, and data organization/presentation.

Statistics

The science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in decision-making.

Descriptive Statistics

The branch of statistics that involves organizing, summarizing, and presenting data to describe the characteristics of a dataset.

Inferential Statistics

The branch of statistics that involves making conclusions or predictions about a population based on information obtained from a sample.

Data

Raw facts or observations collected for analysis.

Population

The complete collection of individuals or objects under study.

Sample

A subset of the population selected for study.

Parameter

A numerical characteristic describing a population.

Statistic

A numerical value calculated from a sample.

Population vs. Sample Comparison

A tabular comparison highlighting key structural and analytical differences between an entire population and a subset sample.

Variable

Any characteristic that differs from one individual to another.

Qualitative Variable

A variable that describes qualities or categories, also known as a categorical variable.

Quantitative Variable

A variable that represents measurable quantities, also known as a numerical variable.

Discrete Variable

A quantitative variable obtained by counting.

Continuous Variable

A quantitative variable obtained by measurement.

Nominal Level

The level of measurement where data are classified into categories without any order.

Ordinal Level

The level of measurement where data are arranged in order.

Interval Level

The level of measurement with equal intervals but no true zero.

Ratio Level

The level of measurement with equal intervals and a true zero.

Primary Data

Data collected directly by the researcher for a specific purpose.

Secondary Data

Data previously collected by other individuals or organizations.

Statistical Notation Symbols

Standard symbols representing population parameters ($N$, $\nu$, $\bar{x}$, $\nu$, $s$, $\nu^2$, $s^2$) and sample statistics.

Data Collection

The systematic process of gathering information for statistical analysis and decision-making.

Census

A data collection process that gathers information from every member of the population.

Sample Survey

A data collection method that gathers information from only a portion of the population.

Sampling Frame

A list of all members of the population from which the sample is selected.

Sampling

The process of selecting a subset of individuals from a population to estimate the characteristics of the entire population.

Probability Sampling

Sampling methods in which each member of the population has a known and non-zero chance of being selected.

Simple Random Sampling

A probability sampling method where every member of the population has an equal chance of selection.

Systematic Sampling

A probability sampling method where every $k^{\text{th}}$ member is selected after a random starting point, where $k = \frac{N}{n}$.

Stratified Sampling

A probability sampling method where the population is divided into homogeneous groups called strata, and samples are randomly selected from each stratum.

Cluster Sampling

A probability sampling method where the population is divided into naturally occurring groups called clusters, and entire clusters are randomly selected.

Multistage Sampling

A probability sampling method that uses two or more sampling techniques in stages.

Non-Probability Sampling

Sampling methods in which not every member of the population has a known chance of selection.

Convenience Sampling

A non-probability sampling method where respondents are selected because they are easy to reach.

Purposive Sampling

A non-probability sampling method where respondents are selected based on the researcher's judgment.

Quota Sampling

A non-probability sampling method where researchers select respondents until predetermined quotas are met.

Snowball Sampling

A non-probability sampling method where current participants recruit future participants.

Sampling Error

The difference between the sample statistic and the true population parameter caused by studying only a sample instead of the entire population.

Non-Sampling Error

Errors that occur during data collection or processing that are not caused by sampling, including response error, nonresponse error, measurement error, processing error, and interviewer bias.

Bias

A systematic error that causes results to differ from the true population values.

Observational Study vs. Experiment Comparison

A comparative guide showing differences between observational studies (no variable manipulation, lower cost, cannot establish causation) and experiments (variable manipulation, tests cause-and-effect).

Raw Data

Observations collected in their original form before being organized or summarized.

Organized Data

Data arranged systematically into tables or graphs.

Frequency Distribution

A table that shows how often each value or group of values occurs.

Ungrouped Frequency Distribution

A frequency distribution used when there are relatively few observations or distinct values.

Grouped Frequency Distribution

A frequency distribution used for large datasets where observations are grouped into class intervals.

Range

The difference between the highest value and the lowest value in a dataset, calculated as $\text{Range} = \text{Highest Value} - \text{Lowest Value}$.

Sturges' Rule

A guideline formula used to estimate the recommended number of classes $k$ based on sample size $n$: $k = 1 + 3.322 \log(n)$.

Recommended Classes Table

A reference table listing suggested numbers of class intervals based on the total number of observations.

Class Interval

The range of values within a class.

Lower Class Limit

The smallest value in a class interval.

Upper Class Limit

The largest value in a class interval.

Class Boundaries

The actual limits separating adjacent classes.

Class Mark (Midpoint)

The midpoint of a class interval, calculated as $\text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$.

Frequency

The number of observations belonging to a class.

Relative Frequency

The proportion or percentage of observations in a class, calculated as $\text{Relative Frequency} = \frac{f}{n}$.

Cumulative Frequency

The running total of frequencies across sequential class intervals.

Bar Graph

A graphical display used for qualitative or categorical data with equal bar widths separated by spaces.

Pie Chart

A chart representing parts of a whole where category sector angles are calculated as $\text{Angle} = \frac{\text{Category Frequency}}{\text{Total Frequency}} \times 360^{\circ}$.

Histogram

A graph used for continuous quantitative data featuring adjacent touching bars whose widths represent class intervals and heights represent frequencies.

Bar Graph vs. Histogram Comparison

A comparison table contrasting bar graphs (categorical data, separated bars, categories) with histograms (continuous data, touching bars, class intervals).

Frequency Polygon

A line graph constructed by connecting the midpoints of each class interval using straight lines.

Ogive

A graph displaying cumulative frequencies (less-than or more-than) used to determine medians, quartiles, and percentiles.

Line Graph

A graph used to display changes over time in time series data.

Scatter Plot

A graph showing the relationship between two quantitative variables.

Stem-and-Leaf Plot

A plot that displays actual data values while showing the distribution by splitting numbers into stems and leaves.

Data Type and Recommended Graph Guide

A reference guide pairing data types (Categories, Percentages, Continuous Data, Time Series, Relationships, Frequency Distribution, Cumulative Data) with their recommended statistical graphs.