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Statistics

The science of collecting

Data

Facts and figures that are collected

Quantitative Data

Data that measure either how much or how many of something.

Qualitative Data

Data that provide labels

Descriptive Statistics

A method for organizing and summarizing data using tables or graphs and descriptive values.

Parameter

A descriptive value for a population.

Statistic

A descriptive value for a sample.

Measures of Central Tendency

Values that summarize a set of data by identifying the central point within that set.

Inferential Statistics

A method for using sample data to make general conclusions about populations.

Population

The entire group of individuals that a researcher is interested in studying.

Sample

A selected subset of a population used to represent the whole in a research study.

Variable

Any characteristic

Discrete Variables

Variables that consist of indivisible categories.

Continuous Variables

Variables that are infinitely divisible into whatever units a researcher may choose.

Levels of Measurement

A set of categories used to classify individuals in a measurement process.

Nominal Scale

Data created by assigning observations into various independent categories and counting the frequency of occurrence within each category.

Ordinal Scale

A scale in which scores indicate only relative amounts or rank order.

Interval Scale

A scale that not only ranks data but also specifies the distance between the ranks.

Ratio Scale

A scale that has a true zero point and allows for the comparison of absolute magnitudes.

Quantitative Data

Data that can be measured and expressed numerically.

Interval Scale

A scale in which equal differences in scores represent equal differences in the amount of the property measured

Ratio Scale

All the properties of an interval scale with the additional property of zero or absolute zero indicating a total absence being measured.

Sample Size

The proportion of the general population that are taking part in the study.

Slovin's Formula

A formula used to determine sample size

Probability Sampling Techniques

Sampling techniques where every unit in the population has a chance of being selected as a sample unit.

Simple Random Sampling

A sampling method where all members of the population have a chance of being included in the sample.

Systematic Sampling

A sampling method where the sampling frame is ordered and elements are selected at regular intervals.

Stratified Random Sampling

A method used when the population is too big to handle

Margin of Error

The amount of error that is acceptable in a statistical estimate

Sampling Frame

A list or database from which a sample is drawn.

k in Systematic Sampling

The interval at which elements are selected

nth Element Formula

The formula to find the nth element in systematic sampling

Random Start

The initial point chosen randomly in systematic sampling to begin selecting elements.

Overrepresentation

A situation where certain groups are represented more than others in a sample.

Population Size (N)

The total number of individuals in the population being studied.

Sample Size (n)

The number of individuals selected from the population for the study.

Confidence Level

The probability that the sample accurately reflects the population

Random Numbers

Numbers generated in such a way that each number has an equal chance of being selected.

Subgroups

Divisions of the population in stratified sampling

Uniform Representation

Ensuring that all sizes of firms are generally represented in the sample.

Example of Simple Random Sampling

Lottery sampling and using a table of random numbers.

Non-Probability Sampling

A random sampling technique where some units of the population have zero chance of selection or the probability of selection cannot be accurately determined.

Purposive Sampling

A form of non-probability sampling where researchers rely on their own judgment when choosing members of the population to participate in surveys.

Frequency Distribution

Provides information on the number of occurrences (frequency) of distinct values distributed within a given period of time or interval.

Grouped Frequency Distribution

A type of frequency distribution where data is organized into classes or intervals.

Ungrouped Frequency Distribution

A type of frequency distribution where data is listed as individual values.

Range

The difference between the largest and smallest values in a set of values

Class Size (K)

Calculated using the formula k = Range (R) / Number of classes (C).

Class Mark

The midpoint of the class interval

Relative Frequency

Calculated as [frequency per class / (n)] x 100.

Lower Boundary

Calculated by subtracting 0.5 from the lower limit per class.

Upper Boundary

Calculated by adding 0.5 to the higher limit per class.

Cumulative Frequency

The running total of frequencies for each class interval.

Mean

The most popular measure of central tendency

Median

The middle score for a set of data arranged in order of magnitude

Mode

The most frequent score in a data set

Standard Deviation (SD)

A measure of how spread out numbers are

Coefficient of Variation

A measure of relative variability

Sampling Bias

A systematic error that occurs when the sample is not representative of the population.

Sampling Error

The error caused by observing a sample instead of the whole population.

Convenience Sampling

A non-probability sampling technique where units are selected based on ease of access.

Quota Sampling

A non-probability sampling technique where researchers ensure equal representation of different subgroups.

Expert Sampling

A non-probability sampling technique where participants are selected based on their expertise in a specific area.

Snowball Sampling

A non-probability sampling technique where existing study subjects recruit future subjects from among their acquaintances.

Sigma Notation

A mathematical notation used to represent the sum of a sequence of terms.

Mean

Mean = σ fx / n

Median

Md = Lmd + (n/2 - σ fm−1) / fm

Mode

Mo = lmo + (fo−f1) / (2fo−f1−f2)

Frequency

The number of times a value occurs in a data set.

Class Mark

The midpoint of a class interval.

Range

Range = highest value - lowest value

Coefficient of Variation

cv = s / mean x 100

Normal Distribution

A bell-shaped frequency distribution curve where most data values cluster around the mean.

Characteristics of Normal Distribution

Normal distributions are symmetric

Z-Score

The standard score measuring how many standard deviations a value is from the mean.

Z-Score Formula for Sample

z = (x - x̄) / s

Z-Score Formula for Population

z = (x - μ) / σ

Area of Normal Curve

The total area under the normal curve is equal to 1.

Correlation

The statistical relationship between two entities

Pearson Product Moment Correlation Coefficient

r = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²][n(Σy²) - (Σy)²]

Spearman's Rank Correlation Coefficient

A non-parametric measure of the strength and direction of association between two variables measured on at least an ordinal scale.

Spearman's Rank Formula

p = 1 - [6Σd²] / [n(n² - 1)]

Strength of Correlation Interpretation

+1 Perfect positive correlation

+0.71 to +0.99

Strong positive correlation

+0.51 to +0.70

Moderately positive correlation

+0.31 to +0.50

Weak positive correlation

+0.01 to +0.30

Negligible positive correlation

0

No correlation

-0.01 to -0.30

Negligible negative correlation

-0.31 to -0.50

Weak negative correlation

-0.51 to -0.70

Moderately negative correlation

-0.71 to -0.99

Strong negative correlation

-1

Perfect negative correlation