Statistical Methods and Research Design Fundamentals

Population vs. Sample

The population represents the total universe of all possible observations, whether real or theoretical, while a sample is a subset of those observations. In experimental research, it is crucial to draw a representative, random sample that is not biased.

Frequency Distribution

A frequency distribution provides a numerical representation of data, helping to create a mental picture of how linguistic phenomena perform.

Descriptive Statistics

• Mode: The most frequent mark. It is quick to identify with a frequency distribution and is applicable to categorical data.
• Median: The score in the middle of an ordered list. It divides data into halves. It does not account for the values of all scores, only those in the middle position, making it a good estimate for abnormally large or small values.
• Mean: The sum of scores divided by the number of scores. Every score is taken into account. It is the most widely used measure, calculated as x = Σx / N.

Types of Scales

• Nominal: Distinguishing by name (e.g., 1. Male, 2. Female; meal preferences).
• Ordinal: Nominal information plus direction (e.g., low, medium, high; faster or slower).
• Interval: Provides information about order and equal intervals between values.
• Rational: Possesses the qualities of nominal, ordinal, and interval scales.

Measures of Variability or Dispersion

• Variance: The sum of squared deviations from the mean.
• Standard Deviation: The square root of the variance.
• Standard Score (z-score): The deviation of a given score from the mean in terms of standard deviations.
• Standard Error (SE): The standard error of the mean.

Normal Distribution

Also known as the Gaussian distribution.

Variables

• Independent Variable: Manipulated by the experimenter; determines the values and may have different levels.
• Dependent Variable: The measure of behavior.

Trial Process

1. Alternative hypothesis
2. Null hypothesis
3. Standard of judgment
4. Data sample

Hypothesis Testing

• Alternative Hypothesis: The hypothesis researchers wish to evaluate.
• Null Hypothesis: The logical opposite of the alternative hypothesis.
• Type I Error: Rejecting the null hypothesis when there is no actual relation between dependent and independent variables.
• Type II Error: Failing to reject the null hypothesis when there is an existing relation between variables.

Tuckman's Criteria for Hypotheses

A hypothesis must be stated clearly and unambiguously in the form of a declarative sentence and must be testable.