Introduction to Statistics

Introduction to Statistics

• Statistics: Branch of applied mathematics involving collection and interpretation of data.

• Two main categories: descriptive statistics and inferential statistics.

Descriptive Statistics

• Purpose: Summarize data and interpret results.

• Measures of Central Tendency: Mean, median, and mode.

• Measures of Variation: Range, variance, and standard deviation.

• Visualization: Various methods to visually present data.

• Continuous Data: Plural; individual metrics are referred to as datum.

• Variables: Characteristics measured, including length, height, weight, and height measured in various units (e.g., meters, inches).

Continuous Data Details

• Can be expressed as decimals; examples include:

  • Length: meters, kilometers, miles

  • Height: usually expressed in feet/inches

  • Weight: pounds, kilograms

  • Other examples: calories, blood pressure.

Categorical Data

• Definition: Data expressed as labels, not in fractions or decimals.

• Examples include gender, nationality, and food preferences.

• Always discrete: you cannot have half a designation.

Mixed Characteristics of Data

• Some continuous data can have discrete characteristics (e.g., game scores: you can't score half a point).

• Research implications of classifying data types.

Inferential Statistics

• Purpose: Drawing conclusions about populations based on sample data.

• Population: Totality of cases sharing a characteristic (e.g., students at a specific university, types of cars).

Challenges in Population Studies

• Practicality: Collecting data from an entire population is often impractical and costly.

• Example: Census data was affected by the COVID-19 crisis, illustrating difficulties in population sampling.

Sample Collection Techniques

• Collecting multiple samples can increase representation accuracy.

• Randomization techniques improve sample quality and representation of populations.

• Convenience sampling is less ideal; try to mimic ideal sampling arrangements.

Statistics Types

• Parametric Statistics: Used with interval or ratio data, normally distributed with sufficient sample size.

• Non-Parametric Statistics: Used with nominal and ordinal data, or with skewed data.

Scales of Measurement

• Nominal Data: Categorical labels (e.g., gender, ethnicity).

• Ordinal Data: Ranked order without equal intervals (e.g., race placements, satisfaction ratings).

  • Ranks do not ensure equal increments.

• Dichotomous Data: Data with only two categories (e.g., yes/no).

• Continuous Data: Includes interval and ratio data.

  • Interval Data: Equal increments, but zero does not indicate absence (e.g., temperature).

  • Ratio Data: Equal increments with a true zero point (e.g., height, weight).

Special Cases of Data

• Count Data: Discontinuous and discrete; can be used to represent quantities (e.g., number of students).

• Continuous and discrete qualities: E.g., the average number of students can be expressed as fractions.

Variables in Research

• Independent Variables (IV): Manipulated by researchers.

• Dependent Variables (DV): Observed or measured outcomes influenced by IV.

• Importance of distinguishing IV and DV in research.

Identifying IV and DV

• DV is what is being measured; IV is manipulated or categorized.

• Use terms like grouping variable or treatment variable for IV.

Hypotheses in Research

• Research Hypotheses: Statements predicting relationships between IV and DV.

• Null Hypothesis: States there is no effect or relationship.

Statistical Symbols and Analysis Tools

• Mean (μ) for population, mean (x̄) for sample.

• Standard deviation (σ) for population, (s) for sample.

• Software Tools: Use of JASP (free) and SPSS (not required but available)

  • JASP download instructions provided during course discussion.