Introduction to Statistics

Introduction to Statistics

• Statistics is the science focused on data collection, organization, presentation, analysis, and interpretation.

Purpose of Statistics

• Provides information and comparisons.
• Aids in discernment of relationships.
• Facilitates decision-making processes.
• Estimates unknown quantities and justifies claims.
• Predicts future outcomes.

Branches of Statistics

• Descriptive Statistics: Methods for collecting, organizing, summarizing, and presenting data.
• Inferential Statistics: Techniques for making predictions or inferences about a population based on sample data.

Population & Sample

• Population: Totality of all elements of interest.
• Sample: A subset of the population.

Census & Survey

• Census: Information collection from the entire population.
• Survey: Information collection from a sample.

Parameter & Statistics

• Parameter: Numerical measure describing a population.
• Statistic: Numerical measure describing a sample.

Constant & Variables

• Constant: Characteristic that makes members of a group similar.
• Variables: Measurable characteristics on all population or sample elements.

Types of Variables

• Qualitative (Categorical): Indicates "what kind" of characteristic.
• Quantitative (Numerical): Indicates "how much" of a characteristic.

Types of Quantitative Variables

• Discrete Variables: Countable values.
• Continuous Variables: Measurable values.

Dependent & Independent Variables

• Dependent Variable: Affected by another variable.
• Independent Variable: Influences the dependent variable.

Scales of Measurement

• Nominal: Categorical scale with no order.
• Ordinal: Categorical scale with an implied order.
• Interval: Numeric values with known distances, no true zero.
• Ratio: Numeric values with meaningful ratios and a true zero point.

Data Presentation

• Textual: Data presented in narrative form.
• Tabular: Data organized in tables, such as frequency distribution tables.

Steps in Constructing Frequency Distribution Table

• Define class size/width, lower and upper class limits, boundaries, midpoints, and relative frequency.

Graphical Presentation of Data

• Pie Chart: Represents any data type.
• Bar Graph: Represents discrete data with gaps; includes histograms for continuous data.
• Line Graph: Utilizes frequency polygons.

Sampling Techniques

• Population: Set including all measurements of interest.
• Sample: Subset of the population.

Types of Sampling

• Probability Sampling: Equal chances for each population member.
• Non-Probability Sampling: Unequal chances for selection.

Non-Probability Sampling Methods

• Convenience Sampling: Uses readily available subjects.
• Purposive Sampling: Targets specific predefined groups.

Probability Sampling Methods

• Simple Random Sampling (SRS): Each member has a chance of inclusion.
• Stratified Sampling: Divides population into strata for sampling.
• Cluster Sampling: Samples from selected clusters.
• Systematic Sampling: Selects every kth member.

Sample Size in Research

• Larger sample sizes yield more reliable results.

Hypothesis Testing

• Hypothesis: An educated guess about a population parameter.
• Null Hypothesis (Ho): A statement expected to be rejected.
• Alternative Hypothesis (Ha): Contradicts Ho and expresses the researcher’s intent.

Level of Significance (α)

• α = 0.05: 95% probability of being correct.
• α = 0.01: 99% confidence level.

Types of Hypothesis Tests

• One-tailed Tests: Predict direction of the effect.
• Two-tailed Tests: Examine differences in either direction.

F-Test (ANOVA)

• Compares means of two or more groups, analyzing variance.
• Types include one-way, two-way, and three-way ANOVA.

Pearson r Correlation

• Measures the relationship between two variables, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).
• Indicates strength and direction of relationships.

Simple Linear Regression Analysis

• Predicts the value of the dependent variable (y) based on the independent variable (x).

Multiple Regression Analysis (MRA)

• Predicts the dependent variable y using two or more independent variables, examining their relationships.

Chi-Square Test

• Compares observed and expected frequencies, includes tests for goodness-of-fit, homogeneity, and independence.