STATISTICS-FOR-QUANTITATIVE-RESEARCH-3

Statistics in Research

  • Definition: Statistics refers to mathematical techniques for collecting, analyzing, interpreting, and presenting data.

  • Purpose: Helps to deduce the soundness of claims in social sciences using scientific terms and organizational elements.

  • Applications: Utilized across various disciplines to build inference models and aiding planning and analysis in social contexts.

  • Roles: Statisticians and others across disciplines provide assistance in hypothesis testing and methodical presentation of findings.

  • Limitations: Results can be misleading without proper methodology and knowledge of probabilities in sampling.

Descriptive Statistics

  • Overview: Analyzes data to describe, summarize, or show meaningful patterns.

  • Limitations:

    • Only offers summations about the measured data.

    • Cannot generalize findings to others not measured.

Measures of Central Tendency

  • Mean: Average of all data points.

  • Median: Middle value that divides data into two equal halves.

  • Mode: Most frequently occurring value in a dataset.

Measures of Dispersion

  • Variance: Measures how much the data varies from the mean.

  • Standard Deviation: Indicates how much individual data points deviate from the mean.

  • Coefficient of Variation: Ratio of the standard deviation to the mean, useful for comparing variability.

Measures of Position

  • Quantiles: Divide data into equal-sized groups.

  • Percentiles: Indicate the value below which a given percentage falls.

Measures of Shape

  • Skewness: Measures the asymmetry of the data distribution.

  • Kurtosis: Describes the peakedness or flatness of the distribution compared to a normal distribution.

Inferential Statistics

  • Definition: Techniques used to analyze sample data and make generalizations about a population from which the sample is derived.

  • Limitations:

    • Requires educated arguments to conduct tests since population data may not be fully measured.

Process of Inferential Statistics

  1. Draw a sample from a population.

  2. Analyze the sample (Descriptive Statistics).

  3. Extend findings to form generalizations about the whole population (Inferential Statistics).

Statistical Methods and Examples

Descriptive vs Inferential

  1. Descriptive Example: Calculating mean test scores of a specific class of 30 students.

  2. Inferential Example: Generalizing findings from a sample of Grade 12 students to the entire population.

Basic Statistical Methods

  • Census vs Survey: Different methodological approaches to data collection.

  • Randomization Techniques: Key to ensuring validity in sampling – includes nonprobability and probability sampling.

  • Hypothesis Testing: Establishes a framework for testing predictions with a defined level of significance.

Types of Data and Statistical Tests

  • Null Hypothesis: A statement asserting there is no effect or association, used in hypothesis testing.

  • Examples:

    • Chi-Square Test for nominal data.

    • Mann Whitney U-test for ordinal data comparison.

Charts and Graphs

  • Types of Charts:

    • Line Chart: Displays trends over a period.

    • Bar Graph: Illustrates magnitude for categories.

    • Pie Chart: Shows proportions.

    • Scatter Plot: Depicts relationships between two quantitative variables.

Summary of Commonly Used Statistical Methods

  • Different tests applicable based on data type and comparison needs, structured around nominal, ordinal, and interval/ratio data classifications.

References

  • Añez-Tandang, N. (2019). Statistical Methods and Analysis.

  • Begum, K. J., & Ahmed, A. (2015). Importance of Statistical Tools in Research.

  • Additional resources providing context on statistical applications and methodologies.