Q4_W5 PR 2

Practical Research 2

Statistics Overview

• Statistics is integral to quantitative research, dealing with the mathematical treatment of variability.

• Applied Statistics: Utilizes already developed and accepted methodologies to aid in research.

Descriptive Statistics

• Summarizes and organizes the characteristics of a data set.

• Data Set: A collection of responses or observations from a sample or population.

• Main Types:

  • Distribution: Frequency of each value in the data.

  • Central Tendency: Averages of the values.

  • Variability: Spread of the values.

Measures of Descriptive Statistics

• Distribution: Characteristics of data values.

• Central Tendency:

  • Mean: Average of all values.

  • Median: Middle value in an ordered set.

  • Mode: Most frequently occurring value.

• Measures of Variability:

  • Range: Difference between highest and lowest values.

  • Standard Deviation: Measure of data spread around the mean.

  • Variance: Average of the squared deviations from the mean.

  • Interquartile Range: Difference between the first and third quartile.

Types of Data Distribution

• Data Distribution: Represents how values are spread, shown using tables, graphs, or histograms.

  • Normal Distribution (Bell Curve): Most values cluster around the mean.

  • Skewed Distribution:

    • Right-skewed: More values on the left.

    • Left-skewed: More values on the right.

  • Uniform Distribution: All values equal in frequency.

Central Tendency

• Mean Calculation: Sum of values divided by the number of values:

  • Example: Test scores calculation, average = 80.

• Median: Middle value of arranged numbers.

  • If odd, single middle value; if even, average of two middle values.

• Mode: Value appearing most frequently, can be bimodal or multimodal.

Measures of Variability

• Dispersion: How tightly or widely values cluster around the mean.

• Range:

  • Formula: Range = Maximum Value - Minimum Value.

  • Example: Range of test scores is 30 points.

• Standard Deviation: Indicates spread of values with respect to the mean.

  • High standard deviation: data widely spread.

  • Low standard deviation: values close to mean.

  • Formula: σ = √(Σ(xi - μ)² / N)

  • Example: Standard deviation for student heights:

    • Mean height ≈ 165 cm, Standard deviation ≈ 10.8 cm.

Inferential Statistics

• Procedures to conclude associations between variables.

• Tests hypotheses:

  • Considers if findings from a sample apply to the larger population.

• Hypothesis forms:

  • Null Hypothesis: No effect or difference.

  • Alternative Hypothesis: There is an effect or difference.

Analysis Types

• Two-group Comparison: Analyzes posttest outcomes of treatment vs. control groups.

  • Uses t-tests or ANOVA (Analysis of Variance) for statistical tests.

• t-test: Compares means of two groups to check for significant differences.

Bivariate Analysis

• Analyzes two variables at a time to determine relationships.

• Helps to make predictions about dependent variables based on independent variables.

Pearson Correlation Coefficient

• Measures relationships between interval/ratio variables:

  • Coefficient (r) ranges from -1 to 1.

  • Positive r: positive relationship; Negative r: negative relationship; r=0: no relationship.

  • Interpretation of correlation sizes provided.

Spearman's rho

• Used for ordinal data or where assumptions for Pearson correlation aren't met.

  • Measures strength and direction of association between ranked variables.

Chi-Square Test

• Applied to contingency tables, assesses relationships between two categorical variables.

• Goodness of Fit: Tests if sample data matches population distribution.

• Test of Independence: Examines associations between two categorical variables.

• Homogeneity: Compares distributions across different populations.

Conclusion

• Reinforces understanding of statistics and its importance in research.

Thank you!