Statistical Sampling and Analysis Techniques
Correlation Coefficients
Pearson Correlation Coefficient (r)
Measures the strength and direction of the linear relationship between two continuous variables.
Key Characteristics
- Range: r values range from -1 to +1.
- r = +1: Perfect positive linear relationship.
- r = -1: Perfect negative linear relationship.
- r = 0: No linear relationship.
Formula: 
Assumptions: Variables are continuous and normally distributed. The relationship between variables is linear. No significant outliers.
Applications: Assessing the
Read MoreStatistical Analysis of Data Distribution and Correlation
| Interval | Class Mark (Xi) | Mean (X) | Momentum in n and n = number raised to the point | Pearson |
|---|---|---|---|---|
| Linf – Lsup | (Linf + Lsup) / 2 | (xi – X) (xi – X) * nfi | b2 = moment4 / (σ2)2 (where σ2 is the population variance)
|
Data Distribution Analysis
The Pearson coefficient (B2) is based on the fourth moment about the mean.
For example, for samples of size 40:
- If B2 < 2.15, the distribution is negatively skewed (platykurtic).
- If B2 > 3.99, the distribution is positively skewed.
- If B2 > 3, the distribution is more pointed
Understanding Regression Analysis and Variable Relationships
Relationship Between Variables and Regression: The term “regression” was introduced by Galton in his 1889 book Natural Inheritance, referring to the universal law of regression: each peculiarity in a person is shared by their descendants, but on average, to a lesser degree (regression to the mean). His work focused on describing the physical traits of descendants (a variable) based on their parents (another variable).
Pearson (Galton’s friend) conducted a study of over 1,000 households, examining
Read MoreTest Validity and Reliability
True or False
V The validity coefficient cannot be higher than the index of reliability.
V The validity coefficient is affected by the reliability of the criterion.
F The standard error of estimate is the difference between obtained and predicted scores.
F The coefficient of validity is an indicator of the stability of scores.
F The validity coefficient of a test is independent of the homogeneity of the sample.
F The validity coefficient expresses the correlation between two parallel forms of a test.
V
Read MoreT-Tests, ANOVA, and Correlation in Statistical Analysis
T-Tests
Understanding T-Distributions
True Statement: The larger the sample size, the more a t distribution resembles a normal curve.
Estimating Population Variance
When estimating the variance of a population from a sample, the sample variance cannot be used directly because it tends to be slightly too small—it underestimates the population variance.
T-Test vs. Z-Test
The difference between a t test for a single sample and a Z test for a single sample lies in how the variance of the known population
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