Summary of "KULIAH STATISTIK - ANALISIS KORELASI"

Main ideas and concepts

Correlation analysis in educational statistics is used to determine the degree of relationship between two or more variables.
The relationship is quantified by a correlation coefficient (r), which describes:
- Form/direction of the relationship:
  - Positive: when one variable increases, the other tends to increase.
  - Negative: when one variable increases, the other tends to decrease.
- Magnitude/strength of contribution (how strong the relationship is).

Positive example: higher learning motivation → higher learning achievement.
Negative example: the longer Corona continues (more time in online learning) → students become bored → diligence decreases.

(Strength depends on the magnitude of the correlation coefficient.)

Simple correlation (focused for this course):
- Relationship between one independent variable (X) and one dependent variable (Y).
- Two methods:
  1. Pearson Product Moment (for interval/ratio data)
  2. Spearman Rank (for ordinal data)

Used when:

Variables/notations mentioned:

Formula (as described):

[ r = \dfrac{n\Sigma XY - (\Sigma X)(\Sigma Y)}{\sqrt{\left[n\Sigma X^2 - (\Sigma X)^2\right]\left[n\Sigma Y^2 - (\Sigma Y)^2\right]}} ]

Example described: sleep length vs emotional stability

Set hypotheses
- H0 (null): no relationship between sleep length and emotional stability (often described as “negative/no relationship”).
- H1 (alternative): there is a relationship.
Compute needed sums from the data
- Calculate: ( \Sigma X ), ( \Sigma Y ), ( \Sigma XY ), ( \Sigma X^2 ), ( \Sigma Y^2 )
- Determine n (number of observations).
Substitute into the Pearson formula to get r-count
- The example yields roughly r-count = 0.91 (stated as “0.913”/similar due to subtitle errors).
Decision rule using r-table
- If r-count ≤ r-table → H0 accepted
- If r-count > r-table → H0 rejected
Determine r-table
- Alpha given: α = 0.05
- Degrees of freedom mentioned as df = n − 2
- r-table obtained around 0.63 (subtitle contains some typos; the intended process is comparison with the table value).
Conclusion
- Because r-count > r-table, the conclusion is:
- Positive relationship between sleep length and emotional stability.

Six steps were explicitly mentioned as the completion structure for Pearson analysis.

Used when:

Formula (as described):

[ \rho = 1 - \dfrac{6\Sigma d^2}{n(n^2 - 1)} ]

Example described: start exam scores vs research methodology exam scores

Set hypotheses
- H0: no relationship between exam results.
- H1: there is a relationship.
Rank the data (from smallest to largest)
- Assign ranks to X values and Y values.
- Ties are handled by using an average rank approach:
  - If a value repeats (e.g., two equal scores), assign the mean of the ranks those positions would occupy.
Compute rank differences
- For each pair: ( d = \text{rank}_X - \text{rank}_Y )
- Then compute d²
Calculate Spearman correlation
- Substitute into the Spearman formula using n and Σd²
- Example yields r-count ≈ 0.854 (subtitle text shows “0.8 54”).
Determine criteria / r-table
- Uses α = 0.05
- Degrees of freedom approach mentioned similarly to Pearson (subtitle states df = n − 2, then references the table).
- r-table obtained around 0.648 (subtitle includes minor typos).
Conclusion
- Since r-count > r-table:
- H0 is rejected
- Conclude a positive relationship between the two exam results.

Choose the correct correlation method based on data scale:
- Interval/ratio → Pearson
- Ordinal → Spearman
Interpret correlation results using:
- Sign (positive/negative direction)
- Magnitude (strength using coefficient values and table comparison)
Use a statistical testing framework:
- Compute correlation coefficient (r-count)
- Compare with r-table at α = 0.05
- Decide accept/reject H0 and state the relationship direction (positive in both examples).