Correlation Analysis

Vocabulary flashcards covering correlation analysis, interpretations of correlation coefficients, and work-life earnings data based on educational attainment.

Negative Correlation

A relationship where the variables are varying in opposite directions, as shown on Page 7.

Doctoral degree (Earnings)

Synthetic Work-Life Earnings estimated at $3.4$\text{ million of } 1999\text{ dollars}.$$

Professional degree (Earnings)

Synthetic Work-Life Earnings estimated at $4.4$\text{ million of } 1999\text{ dollars}.$$

Master's degree (Earnings)

Synthetic Work-Life Earnings estimated at $2.5$\text{ million of } 1999\text{ dollars}.$$

Bachelor's degree (Earnings)

Synthetic Work-Life Earnings estimated at $2.1$\text{ million of } 1999\text{ dollars}.$$

Associate's degree (Earnings)

Synthetic Work-Life Earnings estimated at $1.6$\text{ million of } 1999\text{ dollars}.$$

Some college (Earnings)

Synthetic Work-Life Earnings estimated at $1.5$\text{ million of } 1999\text{ dollars}.$$

High school graduate (Earnings)

Synthetic Work-Life Earnings estimated at $1.2$\text{ million of } 1999\text{ dollars}.$$

Not high school graduate (Earnings)

Synthetic Work-Life Earnings estimated at $1.0$\text{ million of } 1999\text{ dollars}.$$

Very Strong Relationship

A general interpretation for a coefficient size ranging from $0.8\text{ to } 1.0$.$$

Strong relationship

A general interpretation for a coefficient size ranging from $0.6\text{ to } 0.8$.$$

Moderate relationship

A general interpretation for a coefficient size ranging from $0.4\text{ to } 0.6$.$$

Weak relationship

A general interpretation for a coefficient size ranging from $0.2\text{ to } 0.4$.$$

Very Weak or No relationship

A general interpretation for a coefficient size ranging from $0.0\text{ to } 0.2$.$$

Correlation = +0.05

A visual representation showing no discernible linear association between variables x and y.

Correlation = +0.7

A visual representation showing a strong positive association between variables x and y.

Correlation = +0.99

A visual representation showing a very strong (near perfect) positive association between variables x and y.

Correlation = -0.7

A visual representation showing a strong negative (inverse) relationship between variables x and y.

Prejudice Score and Education

An example of variables that exhibit a negative correlation, where higher education typically relates to lower prejudice.

Case 1: Perfect association

A scenario where the relationship between variables is absolute and consistent.

Case 2: Strong association

A scenario where data points cluster closely to a trend line but are not perfectly aligned.

Case 3: Weak association

A scenario where a trend is visible but data points are widely scattered.

Case 4: No association

A scenario where there is no visible trend or relationship between two variables.

Synthetic Work-Life Earnings

Estimates for full-time, year-round workers categorized by educational attainment.

Figure 3 Source

U.S. Census Bureau, Current Population Surveys, March 1998, 1999, and 2000.

Correlation (Dilbert Example)

A statistical analysis exploring the link between disk storage and employee absenteeism.

X-variable example (increasing)

The values $2, 4, 6, 8, 10$ used to demonstrate an independent variable in a negative correlation table.

Y-variable example (decreasing)

The values $9, 7, 5, \text{etc.}$ used to demonstrate a dependent variable in a negative correlation table.

X-variable example (high to low)

The values $50, 40, 30, 20, 10$ used to show the relationship between variables in opposite directions.

Y-variable example (low to high)

The values $24, 26, 28, 30, 32$ representing inverse movement relative to X.

March 1998, 1999, 2000

The specific months and years of the Current Population Surveys used for earnings estimates.

Millions of 1999 dollars

The unit of measurement utilized for the synthetic work-life earnings data set.

Negative Correlation (Definition 2)

Variables that move in opposite directions; as one variable increases, the other decreases.

Coefficient Size 0.8 to 1.0

Interpreted as having a Very Strong Relationship in correlation analysis.

Coefficient Size 0.4 to 0.6

Interpreted as having a Moderate relationship in statistical analysis.

Coefficient Size 0.0 to 0.2

Interpreted as having a Very Weak or No relationship.

Positive Correlation Sign

Represented by the plus sign ($+$, as in $+0.7$) indicating variables move in the same direction.

Negative Correlation Sign

Represented by the minus sign ($$, as in $-0.7$) indicating variables move in opposite directions.

Correlation Coefficient

A numerical index ranging from $-1.0$ to $+1.0$ that quantifies the strength and direction of a relationship.

Educational Attainment

The independent variable in Figure 3 used to predict Work-Life Earnings Estimates.

Highest Earnings Level

Professional degrees, with an estimated $4.4$\text{ million dollars in synthetic earnings.}$$

Second Highest Earnings Level

Doctoral degrees, with an estimated $3.4$\text{ million dollars in synthetic earnings.}$$

Lowest Earnings Level

Not high school graduate, with an estimated $1.0$\text{ million dollars in synthetic earnings.}$$

High School Graduate (Earnings Value)

Estimated at $1.2$\text{ million dollars according to the Census Bureau data.}$$

Associate's Degree (Earnings Value)

Estimated at $1.6$\text{ million dollars, higher than 'some college' and 'high school graduate'.}$$

Bachelor's Degree (Earnings Value)

Estimated at $2.1$\text{ million dollars, serving as the benchmark for a 4-year degree.}$$

Full-Time, Year-Round Workers

The specific demographic used to calculate the Synthetic Work-Life Earnings Estimates.

Inverse Relationship

Another term for negative correlation where variables vary in opposite directions.

Strong association visualization

Data represented by a correlation of $+0.7$ or $-0.7$, showing clear linear clustering.

Data-less Statistics (Dilbert Mockery)

A satirical reference to performing statistical analysis without actually having data.