10/14/2003 Quant

Bivariate correlations

Examples from web-based study

Number of hitsà Final grade in course

Go back to web-based study and define all relationships being studied.

Correlation coefficient ( r ) indicates strength of relationship

Measuring artistic ability

Hours a day spent drawing

Parental ability

Eye-hand coordination

Visual acuity

Understanding of spatial relationships

Get a sample of kids, measure them on all variables.

If some of the variables are related, then we zero in on what exactly artistic ability might be.

Correlational Research

• Explanation of relationships between variables for better understanding
• Exploration of relationships between variables to develop or examine a theory of behavior
• Exploration of relationships between variables as a means of predicting future behavior

CORRELATION IS NOT CAUSATION. We aren't talking about causation right now.

Design requirements

• Measure same individuals on two or more different variables (at same or different times
• Measures of different individuals on the "same" variable"
• Measures of the same individuals on the "same" variables measured at different times

READ TIME ARTICLE BEFORE THURSDAY'S CLASS

"All of statistics is about relationships, but sometimes a design doesn't quite fit correlation as a method of analysis"

If you're talking about one school that has a lot of money and a school that doesn't and you want to look a the difference, then you'll be really helped out when it comes to T-testing.

Assumptions of Pearson r

• Sample size ~30
• Variables are continuous
• 
  Variables are distributed normally

Types of correlation coefficients – check table.

• Always check for normal distributions in data – st. dev., mean, median
• Nice if researchers either give above info or indicate that they have checked for normality. If they don't give either, DING em.
• There's a test in SPSS that checks for normality of data. There's one for skewness, and kurtosis too.

Reading the direction of relationship:

Tilt!

1. Positive: as x increases, y increases (high-high, low-low), from lower left to upper right.
2. Negative: as x increases, y decreases or vice versa (high-low, low-high) from upper left to lower right
3. None: no correlation

All up to a point – need to know range of subjects on which we are collecting data

Shape!

1. Strong relationship: Long & elongated (close to center line)
2. Moderate relationship: Still close to line, but more scattered
3. Weak relationship: Follows line, but spread out, loose, far from line