Day 8 Table of Contents

• Review topics from last week
• Definition and purpose: correlational research
• Designing Correlational Research
• Data Analysis
• Analysis of Scores
• Descriptive Statistics: Normal curve
• Descriptive Statistics: Relative position
• Closure

Review

Descriptive research involves collecting numerical data to test hypotheses or answer questions concerning current status.

Instruments:	Self reported (questionnaire or interview); and observations
Advantages of self report:	Can assess a large number of people (questionnaires); or go in depth (interviews)
Limitations of self report:	Requires careful construction; Can't generalize if sample is not representative
Advantages of observations:	Reflects real-life skills or knowledge if done in field
Limitations of observations:	Must code observations; need to check reliability of observers
Descriptive statistics:	Central tendency (mean, mode, and median); Variability (range, quartile, and standard deviation)

Definition and purpose: correlational research

"Correlational research involves collecting data in order to determine whether, and to what degree, a relationship exists between two or more variables." Gay, p296.

Because scores with a range on one variable are related to scores within a range on another variable, predictions can be made.

• Is computer CPU clock speed of home computer related to success in school?
• Is age of EdTec graduates related to job satisfaction?

Correlational studies:

• Usually examine a complex, major idea by seeing how lesser variables relate to it
  • If variable doesn't relate, can drop from further analysis
  • If variable relates, can do a more expensive causal-correlational or experimental study
    
• Measure variables by the strength of their relationship (coefficient -1.00 to +1.00)
  • No correlation = 0.00

Designing Correlational Research

Sequence of events for a correlational study:

1. Identify variables to examine
   • based on deductive logic (suggested by theory) or inductive logic (based on experience)
   • a small number of carefully selected variables is better than a shotgun approach
     
2. select appropriate sample
   • should have at least 30 members who are available and willing to participate
     
3. administer instruments
   • must be a valid and reliable instrument
   • usually conducted faster than in causal-comparative or experimental studies
     
4. collect data on two or more quantifiable variables (numerical) analyze data

Data Analysis

The type of analysis is dependent on type of data gathered.

Analysis of subgroups can often yield better data than analysis of whole.

Analysis from Scores

The correlational coefficient tells strength and direction of relationship. The larger then number, the more the variables consistently move together.

• 0.00 to +1.00 is a positive relationship (when one goes up, so does the other
  
• 0.00 to -1.00 is a negative relationship (when one goes up, the other goes down).
  

The variance in scores on two variables, for a population, is due to two factors:

• score variance (IQs are not all the same for the population), and
• common variance (as IQ scores vary, so do the GPAs).
  

Common variance is the square of the correlational coefficient.

Descriptive Statistics: Normal curve

Many statistics assume the normal, bell-shaped curve distribution for scores.

Within a population, this is often the case, but may not be true of a sample.

• Sigma refers to the standard deviation of the population (a parameter), whereas
• SD refers to the standard deviation of a sample (a statistic).

The larger the sample, the closer SD approaches s.

A non-normal distribution is referred to as being skewed, and the mean, mode, and median will not be the same (as they are in a normal distribution). A negative skew trails off to the lower end, which pulls the mean and median towards the lower side.

The farther apart the mean and median, the more the distribution is skewed.

Descriptive Statistics: Relative position

The purpose of relative position is to allow you to compare scores from different tests.

Two basic types of relative position:

• Percentile Ranks (median will be at 50th percentile)
  Not used in research, but easily understood
• Standard scores (how far score is from standardized point--usually the mean--in standard deviations). This allows us to average scores from various tests. Assumes normal distribution, and test for specific population.
  
  • z Scores exactly match SD (0 at mean; +1 at 84% and -1 at 16%. Table A3 tells precise percentages for all z values; both positive and negative).
    formula is z = (raw score - mean) / SD
  • T Scores are z Scores manipulated to place the mean at 50 and a SD of 10.
    formula is T = 10z + 50
  • Stanines equal 1/2 SD (except the two ends with expand outward to catch any remainders), with the fifth stanine centered around the mean
    formula is stanine = 2z + 5

Closure; Review and Assignments

Review questions: (To find the answers, click on the question mark icon)

What is, and what is the purpose of, correlational research?
Why do researchers use correlational research if it can't identify cause and effect?
How do you identify variables to be examined in correlational research?
Explain what is meant by a correlational coefficient.
Explain the difference between a parameter and statistic, and identify the terms used to measure variability.
When will the mean be larger than the median?
Of what use are z and T scores

Before next week:

• Prepare for Midterm