330 - Discussion 6
yankeedoodle
cozby11_ppt_ch12.pptUNDERSTANDING RESEARCH RESULTS: DESCRIPTION AND CORRELATION
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Contrast three ways of describing result
Compare group percentages
Correlating scores
Comparing group means
Describe frequency distributions
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Describe the measures of central tendency and variability
Define a correlation coefficient
Define effect size
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Describe the use of a regression equation and a multiple correlation to predict behavior
Discuss how a partial correlation addresses the third-variable problem
Summarize the purpose of structural models
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Nominal
No numerical, quantitative properties
Levels represent different categories or groups
Ordinal
Order the levels from lowest to highest
Interval
Intervals between levels are equal in size
Can be summarized using means
No absolute zero
Ratio
Equal intervals
Absolute zero
Can be summarized using mean
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Three basic ways to describe results:
Comparing Group Percentage
Correlating Individual Scores
Comparing Group Means
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Graphing Frequency Distributions
Pie charts
Bar graphs
Frequency polygons
Histograms
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Central Tendency
Mean
Found by adding all the scores and dividing by the number of scores
Indicates central tendency with interval or ratio scales
Median (Mdn)
The middlemost score, or score that divides the group in half (with 50% scoring below and 50% scoring above the median)
Indicates central tendency with ordinal, interval, and ratio scales
Mode
Most frequently occurring score
Indicates central tendency with all scales including nominal scales
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Variability – the amount of spread in the distribution of scores
Standard deviation = (s) (SD) in reports
Range
Difference between highest and lowest score
Variance (s²)
Square of the standard deviation
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y-axis or ordinate
x-axis or abscissa
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Pearson r: the Correlation Coefficient
Pearson’s r indicates:
Strength of relationship
Direction of relationship
Values of r range from 0.00 to ±1.00
Can be described visually using scatterplots
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Restriction of Range
Curvilinear Relationship
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Refers to the strength of association between variables
Pearson r is one indicator of effect size
Advantage of reporting effect size is that it provides a scale of values that is consistent across all types of studies
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- Differences in effect sizes
- Small effects near r = .15
- Medium effects near r = .30
- Large effects above r = .40
- Squared value of the coefficient r² - transforms the value of r to a percentage
- Percent of shared variance between the two variables
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Infers whether the results will hold up if the experiment is repeated several times, each time with a new sample of research participants
Inferential Statistics
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Calculations used to predict a person’s score on one variable when that person’s score on another variable is already known
General Form:
Y = a + bX
Y = Score we wish to predict
X = Score that is known
a = constant
b = weighing adjustment
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Used to combine a number of predictor variables to increase the accuracy of prediction of a given criterion or outcome variable
Symbolized R
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Provides a Way of Statistically Controlling Third Variables
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- Structural Equation Models
- Describe expected pattern of relationships between / among quantitative, non-experimental variables
- After data collection statistics describe how well the data fits the model
- Path diagrams
- A visual representation of the model being tested
- Show theoretical causal paths
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- Path analysis
- Used to study modeling
- Arrows lead from variable to variable
- Statistics provide path coefficients
- Similar to standardized weights in regression equations
- Indicate the strength of relationship between variables in the path
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Expected Pattern of Relationships Among a Set of Variables
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