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Understanding Research Results:Description and Correlation
Experimental PsychologyArlo Clark-Foos
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Understanding Research ResultsUnderstanding Research Results
• Descriptive Statistics • Inferential StatisticsDescriptive Statistics
– Organize
Inferential Statistics
– Estimates population g
– Summarize
Estimates population parameters using sample statistics
– Graphing
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Analyzing ResultsAnalyzing Results
1 Comparing Group Percentages1. Comparing Group Percentages– Nominal DV
Ex Gender differences in pizza preference– Ex. Gender differences in pizza preference
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Analyzing ResultsAnalyzing Results
2 Correlating Individual Scores2. Correlating Individual Scores– Interval or Ratio DV, IV not manipulated
Ex TV watching & academic performance– Ex. TV watching & academic performance
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Analyzing ResultsAnalyzing Results
3 Comparing Means3. Comparing Means– Interval or Ratio DV; IV manipulated,
controlcontrol– Ex. Sleep consolidates negative memories
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Analyzing ResultsAnalyzing Results
• Regardless of the type of data or type of comparison it is very important to comparison, it is very important to DESCRIBE your data ACCURATELY so that you UNDERSTAND itthat you UNDERSTAND it…
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Frequency DistributionsFrequency Distributions
Displays the number of individuals that Displays the number of individuals that receive each possible score on a variable.
Days with 2+ hours of TV
Frequency
7
6
5
44
3
2
1
0
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Graphing Frequency DistributionsGraphing Frequency Distributions
• Can simplify large data setsCan simplify large data sets
• See patterns more easily in visual displaysSee patterns more easily in visual displays
• May help you to get into graduate schoolMay help you to get into graduate school• GRE may drop geometry in favor of
interpretation of tables and graphste p etat o o tab es a d g ap s
• We won’t get fooled again!We won t get fooled again!
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Graphing Frequency DistributionsGraphing Frequency Distributions
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Graphing Frequency DistributionsGraphing Frequency Distributions
• Pie ChartsPie Charts– Divides a circle into slices that represent
relative percentages Poor visibilityrelative percentages…Poor visibility.
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Graphing Frequency DistributionsGraphing Frequency Distributions
• Bar GraphsBar Graphs– Visual depictions of data when the IV is nominal and the DV is
interval. Each bar typically represents the mean value of the DV for each categoryDV for each category.
– Pareto Chart: Ordered from smallest to largest
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Graphing Frequency DistributionsGraphing Frequency Distributions
• Pictorial GraphsPictorial Graphs– Simply a bar graph with pictures instead of
barsbars.
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Graphing Frequency DistributionsGraphing Frequency Distributions
• Frequency PolygonsFrequency Polygons– y-axis is the frequency of each score, with a
line connecting each dotline connecting each dot.
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Graphing Frequency DistributionsGraphing Frequency Distributions
• HistogramsHistograms– Similar to a frequency polygon, it uses bars
to display the frequency of each score on a to display the frequency of each score on a continuous variable. Bars touch!
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Descriptive StatisticsDescriptive Statistics
Central Tendency vs. Variability
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Descriptive StatisticsDescriptive Statistics
Central TendencyCentral TendencyA number(s) that summarizes the entire
data set How do the data cluster?data set…How do the data cluster?
VariabilityHow the sample is spread out in one or both p p
directions.
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Central Tendency: MeanCentral Tendency: Mean
Arithmetic AverageArithmetic Average– Interval or Ratio Data Only
XM Xμ = = = ∑M X
Nμ = = =
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Central Tendency: MedianCentral Tendency: Median
When data are ordered from lowest score to When data are ordered from lowest score to highest score, the median (Mdn) divides the group of scores in halfthe group of scores in half.
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Central Tendency: ModeCentral Tendency: Mode
The most frequently occurring score(s) The most frequently occurring score(s). – Unimodal, Bimodal, Multimodal
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Central Tendency: Best?Central Tendency: Best?
• Which is the best measure?Which is the best measure?
3 9 12 2 16 2 17 5 11 45 89 32 1 963 9 12 2 16 2 17 5 11 45 89 32 1 96
1 2 2 3 5 9 11 12 16 17 32 45 89 961 2 2 3 5 9 11 12 16 17 32 45 89 96
Mode = 2Median = 11.5Mean = 24.294 9
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Variability: RangeVariability: Range
• Range = Xhi h - XlRange = Xhighest Xlowest
Does not tell us much other – Does not tell us much, other than absolute spread
• How close to the mean?
• How far from the mean is the typical score?
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Variance & Standard DeviationVariance & Standard Deviation
• SD (s2 or σ): Average deviation or SD (s or σ): Average deviation, or difference, of a score from the mean.
• Variance = SD2
SD2 = Σ(X-M)2( )N
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Shapes of DistributionsShapes of Distributions
KurtosisKurtosis– Platykurtic, Mesokurtic, Leptokurtic
platykurtic leptokurtic
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Shapes of DistributionsShapes of Distributions
Skewness: How much one of the tails of the Skewness: How much one of the tails of the distribution is pulled away from the center.
Fl & C ili Eff tFloor & Ceiling Effects
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Lies Damned Lies & StatisticsLies, Damned Lies, & Statistics
• Misleading or Lying with GraphsMisleading or Lying with Graphs
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Correlation CoefficientsCorrelation Coefficients
• It’s all about the strength of relationshipsIt s all about the strength of relationships
• Correlation coefficient: St ti ti th t d ib • Correlation coefficient: Statistic that describes how strongly two or more variables are related.
• Pearson Product-Moment Correlation (r):Used for interval or ratio data only measures Used for interval or ratio data only, measures linear relationships between variables– Range of possible values: -1 ≤ r ≥ +1g p
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Correlation CoefficientsCorrelation Coefficients
Issues with…Issues with…
Restriction of range: Individuals are homogenous Restriction of range: Individuals are homogenous on the variable being studied.
Curvilinear (Nonmonotonic) Relationships
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Positive Correlation CoefficientsPositive Correlation Coefficients
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Negative Correlation CoefficientsNegative Correlation Coefficients
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Effect SizeEffect Size
Strength of relationship between variables Strength of relationship between variables. How much the variability in one variable is explained by the otheris explained by the other.
P ( ) C f Of D i i ( )Pearson (r) … Coef. Of Determination (r2)
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Regression EquationRegression Equation
Used to predict a score on one variable when Used to predict a score on one variable when the score on another variable is known. Uses correlation coef.
)(ˆ XbaY +=Criterion Variable: Future, to be predicted,
)(
behavior.Predictor Variable: Score being used to predict the
otherother.
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Multiple Regression/CorrelationMultiple Regression/Correlation
Combines several predictor variables to Combines several predictor variables to gain accuracy in predicting a criterion variablevariable.
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Partial CorrelationsPartial Correlations
Correlation between two variables with the Correlation between two variables, with the influence of a third variable removed from, or “partialed out of ” the original or partialed out of, the original correlation.
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Structural Equation Modeling (SEM)Structural Equation Modeling (SEM)
Examines a set of relationships among variables using the f p g gnonexperimental method. How well a model fits the data.
Path Analysis: A box model that uses arrows between boxes to depict relationships between variables.