Understanding Research Results:Description and Correlation

Experimental PsychologyArlo Clark-Foos

Understanding Research ResultsUnderstanding Research Results

• Descriptive Statistics • Inferential StatisticsDescriptive Statistics

– Organize

Inferential Statistics

– Estimates population g

– Summarize

Estimates population parameters using sample statistics

– Graphing

Analyzing ResultsAnalyzing Results

1 Comparing Group Percentages1. Comparing Group Percentages– Nominal DV

Ex Gender differences in pizza preference– Ex. Gender differences in pizza preference

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

Analyzing ResultsAnalyzing Results

3 Comparing Means3. Comparing Means– Interval or Ratio DV; IV manipulated,

controlcontrol– Ex. Sleep consolidates negative memories

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…

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

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!

Graphing Frequency DistributionsGraphing Frequency Distributions

Graphing Frequency DistributionsGraphing Frequency Distributions

• Pie ChartsPie Charts– Divides a circle into slices that represent

relative percentages Poor visibilityrelative percentages…Poor visibility.

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

Graphing Frequency DistributionsGraphing Frequency Distributions

• Pictorial GraphsPictorial Graphs– Simply a bar graph with pictures instead of

barsbars.

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.

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!

Descriptive StatisticsDescriptive Statistics

Central Tendency vs. Variability

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.

Central Tendency: MeanCentral Tendency: Mean

Arithmetic AverageArithmetic Average– Interval or Ratio Data Only

XM Xμ = = = ∑M X

Nμ = = =

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.

Central Tendency: ModeCentral Tendency: Mode

The most frequently occurring score(s) The most frequently occurring score(s). – Unimodal, Bimodal, Multimodal

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

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?

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

Shapes of DistributionsShapes of Distributions

KurtosisKurtosis– Platykurtic, Mesokurtic, Leptokurtic

platykurtic leptokurtic

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

Lies Damned Lies & StatisticsLies, Damned Lies, & Statistics

• Misleading or Lying with GraphsMisleading or Lying with Graphs

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

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

Positive Correlation CoefficientsPositive Correlation Coefficients

Negative Correlation CoefficientsNegative Correlation Coefficients

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)

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.

Multiple Regression/CorrelationMultiple Regression/Correlation

Combines several predictor variables to Combines several predictor variables to gain accuracy in predicting a criterion variablevariable.

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.

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.