Review of Basic Concepts Psychological Science 342 Advanced Statistics

Basic Terminology Descriptive statisticsDescriptive statistics XCentral tendency, variability XDisplaying data Inferential statisticsInferential statistics XPopulations and Samples XHypothesis testing Xt tests, ANOVA, Regression

Measurement Basics

Variables Define variableDefine variable XProperty of an object or event that can take on different values Discrete variableDiscrete variable XVariable that can take on only a small set of possible values Continuous variableContinuous variable XVariable that can take on any value Cont.

Variables --cont. Independent variablesIndependent variables XThose variables controlled by the experimenter Dependent variablesDependent variables XThose variables being measured XThe data or score

Random Assignment DefineDefine XEach P has an equal chance of being in any condition XEquates groups XDefines experimental (vs. correlational) procedure XIndependent/Predictor variable

Random Sampling DefineDefine XEach member of a population has an equal chance of being included XGeneralizability XDo psychologists use random sampling?

Scales of Measurement DefinitionDefinition Nominal scalesNominal scales Ordinal scalesOrdinal scales Interval scalesInterval scales Ratio scalesRatio scales

Sample Problems For each of the following identify the IV (s), DV(s), whether the variable is categorical or continuous, and level of measurementFor each of the following identify the IV (s), DV(s), whether the variable is categorical or continuous, and level of measurement

Sample Problems 1. People will read a paragraph more quickly if it has a title than if it doesn’t have a title.1. People will read a paragraph more quickly if it has a title than if it doesn’t have a title. 2. People from collectivist cultures have lower self-esteem than people from individualist cultures, and the difference is larger for males than for females.2. People from collectivist cultures have lower self-esteem than people from individualist cultures, and the difference is larger for males than for females.

Sample Problems 3. The right hemisphere is more specialized (i.e., faster) than the left hemisphere for negative emotion words and the left hemisphere is more specialized than the right hemisphere for positive emotion words.3. The right hemisphere is more specialized (i.e., faster) than the left hemisphere for negative emotion words and the left hemisphere is more specialized than the right hemisphere for positive emotion words.

Sample Problems 4. When taking an exam, increasing levels of noise is associated with better performance for extraverts than for introverts.4. When taking an exam, increasing levels of noise is associated with better performance for extraverts than for introverts. 5. People will retain more information if a text is written in an ugly font than if it is written in a non-ugly font.5. People will retain more information if a text is written in an ugly font than if it is written in a non-ugly font.

Sample Problems 6. People appear to be more outgoing on facebook than in real life.6. People appear to be more outgoing on facebook than in real life. 7. Reported well-being increases as a function of temperature (up to 80F) and whether or not it is sunny.7. Reported well-being increases as a function of temperature (up to 80F) and whether or not it is sunny.

Deciding on a Procedure Decision treeDecision tree What types of variables?What types of variables? How many groups or variables?How many groups or variables?

Choosing a Procedure Cont.

Choosing a Procedure Cont.

Choosing a Procedure

Notation Variable namesVariable names XX and Y Individual valuesIndividual values XX i X versus X iX versus X i Summation notationSummation notation X  X X  X 2 X(  X) 2 X  XY X  X  Y XConstants

Hypothetical data on family size by decade of 20th century

Displaying Data

The Sternberg Example One to five digits displayedOne to five digits displayed Followed by a single digitFollowed by a single digit Was single digit in first set?Was single digit in first set? Predictions of sequential processingPredictions of sequential processing Predictions of parallel processingPredictions of parallel processing

The Following is a Simple Demonstration. Click to Begin

Click Mouse Was the single digit in the comparison set?

Plotting Data HistogramsHistograms XValues of dependent variable on X axis discuss grouping or “bins”discuss grouping or “bins” XFrequency on Y axis XHistogram of Sternberg’s data

Histogram of Reaction Time

Stem-and-Leaf Display Stem-and-leaf of RxTime N = 300 Leaf Unit =

Scatterplots Plot two variables against each other.Plot two variables against each other. Points represent coordinates on each axis.Points represent coordinates on each axis. Dependent variable on Y axis.Dependent variable on Y axis. See next slide for exampleSee next slide for example

Scatterplot of Solar Radiation and Cancer

Describing Distributions SymmetrySymmetry ModalityModality XBimodal XUnimodal SkewnessSkewness XPositively skewed XNegatively skewed

Figure 3.9

Measures of Central Tendency

Mode The most common valueThe most common value There may be severalThere may be several Bimodal distribution has two distinct modes.Bimodal distribution has two distinct modes.

Median Center value in an ordered seriesCenter value in an ordered series XAverage of two center values for an even number of points Median locationMedian location Xlocation of central value Xdefined as (N + 1)/2

Mean What we normally call the “average”What we normally call the “average” Denoted as “xbar”Denoted as “xbar” Calculated asCalculated as This will be our most common statisticThis will be our most common statistic

Advantages & Disadvantages MeanMean XMost common statistic XEasily manipulated algebraically XGood statistical properties XEasily influenced by extreme scores MedianMedian XSlightly less desirable statistical properties than mean XMay not be good to ignore extreme values

Measures of Variability

The General Problem Central tendency only deals with the centerCentral tendency only deals with the center DispersionDispersion XVariability of the data around something XThe spread of the points Example: Mice and MusicExample: Mice and Music

Mice and Music Study by David MerrellStudy by David Merrell Raised some mice in quiet environmentRaised some mice in quiet environment Raised some mice listening to MozartRaised some mice listening to Mozart Raised other mice listening to AnthraxRaised other mice listening to Anthrax Dependent variable is the time to run a straight alley maze after 4 weeks.Dependent variable is the time to run a straight alley maze after 4 weeks.

Results Anthrax mice took much longer to runAnthrax mice took much longer to run Much greater variability in Anthrax groupMuch greater variability in Anthrax group XSee following graphs for Anthrax and Mozart XBoth X axes are 500 units wide We often see greater variability with larger meanWe often see greater variability with larger mean

Range and Related Statistics The rangeThe range XDistance from lowest to highest score XToo heavily influenced by extremes The interquartile range (IQR)The interquartile range (IQR) XDelete lowest and highest 25% of scores XIQR is range of what remains XMay be too little influenced by extremes

Trimmed Samples Delete a fixed (usually small) percentage of extreme scoresDelete a fixed (usually small) percentage of extreme scores Trimmed statistics are statistics computed on trimmed samples.Trimmed statistics are statistics computed on trimmed samples.

Deviation Scores DefinitionDefinition Xdistance between a score and a measure of central tendency Xusually deviation around the mean ImportanceImportance

Variance Definitional formulaDefinitional formula ExampleExample XSee next slide

Calculation

Standard Deviation Definitional formulaDefinitional formula XThe square root of the variance

Computational Formula

Estimators MeanMean XUnbiased estimate of population mean (  ) Define unbiasedDefine unbiased XLong range average of statistic is equal to the parameter being estimated. VarianceVariance XUnbiased estimate of  2 Cont.

Estimators--cont. XUsing gives biased estimate gives biased estimate XStandard deviation use square root of unbiased estimate.use square root of unbiased estimate.

Merrell’s Music Study SPSS Printout WEEK4 TreatmentMeanNStd. Deviation Quiet Mozart Anthrax Total

Boxplots The general problemThe general problem XA display that shows dispersion for center and tails of distribution Calculational steps (simple solution)Calculational steps (simple solution) XFind median XFind top and bottom 25% points (quartiles) Xeliminate top and bottom 2.5% (fences) XDraw boxes to quartiles and whiskers to fences, with remaining points as outliers Boxplots for comparing groupsBoxplots for comparing groups

Combined Merrell Data

Merrell Data by Group