Data Analysis (continued)Data Analysis (continued)

Analyzing the Results of Analyzing the Results of Research InvestigationsResearch Investigations

Two basic ways of describing the resultsTwo basic ways of describing the results1.1. Descriptive statistics (n, %, mean, sd)Descriptive statistics (n, %, mean, sd)

2.2. Inferential statisticsInferential statistics1.1. Correlations/regressionsCorrelations/regressions

2.2. Comparing group means (t-tests: Comparing group means (t-tests: tt, ANOVA: , ANOVA: FF))

3.3. Comparing percentages (Chi Square: Comparing percentages (Chi Square: χχ22))

Graphing DataGraphing DataLevels of IV are on horizontal x-axisLevels of IV are on horizontal x-axisDV values are shown on the vertical y-axisDV values are shown on the vertical y-axis

y-axis

x-axis

Inferential Inferential Statistics:Statistics:

Interpreting dataInterpreting data

What are inferential statistics?What are inferential statistics?

They are a tool used to determine whether They are a tool used to determine whether or not there is a true relationship between or not there is a true relationship between variables or difference between groupsvariables or difference between groups

They are grounded in They are grounded in probability theory.probability theory.

Probability TheoryProbability Theory

procedures/rules used to predict eventsprocedures/rules used to predict events

e.g. regression toward the meane.g. regression toward the mean

True score + random errorTrue score + random errorRandom error will be responsible for some Random error will be responsible for some

difference between groups/scoresdifference between groups/scores

Inferential StatisticsInferential Statistics

Uses:Uses:

1.1. basic probability theorybasic probability theory

2.2. our knowledge about what things should our knowledge about what things should ‘normally’ look like‘normally’ look like

to figure out if what we observe we could to figure out if what we observe we could have observed by chance alonehave observed by chance alone

Samples and PopulationsSamples and Populations

Samples are a subset of a population that Samples are a subset of a population that we hope represents the populationwe hope represents the population

Inferential statistics help determine how Inferential statistics help determine how likely it is we would obtain the same result likely it is we would obtain the same result using numerous samplesusing numerous samples

E.g. “95% Confidence Interval”E.g. “95% Confidence Interval”

““The president’s approval rating is at 31%, The president’s approval rating is at 31%, + or – 3 percentage points, with a 95% + or – 3 percentage points, with a 95% confidence interval.confidence interval.

takes sample size into account (the bigger takes sample size into account (the bigger the sample, the more representative of the the sample, the more representative of the population)population)

Null and Research HypothesesNull and Research Hypotheses

Null hypothesis Null hypothesis HHoo: there is no difference between groups: there is no difference between groups

Research hypothesisResearch hypothesisHH11: there is a difference between groups: there is a difference between groups

Null and Research Hypotheses Null and Research Hypotheses

Goal of research is to reject the null hypothesis Goal of research is to reject the null hypothesis and accept the research hypothesisand accept the research hypothesis

Null hypothesis is rejected when there is a low Null hypothesis is rejected when there is a low probability that the results could be due to probability that the results could be due to random error = random error = statistical significancestatistical significance

if we don’t find a statistically significant if we don’t find a statistically significant difference, we ‘fail to reject the null hypothesis’difference, we ‘fail to reject the null hypothesis’

Probability and Sampling Probability and Sampling DistributionsDistributions

What is the probability of obtaining the What is the probability of obtaining the observed results if ONLY random error is observed results if ONLY random error is operating?operating?

Probability required for significance is Probability required for significance is called the called the alpha level alpha level (e.g. .05, .01, .001) If probability is low (.05 or less), reject the null If probability is low (.05 or less), reject the null

hypothesishypothesis If probability is high (over .05), fail to reject the If probability is high (over .05), fail to reject the

null hypothesisnull hypothesis

Type I and Type II ErrorsType I and Type II Errors

Type I: Made when the null hypothesis is Type I: Made when the null hypothesis is rejected but the null hypothesis is actually rejected but the null hypothesis is actually truetrue

Type II: Made when the null hypothesis is Type II: Made when the null hypothesis is accepted although in the population the accepted although in the population the research hypothesis is trueresearch hypothesis is true

What does it mean if results are What does it mean if results are nonsignificant?nonsignificant?

could mean that there is no relationshipcould mean that there is no relationship

could be a Type II errorcould be a Type II errorweak manipulationweak manipulationdependent measure not adequatedependent measure not adequateother noise interferedother noise interfered low alpha levellow alpha levelsmall sample sizesmall sample size

Correlation CoefficientCorrelation Coefficient

Numerical index that reflects the Numerical index that reflects the relationship between 2 variablesrelationship between 2 variables

Ranges from –1 to +1Ranges from –1 to +1

Pearson product-moment correlation or Pearson product-moment correlation or Pearson’s Pearson’s rr

Understanding a correlationUnderstanding a correlationEyeballing your dataEyeballing your data

.8 to 1.0.8 to 1.0 Very StrongVery Strong

.6 to .8.6 to .8 StrongStrong

.4 to .6.4 to .6 ModerateModerate

.2 to .4.2 to .4 WeakWeak

.0 to .2.0 to .2 Very weakVery weak

ScatterplotScatterplot

Illustrates the relationship between Illustrates the relationship between variablesvariablesX on the horizontal axisX on the horizontal axisY on the vertical axisY on the vertical axis

Positive correlationPositive correlationData from lower left to upper rightData from lower left to upper right

Negative correlationNegative correlationData from upper right to lower leftData from upper right to lower left

Scatterplot for + correlationScatterplot for + correlation

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Scatterplot for - correlationScatterplot for - correlation

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Significance of Pearson r Significance of Pearson r Correlation CoefficientCorrelation Coefficient

Is the relationship statistically significant?Is the relationship statistically significant?Ho: Ho: rr = 0 and H1: = 0 and H1: rr 0 0

Importance of ReplicationsImportance of Replications

Scientists attach little importance to results Scientists attach little importance to results of a single studyof a single study

Detailed understanding requires numerous Detailed understanding requires numerous studies examining same variablesstudies examining same variables