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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
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
YEARS
11109876543
DE
CIS
ION
16
14
12
10
8
6
4
2
Scatterplot for - correlationScatterplot for - correlation
YEARS
11109876543
DE
CIS
ION
16
14
12
10
8
6
4
2
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