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Statistics 101
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Statistics 101 Statistics 101 Tim Poynton Tim Poynton Center for School Counseling Center for School Counseling Outcome Research Outcome Research
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Statistics 101. Tim Poynton Center for School Counseling Outcome Research. Statistics 101. Using data requires an understanding of some basic statistics – nothing too fancy is needed! - PowerPoint PPT Presentation
Transcript of Statistics 101
Statistics 101Statistics 101Tim PoyntonTim Poynton
Center for School Counseling Outcome Center for School Counseling Outcome ResearchResearch
Statistics 101Statistics 101
Using data requires an understanding of some Using data requires an understanding of some basic statistics – nothing too fancy is needed!basic statistics – nothing too fancy is needed!
Having a handle on some common terms will Having a handle on some common terms will allow you to make sense of all the numbers allow you to make sense of all the numbers and increase your ability to use dataand increase your ability to use data
Statistics 101 – Common Statistics 101 – Common TermsTerms
N N - Number of participants- Number of participants
MeanMean – the “average” score – all – the “average” score – all scores are added up and divided by the scores are added up and divided by the NN
Standard DeviationStandard Deviation – how far, on – how far, on average, a single score deviates from average, a single score deviates from the mean scorethe mean score
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
55 70 85 100 115 130 145
Score on IQ test
60
50
40
30
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10
0
A frequency Histogram can be used to show how people scored on a variable – this is useful for demonstrating how several of these concepts work
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
55 70 85 100 115 130 145
Score on IQ testMean = 100, SD = 15
60
50
40
30
20
10
0
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
55 70 85 100 115 130 145
Score on IQ testMean = 100, SD = 30
60
50
40
30
20
10
0
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
55 70 85 100 115 130 145
Score on IQ testMean = 100, SD = 10
60
50
40
30
20
10
0
Statistics 101 – Common Statistics 101 – Common TermsTerms
MedianMedian – the “middle” number. – the “middle” number. Obtained by putting all the observed Obtained by putting all the observed values on a line and finding the one values on a line and finding the one that lands in the middle. Useful for that lands in the middle. Useful for describing “skewed” distributionsdescribing “skewed” distributions
ModeMode – the most frequent number – the most frequent number
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
55 70 85 100 115 130 145
Score on IQ testMean = 100, Median = 100, Mode = 100
60
50
40
30
20
10
0
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
55 70 85 100 115 130 145
Score on IQ testMean = 100, Median = 90, Mode = 80
60
50
40
30
20
10
0
Statistics 101 – Common Statistics 101 – Common TermsTerms
Num
ber
of
people
15 30 45 60 75 90 105Household Income (in thousands)
Mean = 62, Median = 47, Mode = 40
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50
40
30
20
10
0
Statistics 101 – Common Statistics 101 – Common TermsTerms
Z-ScoreZ-Score – a “standardized score”. – a “standardized score”. The person’s mean score divided by The person’s mean score divided by the standard deviationthe standard deviation
Percentile RankPercentile Rank – tells you the – tells you the relative position of a person’s score, relative position of a person’s score, compared to other people’s scorescompared to other people’s scores
From http://www.webenet.com/bellcurve2.gif
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Categorical VariableCategorical Variable – a variable that divides – a variable that divides data into groups; has little or no numeric meaningdata into groups; has little or no numeric meaning
Dependent VariableDependent Variable – a variable that contains – a variable that contains information you are interested in that has numeric information you are interested in that has numeric valuevalue
DisaggregationDisaggregation – sorting a dependent variable – sorting a dependent variable by a categorical variable (or variables)by a categorical variable (or variables)
CorrelationCorrelation – a number between -1 and +1 used – a number between -1 and +1 used to describe the relationship between two variablesto describe the relationship between two variables
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Disaggregation Graph - Disaggregating Mean # of Days abs by Ethnicity
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Ethnicity
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s ab
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Disaggregation Graph - Disaggregating Mean # of Days absent by Ethnicity, then by Gender.
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AfricanAmer
Latino White Asian/PI AmericanIndian
Other
Ethnicity
Days
abs
Male Female
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
T-TestsT-Tests– one sample – compare a group to a known value one sample – compare a group to a known value
For example, comparing the IQ of convicted felons to the known average For example, comparing the IQ of convicted felons to the known average of 100)of 100)
– paired samples – compare one group at two points in timepaired samples – compare one group at two points in time For example, comparing pretest and posttest scoresFor example, comparing pretest and posttest scores
– independent samples – compare two groups to each otherindependent samples – compare two groups to each other
ANOVAANOVA - compare two or more groups, OR, - compare two or more groups, OR, compare at two or more points in time (repeated compare at two or more points in time (repeated measures)measures)
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Paired Samples T-Test of Pretest and Posttest
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Pretest Posttest
Paired Variables
Mea
n S
core
Statistics 101 – Common Statistics 101 – Common ApplicationsApplicationsIndependent Samples T-Test
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Male Female
Groups
Day
s ab
s
Statistics 101 – Common Statistics 101 – Common ApplicationsApplicationsIndependent Samples T-Test
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Male Female
Groups
Day
s ab
s
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Days AbsentNon-significant t-test
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0
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Num
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people
Male Female
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Days AbsentSignificant t-test
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0
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Num
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people
Male Female
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Days AbsentNon-significant t-test (SD’s increased)
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50
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30
20
10
0
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Num
ber
of
people
Male Female
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
ANOVA - Days abs Disaggregated by Ethnicity
02468101214161820
AfricanAmer
Latino White Asian/PI AmericanIndian
Other
Ethnicity
Day
s ab
s
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Scatterplot of Days absent and Grade totalr = -.92
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Days abs
Gra
de to
tal
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Scatterplot of Days absent and Grade totalr = -.92
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Days abs
Gra
de
tota
l
Statistics 101 – Common Statistics 101 – Common ApplicationsApplications
Scatterplot of Days abs and IQr = .12
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Days abs
Pre
test
Thank You!Thank You!Center for School Counseling Center for School Counseling
Outcome ResearchOutcome Researchwww.cscor.orgwww.cscor.org
