Statistics & SPSS Review

Fall 2009

Types of Measures / Variables

• Nominal / categorical– Gender, major, blood type, eye color

• Ordinal– Rank-order of favorite films; Likert scales?

• Interval / scale– Time, money, age, GPA

Variable Type Example Commonly-used Statistical

Method

Nominal by Nominal blood type by gender

Chi-square

Scale by Nominal GPA by gender

GPA by major

t-test

Analysis of Variance

Scale by Scale weight by heightGPA by SAT

RegressionCorrelation

Main Analysis Techniques

Variable Type Example Commonly-used Statistical

Method

Nominal by Nominal blood type by gender

Chi-square

Scale by Nominal GPA by gender

GPA by major

t-test

Analysis of Variance

Scale by Scale weight by heightGPA by SAT

RegressionCorrelation

Main Analysis Techniques

SPSS Cross –tab with Chi-Squarevictim gender * probation or jail Crosstabulation

3 21 24

12.5% 87.5% 100.0%

9 15 24

37.5% 62.5% 100.0%

12 36 48

25.0% 75.0% 100.0%

Count

% within victim gender

Count

% within victim gender

Count

% within victim gender

female

male

victim gender

Total

probation jail

probation or jail

Total

Chi-Square Tests

4.000b 1 .046

2.778 1 .096

4.144 1 .042

.093 .047

3.917 1 .048

48

Pearson Chi-Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count is 6.00.

b.

SPSS Cross –tab with Chi-Squarevictim gender * probation or jail Crosstabulation

3 21 24

12.5% 87.5% 100.0%

9 15 24

37.5% 62.5% 100.0%

12 36 48

25.0% 75.0% 100.0%

Count

% within victim gender

Count

% within victim gender

Count

% within victim gender

female

male

victim gender

Total

probation jail

probation or jail

Total

Chi-Square Tests

4.000b 1 .046

2.778 1 .096

4.144 1 .042

.093 .047

3.917 1 .048

48

Pearson Chi-Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count is 6.00.

b.

p < .05

Variable Type Example Commonly-used Statistical

Method

Nominal by Nominal blood type by gender

Chi-square

Scale by Nominal GPA by gender

GPA by major

t-test

Analysis of Variance

Scale by Scale weight by heightGPA by SAT

RegressionCorrelation

Main Analysis Techniques

SPSS t-test Output

Group Statistics

24 16.04 12.723 2.597

24 6.00 9.227 1.883

victim genderfemale

male

lengthofsentave11N Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

.824 .369 3.130 46 .003 10.042 3.208 3.584 16.499

3.130 41.951 .003 10.042 3.208 3.567 16.516

Equal variancesassumed

Equal variancesnot assumed

lengthofsentave11F Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

SPSS t-test Output

Group Statistics

24 16.04 12.723 2.597

24 6.00 9.227 1.883

victim genderfemale

male

lengthofsentave11N Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

.824 .369 3.130 46 .003 10.042 3.208 3.584 16.499

3.130 41.951 .003 10.042 3.208 3.567 16.516

Equal variancesassumed

Equal variancesnot assumed

lengthofsentave11F Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

1. Read means

2. Read Levene’s Test 3. Read p value

Variable Type Example Commonly-used Statistical Method

Nominal by Nominal blood type by gender

Chi-square

Scale by Nominal GPA by gender

GPA by major

t-test

Analysis of Variance

Scale by Scale weight by heightGPA by SAT

RegressionCorrelation

Analysis of Variance

SPSS ANOVA output

Descriptives

lengthofsentave11

19 14.26 15.183 3.483 6.94 21.58 0 60

14 7.43 8.474 2.265 2.54 12.32 0 24

15 10.27 10.067 2.599 4.69 15.84 0 36

48 11.02 12.109 1.748 7.50 14.54 0 60

natural science

social science

arts and humanities

Total

N Mean Std. Deviation Std. Error Lower Bound Upper Bound

95% Confidence Interval forMean

Minimum Maximum

ANOVA

lengthofsentave11

388.933 2 194.467 1.346 .271

6502.046 45 144.490

6890.979 47

Between Groups

Within Groups

Total

Sum ofSquares df Mean Square F Sig.

SPSS ANOVA outputDescriptives

lengthofsentave11

19 14.26 15.183 3.483 6.94 21.58 0 60

14 7.43 8.474 2.265 2.54 12.32 0 24

15 10.27 10.067 2.599 4.69 15.84 0 36

48 11.02 12.109 1.748 7.50 14.54 0 60

natural science

social science

arts and humanities

Total

N Mean Std. Deviation Std. Error Lower Bound Upper Bound

95% Confidence Interval forMean

Minimum Maximum

ANOVA

lengthofsentave11

388.933 2 194.467 1.346 .271

6502.046 45 144.490

6890.979 47

Between Groups

Within Groups

Total

Sum ofSquares df Mean Square F Sig.

p value

Variables & Statistical TestsVariable Type Example Common Stat

Method

Nominal by nominal

Blood type by gender

Chi-square

Scale by nominal GPA by genderGPA by major

T-testAnalysis of Variance

Scale by scale Weight by heightGPA by SAT

RegressionCorrelation

Variance

x i - Mean )2

Variance = s2 = ----------------------- N

 

Standard Deviation = s = variance

Regression line

W = 3.3 H - 73

Scatterplot: Sentence by G.P.A.

Regression Coefficients

Coefficientsa

17.853 12.097 1.476 .155

-3.534 3.368 -.223 -1.049 .306

(Constant)

grade point average

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: jail sentencea.

Sentence = -3.5 G.P.A. + 18

Correlation

Correlation: Sentence & G.P.A.

Correlations

1 -.223

. .306

23 23

-.223 1

.306 .

23 24

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

grade point average

jail sentence

grade pointaverage jail sentence

Correlation: Sentence & G.P.A.

Correlations

1 -.223

. .306

23 23

-.223 1

.306 .

23 24

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

grade point average

jail sentence

grade pointaverage jail sentence

p value

Interpreting r as r2

r = -.22 r2 = .05

G.P.A. “explains” 5% of variance in SENTENCE length

Correlation