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California State University, Northridge

Department of PsychologyStatistical Methods Lab: PSY320L

SPSS 12.0

COURSE READER

Developed and Written by:

Janice C. McMurray, M.A.

Teaching Assistant

Supervising Professor:

Gary S. Katz, Ph.D.



2

Contents

1 Using SPSS 31.1 SPSS Availability in Sierra Hall 31.2 Finding Course Files on the Internet 3

2 Becoming Familiar with SPSS 42.1 Introduction 42.2 Two Views 42.3 Entering Data 5

3 Data Screening 63.1 Descriptive Information 6

3.1.1 SPSS Explore 63.1.2 Output from Explore 93.1.3 Linearity and Homoscedasticity: Two-Variable Relationships 113.1.4 What if the Data are Not Normal? 11

3.2 Measures of Central Tendency 12

3.2.1 Analyze Central Tendency and Variability of Scores 12

4 Data Management 154.1 Sort Your Data 154.2 Correct Data Entry Errors 154.3 Analyzing Linear Transformations of Your Data 15

4.3.1 Linear Transformations of a Current Variable Using Addition 164.3.2 Linear Transformations of a Current Variable Using Subtraction 164.3.3 Linear Transformations of a Current Variable Using Multiplication 174.3.4 Linear Transformations of a Current Variable Using Division 174.3.5 Linear Transformations of a Variable Using Subtraction and Division 17

5 Percentiles 195.1 Definition 195.2 Computing Percentiles 195.3 Select Cases 20

5.3.1 Select Cases if a Defined Condition is Satisfied 205.3.2 Select a Random Sample of Cases 21

6 Examining Relationships Between Variables 23 6.1 Producing scatterplots 23

6.1.1 Matrix Scatterplots 236.1.2 Simple Scatterplots 23

6.2 Analyzing Correlation Coefficients 24

7 Predicting Outcomes 26 7.1 The Linear Regression Analysis 26

8 Testing Hypotheses by Comparing Means 288.1 The One-Sample t Test 288.2 The Two Independent Samples t Test 298.3 One-Way Analysis of Variance (ANOVA) 328.4 General Linear Model (GLM) 35



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Chapter 1

Using SPSS

1.1 SPSS Availability in Sierra Hall

• SPSS is loaded on all the computers in the open computer lab at the east end of thethird floor (SH392). Lab hours are Monday - Thursday 7:45 am - 11 pm, Friday 7:45

am - 5 pm.

• There are limited hours available with a tutor in this lab (SH341). Tutor lab hours will be posted on the window of the door into the lab.

• Additional tutoring is available in SH385 (there are no computers in that room). The

tutoring schedule will be posted on the door into the room.

1.2 Finding Course Files on the Internet

• Open Internet Explorer

• All files used for this course may be retrieved at the Course Web Site:

http://www.csun.edu/~gk45683/psy320/

• Open a file from the Course Web Site

Click once on that fileA pop-up File Download screen will appear

Choose Open and the file will open on your Desktop



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Chapter 2

Becoming Familiar with SPSS

2.1 Introduction

• SPSS for Windows is just like any other Windows program. Many familiar Windowsfeatures are available in SPSS (e.g., menu bar, tool bar, cut, copy, and paste).

• Many features of the data editor are similar to those found in spreadsheet applications(e.g., MS Excel).

• SPSS is designed to run analyses with:

• Subjects entered one per row going down the screen, and

• Variables entered one per column going across the screen.

2.2 Two Views

• Take a moment now to click on the “Variable View” tab near the bottom left of the

screen (Figure 2.2 next page) to see the difference in the set-up screen. Before entering

new data, we need to define each variable in the data set. Not only may we definevariables, but we may also define levels of these variables. There are a few restrictions

in naming your variables:

• Variable names must begin with a letter not a number

• Variable names cannot end with a period

• Variable names that end with an underscore should be avoided

• The length of the name (in the name column) cannot exceed eight characters

• Blanks and special characters cannot be used • Each variable name must be unique

• Click back to “Data View” now.

• Move your mouse WITHOUT CLICKING over a few of the variable names at the topof your columns. SPSS will show you the variable labels defined for this data set.

subject anxiety tension trial 1 trial 2 trial 31 1 1 18 14 122 1 1 19 12 83 1 1 14 10 64 1 2 16 12 105 1 2 12 8 6

S u b j e c t s

Variables



5

Figure 2.2: SPSS Data View

2.3 Entering Data

• Open a blank worksheet. Click on:

File

NewData

• Using the data from our lab survey define your variables using the “Variable View.”



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Chapter 3

Data Screening

Before any analysis is performed, you must do everything possible to ensure a data file is clean

(e.g., meets the necessary assumptions of a statistical procedure). It is also important to organizeyour input so it is easier to extract meaning from the data.

3.1 Descriptive Information

3.1.1 SPSS Explore

• The best method for data screening via descriptive information is the Explore

procedure. To start, download a course file and click on:

Analyze

Descriptive StatisticsExplore (Figure 3.1)

Figure 3.1: Explore Command



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• The box on the left lists all the variables from your data set (Figure 3.2)

Variables categorized by numbers have a “#” in front of them (age).Variables categorized by words have an “A” in front of them (gender).

Click once on a variable to highlight it, and then click on the arrow button to move

it over to the Dependent List.

Figure 3.2: Explore Dialog Box

• Click on the rectangular Statistics button (Figure 3.2). Check:

Descriptives (Figure 3.3)

Outliers; by checking Outliers, SPSS will produce the five highest and lowestscores with their case numbers.

Continue

Figure 3.3: Statistics Dialog Box

V a r i a b l e s



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• Click on the Plots button (Figure 3.2). Check:

Histogram (Figure 3.4)Uncheck Stem-and-leaf (now that computers have the ability to generate high-

resolution charts, it is not useful). Leave “Factor levels together” checked.

Continue

Figure 3.4: Plots Dialog Box

• Click on the Options button. Choose (Figure 3.5):

Exclude cases pairwise (correlations are computed using only those cases for each

subject that have values for all correlated variables). You can always go back and exclude cases listwise if you like (all data are completely discarded for

subjects with a missing value for any variable at all).Continue

OK

Figure 3.5: Options Dialog Box

• Print your graphs using the menu bar: File, Print. Make sure that “All Visible Output”is selected when you print.

• Once you have printed, close the SPSS Viewer Window.



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3.1.2 Output from Explore

• Case Processing Summary is produced first (Figure 3.6). This table shows the number

of total cases for each variable with the number of cases that you are missing.

Figure 3.6: Explore Output

• Descriptives is produced next (Figure 3.7), showing the mean, median, variance,standard deviation, and range for each variable.


Case Processing Summary

75 100.0% 0 .0% 75 100.0%cups of coffee drink / dayN Percent N Percent N Percent

Valid Missing Total

Cases

Descriptives

.7067 .11032

.4868

.9265

.6037

.0000

.913

.95540

.00

4.00

4.00

1.0000

1.295 .277

1.131 .548

Mean

Lower BoundUpper Bound

95% ConfidenceInterval for Mean

5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

cups of coffee drink / dayStatistic Std. Error



10

cups of coffee drink / day

4.03.02.01.00.0

Histogram

F r e q u e n c y

50

40

30

20

10

0

Std. Dev =.96

Mean =.7

N =75.0075N =

cups of coffee drink

5

4

3

2

1

0

-1

757130

41

• Next, the Extreme Values Table is produced (Figure 3.8) showing the five highest and lowest values along with their case numbers. This is very useful in detecting outliers.


• The Histograms and Boxplots are produced next (Figures 3.9 and 3.10). It is always agood idea to have a picture, and these are also useful in detecting outliers.

Figure 3.9: Explore Output Figure 3.10: Explore Output

Outliers

Extreme Values

41 4.00

30 3.00

71 3.00

75 3.00

52 .a

36 .00

24 .00

25 .00

29 .00

21 .b

1

2

3

4

5

1

2

3

4

5

Highest

Lowest

cups of coffee drink / day Case Number Value

Only a partial list of cases with the value 2 are shown in the table of

upper extremes.

a.

Only a partial list of cases with the value 0 are shown in the table of lower extremes.

b.



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3.1.3 Linearity and Homoscedasticity: Two-Variable Relationships (later in this course)

• To check for linearity and homoscedasticity, use scatterplots by clicking:

Graphs

Scatter

Matrix (Figure 3.11)Define

Click and move your variables over (Figure 3.12)(If you notice something strange use Simple to get a larger view of the problem.)

OK

Figure 3.11: Scatterplot Box

Figure 3.12: Scatterplot Matrix Dialog Box

3.1.4 What if the Data are Not Normal?

• Rely on the robustness of a method of analysis (do nothing approach)

• Transform the variables (later statistics courses)



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3.2 Measures of Central Tendency and Variability

• These measures include the mean, the median, the mode, the range, and the standard deviation.

3.2.1 Analyze Central Tendency and Variability of Scores

• The best method for looking at these measures in univariate statistics is by using

Frequencies (Figure 3.13). Frequencies is an efficient means of computing descriptivestatistics for continuous variables. Download a course file and click:

AnalyzeDescriptive Statistics

Frequencies

Click once on each variable you are interested in and arrow it over to the Variable

box (Figure 3.14)

Figure 3.13: Frequencies Command



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Figure 3.14 Frequencies Dialog Box

• Choose your methods to analyze variability of scores by clicking on:

Statistics button (Figure 3.14)

Under Central Tendency check Mean, Median, and Mode (Figure 3.15)Under Dispersion check Standard Deviation, Range, Minimum, and Maximum

Continue

BE SURE TO unclick the Display Frequency Tables (Figure 3.14)




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Statistics

Group IQ Test Score

88

0

100.26

100.00

95

12.985

62

75

137

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Range

Minimum

Maximum

Click on the Charts button (Figure 3.14)Select Histograms (Figure 3.16)

Check With normal curve (to get an overlaid drawing of a normal curve)

ContinueOK

Figure 3.16: Charts Dialog Box

• SPSS output will show a statistics table (Figure 3.17) and a histogram (Figure 3.18).

Figure 3.17: Frequencies Output Figure 3.18: Frequencies Histogram

Group IQ Test Score

135.0

130.0

125.0

120.0

115.0

110.0

105.0

100.0

95.0

90.0

85.0

80.0

75.0

Group IQ Test Score

F r e q u e n c y

14

12

10

8

6

4

2

0

Std. Dev =12.98

Mean =100.3N =88.00



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Chapter 4

Data Management

4.1 Sort Your Data• Many times, it is helpful to sort your data set into a certain order. This makes it easier

to extract meaning from your data. To do this, download a course file and click:

DataSort Cases

Click once on the variable (column) you want sorted and arrow it over to the

Variable box (Figure 4.1)Select Descending (5, 4, 3, 2, 1) or Ascending (1, 2, 3, 4, 5) for Sort Order

OK

Figure 4.1: Sort Cases Dialog Box

• Take a look at the variable (column) in your data set – it is sorted!

4.2 Correct Data Entry Errors

• Change any number in your data set (click once in the cell and type in the new

number). In essence, you are creating an outlier.

• Run the Frequencies analysis on your revised data set to see how the outlier skews your analysis (Table 3.13):


Frequencies

OK

4.3 Analyzing Linear Transformations of Your Data

Remember to change the number you revised in 4.2 back to the original number.



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4.3.1 Linear Transformations of a Current Variable Using Addition

• To increase the values of a variable using addition click:

Transform

Compute

In the Target Variable box type in the name for your new variable (Figure 4.2)Click once on the variable to be increased and arrow it over to the Numeric

Expression box

After the variable type in the amount of increase (e.g., +50)OK

Figure 4.2: Compute Variable Dialog Box

• Scroll over in your Data View and take a look at the new column you have just defined

• Run the Frequencies analysis on your new variable (Section 3.2.1)

Analyze

Descriptive StatisticsFrequencies

Click once on any/each variable you are interested in and arrow it over to the

Variable box

OK

4.3.2 Linear Transformations of a Current Variable Using Subtraction

• To decrease the values of a variable using subtraction click:

TransformCompute

Reset



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In the Target Variable box type in the name for your new variable

Click once on the variable to decrease and arrow it over to the Numeric Expression box

After the variable type in the amount of decrease (e.g., iq-30)

OK

•

Scroll over in your Data View and take a look at the new column you have just defined


4.3.3 Linear Transformations of a Current Variable Using Multiplication

• To increase the values of a variable using multiplication click:

Transform

ComputeReset


Click once on variable to increase and arrow it over to the Numeric Expression box

After the variable type in the amount of increase (e.g., iq*5)OK



4.3.4 Linear Transformations of a Current Variable Using Division

• To decrease the values of a variable using division click:

TransformCompute

Reset


Click once on variable to decrease and arrow it over to the Numeric Expression boxAfter the variable type in the amount of decrease (e.g., iq/3)

OK



4.3.5 Linear Transformations of a New Variable Using Subtraction and Division

• To decrease the values of a variable using subtraction and division click:

TransformCompute



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Reset

In the Target Variable box type in the name for your new variableClick once on variable to be decreased and arrow it over to the Numeric Expression

box

After the variable type in the amount of the multiple decrease using parentheses[e.g., (iq-100)/13].

OK





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Chapter 5

Percentiles

5.1 Definition

• Percentiles are the point (not percentage) below which a specified percentage of the

observations fall. For example, if a student beats 91% of the class on an exam, he/she isat the 91st percentile (even though he/she may have earned an 86%).

5.2 Computing Percentiles

• We will be using the Frequency analysis again, but now we will be adding percentile

values to our analysis (Figure 3.15).


Frequencies

Click and arrow over the variable you are testing (Figure 3.9)Uncheck the Display frequency tables (Save trees! We don’t need this info).

• Choose your methods to analyze spread of scores by clicking:

Statistics button (Figure 5.1)

Central Tendency: check Mean

Dispersion: check Standard DeviationPercentile Values:

Check Quartiles – this will give you the 25th, 50th, and 75th percentiles

Check Percentiles – add the 1st, 5

th, 10

th, 90

th, 95

th, and 99

thpercentiles by

typing each number into the white box and clicking add Continue




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• Choose your graph by clicking on (Figure 3.11):

Charts button

Histogram

With normal curve

ContinueOK

5.3 Select Cases

• Select Cases allows SPSS to perform analysis on only certain cases. Cases can be

selected by certain criteria you may want to consider in your study such as gender, age,

IQ, having ADHD or not, etc. Cases may be selected several ways.

• It is helpful to first go to the Variable View of your data set and double-check how younumerically defined the levels you want to consider (for gender, 1 = “male” and 2 =

“female”) Figure 5.2.

Figure 5.2: Value Labels Dialog Box

5.3.1 Select Cases if a Defined Condition is Satisfied

• To tell SPSS to only analyze incidences within each variable that match certain criteria

you want to look at, click:

Data

Select CasesClick the radio button If condition is satisfied (Figure 5.3)Click the If button

Click and arrow over the variable you want to analyze (Figure 5.4)Type in an equation that defines the way/s you want to limit your variable

(dropout=0, or dropout=1)

ContinueOK



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Figure 5.3: Select Cases Dialogue Box

Figure 5.4: Select Cases II Dialog Box

• Run your percentile analysis (Section 5.2)

5.3.2 Select a Random Sample of Cases

• To allow SPSS to randomly select varying samples within your variable click:

Data

Select Cases



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Click the radio button Random sample of cases (Figure 5.5)

Click the Sample buttonClick the radio button Exactly (Figure 5.6)

Define the Exact cases by clicking in the first block (10) and From the first (88)

cases by clicking in the second block Continue

OK

Figure 5.5: Select Cases Dialog Box

Figure 5.6: Random Sample Dialog Box

• Run your percentile analysis

• Repeat Section 5.3.2 as many times as you want to obtain several random samples



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Chapter 6

Examining Relationships Between Variables

6.1 Producing Scatterplots

6.1.1 Matrix Scatterplots

• A matrix scatterplot is a collection of all possible scatterplots that can be produced toshow the relationship between the variables in your study. To create a matrix

scatterplot open a course file and click:

GraphsScatter

Matrix (Figure 3.2)

DefineClick and arrow over ALL the variables (Figure 6.1)

OK

Figure 6.1: Scatterplot Matrix Dialog Box

6.1.2 Simple Scatterplots

• Simple scatterplots show all possible relationships between two variables. To create a

simple scatterplot click:

Graphs

Scatter

Simple (Figure 3.2)



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Define

Click and arrow over one variable to the Y-Axis box, and another variable to the X-Axis box (Figure 6.2). When running analyses, you should place your

independent variable (“input variable,” variable that is independent of the

subject, variable you manipulate) on the X-Axis, and your dependent variable(“output variable,” variable that is dependent on the subject, variable you

measure) on the Y-Axis.If you want to look at differences in levels of a variable, move it over into Set

Markers by so you can plot different shapes or colors for the levels (e.g.,Gender - males vs. females).

OK

Figure 6.2: Simple Scatterplot Dialog Box

6.2 Analyzing Correlation Coefficients• The correlation coefficient, Pearson r , is a quantitative measure of the relationship

between two interval or ratio variables (and the value it gives us is between -1 and +1).

The Pearson r tells us the direction of the relationship (either positive or negative), and

indicates the strength of the relationship (close to 0 means no relationship, close to – 1/+1 means a strong relationship). What we want to know about the variables is “when

one increases in value, does the other?” As a country’s expenditure on health care

increases, does its citizens’ life expectancy also increase?

To calculate a correlation coefficient click:Analyze

CorrelateBivariate

Click and arrow over the two variables from your first simple scatterplot from

Section 6.1.2 (Figure 6.3)

Make sure Pearson, Two-tailed, and Flag significant correlations are checked OK



25

Figure 6.3: Bivariate Correlations Dialog Box

• The SPSS output will tell you several important things about the relationship between

the two variables (Figure 6.4).

Figure 6.4: Correlation Coefficient Output

• First, you should look at whether or not the two variables are significantly related toeach other (shown with arrows above). If your Sig. (significance) value is less than .05

( p < .05), then your two variables are “significantly” related to each other, and wereject the null hypothesis (which states the two are not related).

• In this case, p = .000, and is < .05, so we reject H0. *Report this as:

There is a significant relationship between ADD scores and 9th

grade

GPA, p = .000 [be sure to use your p value].

• Second, by looking at the Pearson Correlation value (circled above), you can tellwhether the relationship between the two variables is negative or positive. The circled

Pearson Correlation value in Figure 6.4, -.615, shows a negative relationship.

Correlations

1 -.615**

. .000

88 88

-.615** 1

.000 .

88 88

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

ADD Score

9th grade GPA

ADD Score9th grade

GPA

Correlation is significant at the 0.01 level (2-tailed).**.



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Chapter 7

Predicting Outcomes

7.1 The Linear Regression Analysis

• When we are interested in looking at whether or not the relationship between one (or

more) variable/s is strong enough so that we can predict an outcome we use the

regression analysis. For example, does stress predict poor mental health?

To run a regression in SPSS download a course file and click:

AnalyzeRegression

Linear

Click and arrow over your dependent (Y) and independent (X) variables (Fig. 7.1)OK

Figure 7.1: Linear Regression Dialog Box

• Similar to the correlation analysis, this output will tell us several things.

• First, you should look at the ANOVA table to see whether the dependent (outcome)

variable is significantly predicted by the independent (predictor) variable (Figure 7.2).Again, if your Sig. (significance) value is less than .05 ( p < .05), your independent

variable significantly predicts your dependent variable and you reject H0 (which states

that there is zero prediction). ANOVA also reports the value of the F test.

* Report this as:

Brain size significantly predicts IQ, F (1, 39) = 5.573, p = .023 [use your numbers].

Y



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ANOVAb

2892.989 1 2892.989 5.573 .023a

19724.911 38 519.077

22617.900 39

Regression

Residual

Total

Model1

Sum of Squares df Mean Square F Sig.

Predictors: (Constant), Number of pixels on MRIa.

Dependent Variable: FSIQb.

Coefficientsa

5.168 46.008 .112 .911

1.192E-04 .000 .358 2.361 .023

(Constant)

Number of pixels on MRI

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: FSIQa.

Model Summary

.358a .128 .105 22.7833

Model1

R R SquareAdjustedR Square

Std. Error of the Estimate

Predictors: (Constant), Number of pixels on MRIa.

In this case, a person’s brain size (number of pixels on MRI) significantly predicts their

full scale IQ (FSIQ). In other cases, we may look at whether cell phone use predictscancer, or whether successfully earning a college degree increases chances of success

in marriage.

Figure 7.2: Regression ANOVA Table

•

Second, by looking at the Coefficients table (Figure 7.3) we can see whether the prediction of the dependent variable is negative (a decrease) or positive (an increase).

• Third, by looking at the slope (Figure 7.3) of the regression line (.000192 in this case)we can tell that for a one-unit increase in a person’s brain size (number of pixels on

MRI) we can significantly predict a .000192 increase in full scale IQ.

Figure 7.3: Coefficients Table

Intercept (“E-04” means move decimal point 4 places left)Slope

• Fourth, by looking at the standard error of estimate, r 2

value (Figure 7.4), we can tell

how variable the errors within our prediction are. For example, in this case, r 2

= .128,meaning that 12.8% of our prediction of IQ is due to the Number of pixels on the MRI

(brain size) and the other 87.3% is related to other factors.

Figure 7.4: Regression Coefficient Model Summary



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One-Sample Statisti cs

88 100.26 12.985 1.384Group IQ Test ScoreN Mean Std. Deviation

Std. Error

Mean

One-Sample Test

.189 87 .851 .26 -2.49 3.01Group IQ Test Scoret df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

Test Value =100

Chapter 8

Testing Hypotheses by Comparing Means

8.1 The One-Sample t Test

• Here we are analyzing whether our sample comes from a particular population. For

example, do children being tested actually come from a population of ADHD children?

Also, we can perform repeated measures tests on the same person to tell whether atreatment is effective: does family therapy intervention result in weight gain in

anorexic teenage girls. We perform this analysis by opening a course file and clicking:

Analyze

Compare MeansOne-Sample T Test

Click and arrow over the variable you want to test (Figure 8.1)

Type in your Test Value (µ)OK

Table 8.1: One-Sample T Test Dialog Box

µ

• The output tables show several things (Figure 8.2):



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This output shows: N = 88

Mean = 100.26

Standard Deviation = 12.985t value (not T-score) = .189

df = 87 p =.851

• Keep in mind what the value of the µ (mean) you are testing is (in this case, it was100), Figure 8.1.

• We see that our significance value of .851 is NOT < .05, so we retain H 0 and state thatthere is no significant difference between our sample mean and the population mean –

our sample did come from a population with a mean of 100.

• The df (degrees of freedom) is obtained by starting with the number of observations we

have, n=88, and subtracting the number of observations we estimate, 1 (a single mean).

8.2 The Two Independent Samples t Test

• Here we are no longer comparing samples from the same person rather we arecomparing samples from two different (independent) people or groups. For example,

we may want to study whether 12-year-old boys are more socially inept than 12-year-old girls. In this case, we would need a sample of boys and a second, independent

sample of girls.

• Since we are no longer comparing one person to him/herself, we need to ensure thatour two groups are similar enough (homogeneous enough) to allow a comparison. Wemust meet this assumption in order to use an Independent Samples t Test as our

analysis. SPSS tests homogeneity between two independent groups by Levene’s Testof equality of variances.

• One of the most common uses of the t test involves testing the difference between the

means of two independent groups. In a memory study, we might want to compare

levels of retention for a group of college students asked to recall a list of visually

presented nouns and a group asked to recall a list of orally presented nouns.

• In SPSS we perform an Independent Samples t Test by opening a course file and clicking:

Analyze

Compare Means

Independent Samples T TestClick and arrow over the Test Variable you want to study the effect of (Figure 8.3)

Click and arrow over the Grouping Variable from which you will derive your two

groups (Figure 8.3)



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Figure 8.3: Independent-Samples T Test Dialog Box

Click Define Groups to define each of your groups (check your data set to see how

you originally defined your groups), Figure 8.4Continue

OK

Figure 8.4: Define Groups



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Group Statistics

29 24.07 10.060 1.868

35 14.29 11.498 1.944

Group MembershipHomophobic

Nonhomophobic

AROUSALN Mean Std. Deviation

Std. ErrorMean

• Your output tells you whether your two independent samples come from the same

population (Figure 8.5).

Figure 8.5: Independent Sample T Test Output

• First, we check the significance level of Levene’s Test for equality of variances.Opposite of what we usually want to see as a significance level ( p < .05), here we do

NOT want the significance level to be < .001.

Here, the significance is .706, so we use the top line in the output table, “Equal

variances assumed,” for our analysis.

(Were the significance actually < .001, we would use the SPSS-adjusted second line,“Equal variances not assumed,” for our analysis.)

• Now that we have determined which “line” of our analysis we will be using, we look atwhether or not the means of our two groups are equal. In this case our significance (2-

tailed) is .001, which is < .05 and therefore is significant. This tells us that the means of

our two groups are significantly different from each other, so we reject H0 (which

states that they are not different from each other: µ1 = µ2).

• We also see the degrees of freedom = 62 (our total observations or “n” = 64, minus thetwo observations we estimate – the two group means), and the t value.

• Finally, to discover which group mean is greater than the other, we look at the first

output table, the Group Statistics. Here we see that the mean for the HomophobicGroup, M = 24.07, is greater than the mean for the Nonhomophobic Group, M = 14.29.

* Report this as: Homophobic males ( M = 24.07, SD = 10.060) have significantly higher arousal then

nonhomophobic males ( M = 17.29, SD = 11.498), t (62) = 3.583, p = .001.

Independent Samples Test

.144 .706 3.583 62 .001 9.78 2.730 4.326 15.241

3.629 61.796 .001 9.78 2.696 4.394 15.172

Equal variances

assumedEqual variancesnot assumed

AROUSALF 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



32

8.3 One-Way Analysis of Variance (ANOVA)

• This is the most popular analysis for psychological research for two main reasons.

First, instead of comparing just two means (as with the Independent Samples t Test),

ANOVA can compare any number of means to see if they differ.

Second, with ANOVA we can compare a multiple number of independent variables all

at once. Not only can we see an effect of each individual variable, but we can also see

any interaction effects between the variables.

• The ANOVA analysis is performed by opening a course file and clicking:

AnalyzeCompare Means

One-Way ANOVA

Click and arrow over the “Factor” variable with the levels you want to compare

(Figure 8.6)Click and arrow over the “Dependent” variable you want to study the effect on.

Figure 8.6: One-Way ANOVA Dialog Box

Click the Options button (Figure 8.7)

Check Descriptive

Check Homogeneity-of-varianceCheck Means plotLeave Exclude cases analysis by analysis checked

Continue

OK



33

Descriptives

Group IQ Test Score

14 103.79 12.479 3.335 96.58 110.99 81 127

64 100.89 13.054 1.632 97.63 104.15 79 13710 91.30 10.034 3.173 84.12 98.48 75 105

88 100.26 12.985 1.384 97.51 103.01 75 137

college prep

generalremedial

Total

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

95% Confidence Interval forMean

Minimum Maximum

Test of Homogeneity of Variances

Group IQ Test Score

.547 2 85 .581

LeveneStatistic df1 df2 Sig.

Figure 8.7: One-Way ANOVA Options Box

•

The “Descriptives” output appears first and is answers questions such as, “Whichgroup scored higher?” This is the first question you answer whenever you have asignificant ANOVA analysis (F test), Figure 8.8.

Figure 8.8: SPSS ANOVA Output

• Next, we see the test of homogeneity, Levene’s test, which should be NOT significantat the .001 level (Figure 8.9).




34

ANOVA

Group IQ Test Score

1002.297 2 501.149 3.117 .049

13666.692 85 160.785

14668.989 87

Between Groups

Within Groups

Total

Sum of Squares df Mean Square F Sig.

• Third, we see the ANOVA summary table (Figure 8.10). In this case, our p value was.049, which is significant, < .05 (although just barely).


* Report this as:

There is a significant difference between the level of English language skills a

person has in the 9th

grade and that person’s IQ test score, F (2, 87) = 3.117, p =.049.

From this test, we only know that at least one group is different, we do not yet knowwhich group/s is/are different.

• Our next question is, “Which group scored highest?” and we find this information in

the Descriptives table (Figure 8.8) by looking at the means.

* Report this as:

The 9th

grade group with the college prep level language skills had the highest IQ( M = 103.79, SD = 12.497), the group with the general level language skills had the

next highest IQ ( M = 100.89, SD = 13.054), and the group with the remedial level

language skills had the lowest IQ ( M = 91.30, SD = 10.034).

• The means plot is a pictorial rendering of the data in the descriptives table.

English Level 9th Grade

remedialgeneralcollege prep

M e a n o f G r o u p I Q T

e s t

S c o r e

106

104

102

100

98

96

94

92

90



35

8.4 General Linear Model (GLM)

• The ANOVA analyses we performed in the last chapter looked at the interaction of one

dependent variable with more than two independent variables. Now we will be

analyzing mean differences on our dependent variable among one independent

variable, between and across another independent variable. We can choose from twoanalyses in order to look at these mean differences:

1. General Linear Model (GLM) Univariate Analysis – we use this method whenour analysis has no repeated measures.

2. General Linear Model (GLM) Repeated Measures Analysis – we use this

method when our analysis involves any repeated measures (any repeated tests).

Looking for a repeated measures variable is the first and key thing to look at when

deciding which analysis to use. For example, we may give an ADHD child a

continuous performance test (CPT) and score how they perform. Then, we mayadminister a specific level of Ritalin to the child and have them re-take the same

CPT an hour later.

If you are not sure whether or not your data set contains any repeated measures there isan easy way for you to tell! Think of each row in your Data View as one subject. If

your Data View looks like this, you can see that each subject has a single score for

each variable and is a member of only one group:

Figure 8.11: Data Set Containing Non-Repeated Measures Data



36

If, on the other hand your Data View looks like this, you can see that each subject was

measured several times, repeatedly:

Figure 8.12: Data Set Containing Repeated Measures Data

The GLM Factorial Analysis is performed by opening a course file and clicking:

AnalyzeGeneral Linear Model

Univariate (Figure 8.13)Arrow over the Dependent Variable (what you want to measure) into the

Dependent Variable box (Figure 8.13)

Arrow over the Fixed Factor Variables (your independent variables,what you want to measure the effect of) into the Fixed Factor box

Arrow over the Random Factor Variable (independent variable that onlysome subjects received as a treatment) into the Random Factor box.

Arrow over the Covariate Variable (a variable whose effects you wantto statistically control for) into the Covariate box

Figure 8.13: GLM Univariate Dialog Box



37

Click on the Plots button (Figure 8.14)

Arrow your top variable over into the Horizontal Axis box

Arrow your next variable over into the Separate Lines box

Click on the Add buttonArrow your bottom variable over into the Horizontal Axis box

Arrow your top variable over into the Separate Lines boxClick on the Add button

[It is a good idea to create separate plots showing each of the contrastsyou are measuring between each set of variables.]

Continue

Figure 8.14: GLM Univariate Profile Plots

Click on the Post Hoc button [Only independent variables with at least

three levels will appear in the Factor(s) box.] (Figure 8.15)

Arrow all of your variables over into the Post Hoc Tests for box

Click in the Scheffe box [This is the most conservative and flexible adjustment we can make in order to avoid making

a Type I error in our analysis.]Continue



38

Figure 8 15: Univariate: Post Hoc Multiple Comparisons

Click on the Options button (Figure 8:16)

Click in the Descriptive statistics box, do not click anything else

ContinueOK

Figure 8.16: Univariate: Options



39

Tests of Between-Subjects Effects

Dependent Variable: SCORE

12053.250a 3 4017.750 10.327 .001

66822.250 1 66822.250 171.761 .000

10609.000 1 10609.000 27.270 .000

1024.000 1 1024.000 2.632 .131

420.250 1 420.250 1.080 .319

4668.500 12 389.042

83544.000 16

16721.750 15

SourceCorrected Model

Intercept

SCREEN

LIQUID

SCREEN * LIQUID

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared =.721 (Adjusted R Squared =.651)a.

Descriptive Statistics

Dependent Variable: SCORE

41.7500 25.55223 4

36.0000 17.83255 4

38.8750 20.62895 8

103.5000 18.91208 4

77.2500 15.08587 4

90.3750 21.15884 8

72.6250 39.01991 8

56.6250 26.83248 8

64.6250 33.38837 16

LIQUIDLow

High

Total

Low

High

Total

Low

High

Total

SCREENCourse

Fine

Total

Mean Std. Deviation N

Your GLM output will tell you several things. First, we will look at whether our

analysis showed there to be a significant relationship among the variables (Fig. 8. 17).

Figure 8.17: Tests of Between-Subjects Effects

*1 This line tells us whether there is a significant difference inscores (our dependent variable) between course and fine

screen (our first independent variable) averaged across theconcentration of liquid (our second independent variable). This

is the main effect of screen.

*2 This line tells us whether there is a significant difference inscores between low and high concentrations of liquid averaged across the screen type. This is the main effect of liquid.

*3 This line tells us whether the pattern of difference on the scores

among concentrations of liquid is different between course and

fine screen. This is the interaction effect of screen and liquid .

If one of our p values is significant our next question is, which level of the significant

variable(s) is higher? To answer this question we look at the means in the DescriptiveStatistics table (Figure 8.18). For this analysis, we see that at each concentration of

liquid, the means are all highest for the fine screen condition.

Figure 8.18: Descriptive Statistics

Significant

Both are not

significant

*1

*2

*3



40

The GLM Repeated Measures Analysis is used when our study involves any repeated

measures (any repeated tests). The Repeated Measures Analysis is performed byopening a course file and clicking:

AnalyzeGeneral Linear Model

Repeated Analysis (Figure 8.19)Type the name of your repeated measures variable into the top box

Type in the number of levels of the variable at which you are lookingClick Add

Define

Figure 8.19: Repeated Measures Define Factor(s)

In the Repeated Measures Dialog Box (Figure 8.20), you must choose which of

your variables to arrow over into each level of your repeated measure. To do

this, click on the first variable you want to arrow over, then click the little arrow button; repeat this until the appropriate variables have all been arrowed over.

Figure 8.20: Repeated Measures Dialog Box



Click on the Options button

Click in the Descriptive Statistics boxContinue

OK

By looking at the Between-Subjects Effects table (Figure 8.20), we can see that we do

have a significant effect on the means in this analysis.

Figure 8.21: Tests of Between-Subjects Effects

To see in which direction the means were affected, we look at the DescriptiveStatistics table (Figure 8.22).

Figure 8.22: Descriptive Statistics

Tests of Between-Subjects Effects

Measure: MEASURE_1

Transformed Variable: Average

36226.082 1 36226.082 85.781 .000

6334.611 15 422.307

SourceIntercept

Error

Type III Sumof Squares df Mean Square F Sig.

Descriptive Statistics

25.000 .0000 16

23.938 1.8786 16

19.000 6.6332 16

15.562 7.5097 16

13.813 7.7908 1612.625 7.4911 16

11.313 7.5958 16

10.313 7.2730 16

9.500 7.0048 16

8.375 6.2276 16

7.813 5.8790 16

7.500 5.8310 16

6.813 5.5644 16

DAY1

DAY2

DAY4

DAY5

DAY6DAY7

DAY8

DAY10

DAY11

DAY12

DAY13

DAY14

DAY15

Mean Std. Deviation N

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