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Analyzing Data using SPSS

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Title: Analyzing Data using SPSS


1
Analyzing Data using SPSS
2
Testing for difference
3
Parametric Test
4
t-test
  • Is used in a variety of situations involving
    interval and ratio variables.
  • Independent Samples
  • Dependent - Samples

5
Independent-Samples T-Test
  • What it does The Independent Samples T Test
    compares the mean scores of two groups on a given
    variable.

6
  • Where to find it Under the Analyze menu, choose
    Compare Means, the Independent Samples T Test.
    Move your dependent variable into the box marked
    "Test Variable." Move your independent variable
    into the box marked "Grouping Variable." Click on
    the box marked "Define Groups" and specify the
    value labels of the two groups you wish to
    compare.

7
  • Assumptions-The dependent variable is normally
    distributed. You can check for normal
    distribution with a Q-Q plot.-The two groups
    have approximately equal variance on the
    dependent variable. You can check this by looking
    at the Levene's Test. See below.-The two groups
    are independent of one another

8
  • HypothesesNull The means of the two groups are
    not significantly different.Alternate The means
    of the two groups are significantly different.

9
SPSS Output
  • Following is a sample output of an independent
    samples T test. We compared the mean blood
    pressure of patients who received a new drug
    treatment vs. those who received a placebo (a
    sugar pill).

10
  • First, we see the descriptive statistics for the
    two groups. We see that the mean for the "New
    Drug" group is higher than that of the "Placebo"
    group. That is, people who received the new drug
    have, on average, higher blood pressure than
    those who took the placebo.

11
                                                
                                 Our
  • Finally, we see the results of the Independent
    Samples T Test. Read the TOP line if the
    variances are approximately equal. Read the
    BOTTOM line if the variances are not equal. Based
    on the results of our Levene's test, we know that
    we have approximately equal variance, so we will
    read the top line

12
  • Our T value is 3.796.
  • We have 10 degrees of freedom.
  • There is a significant difference between the two
    groups (the significance is less than .05).
  • Therefore, we can say that there is a significant
    difference between the New Drug and Placebo
    groups. People who took the new drug had
    significantly higher blood pressure than those
    who took the placebo.

13
Example Independent samples t test
  • A study to determine the effectiveness of an
    integrated statistics/experimental methods course
    as opposed to the traditional method of taking
    the two courses separately was conducted.
  • It was hypothesized that the students taking the
    integrated course would conduct better quality
    research projects than students in the
    traditional courses as a result of their
    integrated training.
  • Ho there is no difference in students
    performance as a result of the integrated versus
    traditional courses.
  • H1 students taking the integrated course would
    conduct better quality research projects than
    students in the traditional courses

14
Output SPSS
  • Students taking the integrated course would
    conduct better
  • quality research projects than students in the
    traditional courses

15
Exercise1
  • The following data were obtained in an experiment
    designed to check whether there is a systematic
    difference in the weights (in grams) obtained
    with two different scales.

Rock specimen Scale I Scale II
1 2 3 4 5 6 7 8 9 10 12.13 17.56 9.33 11.40 28.62 10.25 23.37 16.27 12.40 24.78 12.17 17.61 9.35 11.42 28.61 10.27 23.42 13.26 12.45 24.75
16
  • Use the 0.01 level of significance to test
    whether the difference between the means of the
    weights obtained with the two scales is
    significant
  • Ho there is no significant difference between
    the means of the weight obtained with the two
    scales.
  • H1 there is significant difference between the
    means of the weight obtained with the two scales.

17
Exercise 2
  • The following are the scores for random samples
    of size ten which are taken from large group of
    trainees instructed by the two methods.
  • Method 1 teaching machine as well as some
    personal attention by an instructor
  • Method 2 straight teaching-machine instruction

Method 1 81 71 79 83 76 75 84 90 83 78
Method 2 69 75 72 69 67 74 70 66 76 72
What we can conclude about the claim that the
average amount by which the personal attention
of an instructor will improve trainees score.
Use ?5.
18
Paired samples t-test
19
Paired Samples T Test
  • What it does The Paired Samples T Test compares
    the means of two variables. It computes the
    difference between the two variables for each
    case, and tests to see if the average difference
    is significantly different from zero.

20
Paired Samples T Test
  • Where to find it Under the Analyze menu, choose
    Compare Means, then choose Paired Samples T Test.
    Click on both variables you wish to compare, then
    move the pair of selected variables into the
    Paired Variables box.

21
Paired Samples T Test
  • Assumption-Both variables should be normally
    distributed. You can check for normal
    distribution with a Q-Q plot.

22
Paired Samples T Test
  • HypothesisNull There is no significant
    difference between the means of the two
    variables.Alternate There is a significant
    difference between the means of the two variables

23
SPSS Output
  • Following is sample output of a paired samples T
    test. We compared the mean test scores before
    (pre-test) and after (post-test) the subjects
    completed a test preparation course. We want to
    see if our test preparation course improved
    people's score on the test.

24
First, we see the descriptive statistics for both
variables.
  • The post-test mean scores are higher than
    pre-test scores

25
Next, we see the correlation between the two
variables
  • There is a strong positive correlation. People
    who did well on the pre-test also did well on the
    post-test.

26
  • Finally, we see the results of the Paired Samples
    T Test. Remember, this test is based on the
    difference between the two variables. Under
    "Paired Differences" we see the descriptive
    statistics for the difference between the two
    variables

27
(No Transcript)
28
To the right of the Paired Differences, we see
the t, degrees of freedom, and significance.
The t value -2.171 We have 11 degrees of
freedom Our significance is .053 If the
significance value is less than .05, there is a
significant difference.If the significance value
is greater than. 05, there is no significant
difference. Here, we see that the significance
value is approaching significance, but it is not
a significant difference. There is no difference
between pre- and post-test scores. Our test
preparation course did not help!
29
Example
  • Twenty first-grade children and their parents
    were selected for a study to determine whether a
    seminar instructing on inductive parenting
    techniques improve social competency in children.
    The parents attended the seminar for one month.
    The children were tested for social competency
    before the course began and were retested six
    months after the completion of the course.

30
Hypothesis
  • Ho there is no significant difference between
    the means of pre and post seminar social
    competency scores
  • In other words, the parenting seminar has no
    effect on child social competency scores

31
  • There is a strong positive correlation. children
    who did well on the pre-test also did well on the
    post-test.

There is significant difference between pre- and
post-test scores. the parenting seminar has
effect on child social competency scores!
32
Exercise 3
  • The table below shows the number of words per
    minute readings of 20 student before and after
    following a particular method that can improve
    reading.

Student Pre Post
11 50 64
12 56 62
13 75 87
14 49 62
15 66 62
16 86 90
17 90 84
18 58 62
19 41 40
20 82 77
Student Pre Post
1 48 57
2 89 102
3 78 81
4 50 61
5 70 74
6 98 100
7 78 83
8 98 86
9 58 67
10 61 71
33
  • Using a 0.05 level of significance, test the
    claim that the method is effective in improve
    reading.

34
Exercise 4
  • The table below shows the weight of seven
    subjects before and after following a particular
    diet for two months
  • Subject A B C D E F G
  • After 156 165 196 198 167 199 164
  • Before 149 156 194 203 153 201 152
  • Using a 0.01 level of significance, test the
    claim that the diet is effective in reducing
    weight.

35
One-WayANOVA
  • Similar to a t-test, in that it is concerned with
    differences in means, but the test can be applied
    on two or more means.
  • The test is usually applied to interval and ratio
    data types. For example differences between two
    factors (1 and 2).
  • The test can be undertaken using the Analyze -
    Compare Means - One-Way ANOVA menu items, then
    select for appropriate variables.
  • You will observe the One-Way ANOVA for factor 1
    and factor 2

36
Procedure
  • 1. You will need one column of group codes
    labelling which group your data belongs to. The
    codes need to be numerical, but can be labelled
    with text.
  • 2. You will also need a column containing the
    data points or scores you wish to analyze.
  • 3. Select One-way ANOVA from the Analyze and
    Compare Means menus.
  • 4. Click on your dependent variables (data
    column) and click on the top arrow so that the
    selected column appears in the dependent list
    box.
  • 5. Click on your code column (your condition
    labels) and click on the bottom arrow so that the
    selected column appears in the factor box.

37
  • 6. Click on Post Hoc if you wish to perform
    post-hoc tests.(optional).
  • 7. Choose the type of post-hoc test(s) you wish
    to perform by clicking in the small box next to
    your choice until a tick appears. Tukey's and
    Scheffe's tests are commonly used.
  • 8. Click on Dunnett to perform a Dunnett's test
    which allows you to compare experimental groups
    with a control group.Choose whether your control
    category is the first or last code entered in
    your code column.

38
  • The main output table is labelled ANOVA. The
    F-ratio of the ANOVA, the degrees of freedom and
    the significance are all displayed. The top value
    of the df column is the df of the factor, the
    bottom value is the df of the error term.
  • Tukey's test will also try to find combinations
    of similar groups or conditions.
  • In the Score table there will be one column for
    each pair of conditions that are shown to be
    'similar'. The mean of each condition within the
    pair are given in the appropriate column. The
    p-value for the difference between the means of
    each pair of groups is given at the bottom of the
    appropriate column.

39
Example one-way ANOVA
  • We would like to determine whether the scores on
    a test of aggression are different across 4
    groups of children (each with 5 subjects)
  • Each child group has been exposes to differing
    amounts of time watching cartoons depicting toon
    violence

40
At the 0.05 significance level, test the claim
that the four groups have the same mean if the
following sample results have been obtained.
41
Output SPSS
42
Exercise 5
  • At the same time each day, a researcher records
    the temperature in each of three greenhouses. The
    table shows the temperatures in degree Fahrenheit
    recorded for one week.
  • Greenhouse 1 greenhouse 2 greenhouse 3
  • 73 71 61
  • 72 69 63
  • 73 72 62
  • 66 72 61
  • 68 65 60
  • 71 73 62
  • 72 71 59
  • Use a 0.05 significance level to test the claim
    that the average temperature is the same in each
    greenhouse.

43
Nonparametric Test
44
Sign Test
  • A sign test compares the number of positive and
    negative differences between related conditions

45
Procedure
  • 1. You should have data in two or more columns -
    one for each condition tested.
  • 2. Select 2 Related Samples from the Analyze -
    Nonparametric Tests menu.
  • 3. Click on the first variable in the pair and
    the second variable in the pair.
  • The names of the variables appear in the current
    selections section of the dialogue box.
  • 5. Click on the central selection arrow when you
    are happy with the variable pair selection.
  • The chosen pair appairs in the Test Pair(s) List.
  • Make sure the Sign box is ticked and remove the
    tick from the Wilcoxon box

46
Example
  • The data in table on the next slide are matched
    pairs of heights obtained from a random sample of
    12 male statistics students. Each student
    reported his height, then his weight was
    measured. Use a 0.05 significance level to test
    the claim that there is no difference between
    reported height and measured height.

47
Reported and measured height of male statistics
student
Reported height 68 74 82.25 66.5 69 68 71 70 70 67 68 70
Measured height 66.8 73.9 74.3 66.1 67.2 67.9 69.4 69.9 68.6 67.9 67.6 68.8
Ho there is no significant difference between
reported heights and measured heights H1
there is a difference
48
Output
Reject Ho. There is sufficient evidence to reject
the claim that no significant difference between
the reported and measured heights.
49
Exercise 6
  • Listed here are the right- and left-hand reaction
    times collected from 14 subject with right
    handed. Use 0.05 significance level to test the
    claim of no difference between the right hand-
    and left-hand reaction times.

50
Right/left reaction times
Right 191 97 116 165 116 129 171 155 112 102 188 158 121 133
Left 224 171 191 207 196 165 171 165 140 188 155 219 177 174
51
Wilcoxon
  • The Wilcoxon test is used with two columns of
    non-parametric related (linked) data.
  • Either one person has taken part in two
    conditions or paired participants (e.g. brother
    and sister) have taken part in the same
    condition.
  • This is the non-parametric equivelant of the
    paired sample t-test

52
Procedure
  • 1. Put your data in two or more columns, one for
    each condition tested.
  • 2. Select 2 Related Samples from Analyze -
    Nonparametric Tests menu.
  • 3. Click on the first variable in the pair.
  • 4. Click on the second variable in the pair.
  • 5. Make sure the Wilcoxon box is ticked
  • The Ranks table produced in the output window
    summarises the ranking process.
  • In the Test Statistics table the Z statistic is
    the result of the Wilcoxon test.
  • The p-value for this statistic is shown below it.
    This is the two tailed significance.

53
Example
  • Use the previous data to test the claim that
    there is no difference between reported heights
    and measured heights using Wilcoxon test at 0.05
    significance level.

54
Output
Reject Ho. There is sufficient evidence to reject
the claim that no difference between reported
and measured heights.
55
Mann-Whitney
  • The Mann-Whitney test is used with two columns of
    independent (unrelated) non-paramteric data.This
    is the non-parametric equivalent of the
    independent samples t-test.

56
Procedure
  • Put all of your measured data into one column.
  • 2. Make a second column that contains codes to
    indicate the group from which each value was
    obtained.
  • 3. Select 2 Independent Samples from the Analyze
    - Nonparametric Tests menu.
  • 4. Select the column containing the data you want
    to analyse and click the top arrow.
  • 5. Select the Grouping Variable - the column
    which contains your group codes - and click the
    bottom arrow.
  • 6. Make sure the Mann-Whitney U option is
    selected.

57
  • The output is produced in the output window.
  • The top table summarises the ranking process.
  • The result of the Mann-Whitney test is given at
    the top of the Test Statistics table.
  • The two-tailed significance of the result is
    given in the same table.

58
Example
  • One study used x-ray computed tomography (CT) to
    collect data on brain volumes for a group of
    patients with obsessive-compulsive disorders and
    a control group of healthy persons. The following
    data shows sample results (in mm) for volumes of
    the right cordate.

59
Volumes of the right cordate
Obsessive-compulsive patients 0.308 0.210 0.304 0.344 0.407 0.455 0.287 0.288 0.463 0.334 0.340 0.305
Control group 0.519 0.476 0.413 0.429 0.501 0.402 0.349 0.594 0.334 0.483 0.460 0.445
60
Output
61
Kruskal-Wallis
  • examines differences between 3 or more
    independent groups or conditions.

62
Procedure
  • 1 Put all your measured data into one column.
  • 2. Make a second column that contains codes to
    indicate the group from which each value was
    obtained.
  • 3. Select K Independent Samples from the Analyze
    - Non-parametric Tests menu.
  • 4. Select the grouping variable, the column that
    contains your group codes, then click on the
    bottom arrow.
  • Make sure the Kruskal-Wallis box is checked
  • In the output window the chi-square statistic is
    shown in the test statistic section, as is the
    P-value.

63
Example
  • We would like to determine whether the scores on
    a test of Spanish are different across three
    different methods of learning
  • Method 1 classroom instruction and language
    laboratory
  • Method 2 only classroom instruction
  • Method3 only self-study in language laboratory.

64
The following are the final examination scores of
samples of students from the three group
Method 1 94 88 91 74 86 97 Method 2 85 82 79
84 61 72 80 Method 3 89 67 72 76 69
At the 0.05 level of significance, test the null
hypothesis that the population sampled are
identical .
65
Output SPSS
66
Exercise 7
  • The following are the miles per gallon which a
    test driver got in random samples of six tankfuls
    of each of three kinds of gasoline
  • Gasoline 1 30 15 32 27 24 29
  • Gasoline 2 17 28 20 33 32 22
  • Gasoline 3 19 23 32 22 18 25
  • Test the claim that there is no difference in the
    true average mileage yield of the three kinds of
    gasoline. (use 0.05 level of significance)

67
Testing for Relationships
68
Pearson's Correlation
  • Pearson's correlation is a parametric test for
    the strength of the relationship between pairs of
    variables.

69
  • What it does The Pearson R correlation tells you
    the magnitude and direction of the association
    between two variables that are on an interval or
    ratio scale.

70
  • Where to find it Under the Analyze menu, choose
    Correlations. Move the variables you wish to
    correlate into the "Variables" box. Under the
    "Correlation Coefficients," be sure that the
    "Pearson" box is checked off.

71
  • Assumption -Both variables are normally
    distributed. You can check for normal
    distribution with a Q-Q plot.

72
  • HypothesesNull There is no association between
    the two variables.Alternate There is an
    association between the two variables.

73
  • SPSS Output
  • Following is a sample output of a Pearson R
    correlation between the Rosenberg Self-Esteem
    Scale and the Assessing Anxiety Scale.

74
SPSS creates a correlation matrix of the two
variables. All the information we need is in the
cell that represents the intersection of the two
variables
SPSS gives us three pieces of information -the
correlation coefficient-the significance-the
number of cases (N
75
  • The correlation coefficient is a number between
    1 and -1. This number tells us about the
    magnitude and direction of the association
    between two variables.
  • The MAGNITUDE is the strength of the correlation.
    The closer the correlation is to either 1 or -1,
    the stronger the correlation. If the correlation
    is 0 or very close to zero, there is no
    association between the two variables. Here, we
    have a moderate correlation (r -.378).

76
  • The DIRECTION of the correlation tells us how the
    two variables are related. If the correlation is
    positive, the two variables have a positive
    relationship (as one increases, the other also
    increases). If the correlation is negative, the
    two variables have a negative relationship (as
    one increases, the other decreases). Here, we
    have a negative correlation (r -.378). As
    self-esteem increases, anxiety decreases

77
Example
  • The following data were obtained in a study of
    the relationship between the resistance (ohms)
    and the failure time (minutes) of certain
    overloaded resistors.
  • Resistance 48 28 33 40 36 39 46 40 30 42 44 48
    39 34 47
  • Failure time 45 25 39 45 36 35 36 45 34 39 51 41
    38 32 45
  • Test the null hypothesis that there is a
    significant correlation between resistance and
    failure time.

78
Output SPSS
There is significant positive correlation between
resistance and failure time, indicating that
failure time increases as resistance increases.
79
Exercise 8
  • An aerobics instructor believes that regular
    aerobic exercise is related to greater mental
    acuity, stress reduction, high self-esteem, and
    greater overall life satisfaction.
  • She asked a random sample of 30 adult to fill out
    a series of questionnaire.
  • The result are as followstest whether there is
    significant correlation between aerobic exercise
    and high self-esteem

80
Subject Exercise Self-esteem Satisfaction stress
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 10 33 9 14 3 12 7 15 3 21 2 20 4 8 0 25 37 12 32 22 31 30 30 15 34 18 37 19 33 10 45 40 30 39 27 44 39 40 46 50 29 47 31 38 25 20 10 13 15 29 22 13 20 25 10 33 5 23 21 30
Subject Exercise Self-esteem Satisfaction stress
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 17 25 2 18 3 27 4 8 10 0 12 5 7 30 14 35 39 13 35 15 35 17 20 22 14 35 20 29 40 30 42 40 30 47 28 39 32 34 41 27 35 30 30 48 45 13 10 27 9 25 7 34 20 15 35 20 23 12 14 15
81
The Spearman Rho correlation
82
The Spearman Rho correlation
  • What it does The Spearman Rho correlation tells
    you the magnitude and direction of the
    association between two variables that are on an
    interval or ratio scale.

83
The Spearman Rho correlation
  • Where to find it Under the Analyze menu, choose
    Correlations. Move the variables you wish to
    correlate into the "Variables" box. Under the
    "Correlation Coefficients," be sure that the
    "Spearman" box is checked off.

84
The Spearman Rho correlation
  • Assumption -Both variables are NOT normally
    distributed. You can check for normal
    distribution with a Q-Q plot. If the variables
    are normally distributed, use a Pearson R
    correlation.

85
The Spearman Rho correlation
  • HypothesesNull There is no association between
    the two variables.Alternate There is an
    association between the two variables.

86
SPSS Output
  • Following is a sample output of a Spearman Rho
    correlation between the Rosenberg Self-Esteem
    Scale and the Assessing Anxiety Scale.

87
  • SPSS creates a correlation matrix of the two
    variables. All the information we need is in the
    cell that represents the intersection of the two
    variables.
  • SPSS gives us three pieces of information -the
    correlation coefficient-the significance-the
    number of cases (N)

88
  • The correlation coefficient is a number between
    1 and -1. This number tells us about the
    magnitude and direction of the association
    between two variables.
  • The MAGNITUDE is the strength of the correlation.
    The closer the correlation is to either 1 or -1,
    the stronger the correlation. If the correlation
    is 0 or very close to 0, there is no association
    between the two variables. Here, we have a
    moderate correlation (r -.392).

89
  • The DIRECTION of the correlation tells us how the
    two variables are related. If the correlation is
    positive, the two variables have a positive
    relationship (as one increases, the other also
    increases). If the correlation is negative, the
    two variables have a negative relationship (as
    one increases, the other decreases). Here, we
    have a negative correlation (r -.392). As
    self-esteem increases, anxiety decreases.

90
Example
  • The following are the numbers of hours which ten
    students studied for an examination and the
    grades which they received

Number of hour studied grade in examination
9 5 11 13 10 5 18 15 2 8 56 44 79 72 70 54 94 85 33 65
Is there any relationship between number of
our studied and grade in examination
91
Output SPSS
92
Exercise 9
  • The following table shows the twelve weeks sales
    of a downtown department store, x, and its
    suburban branch, y
  • X 71 64 67 58 80 63 69 59 76 60 66 55
  • Y 49 31 45 24 68 30 40 37 62 22 35 19
  • Is there any significant relationship between x
    and y?

93
Two way chi-square from frequencies
  • A chi-square test is a non-parametric test for
    nominal (frequency data).
  • The test will calculate expected values for each
    combination of category codes based on the null
    hypothesis that there is no association between
    the two variables.

94
Procedure
  • 1. You will need two columns of codes. Each value
    in each column provides a code to a group or
    criteria category within the appropriate
    variable. You should have one row for each
    combination of category code.
  • 2. You will also need a column giving the
    frequency that each combination of codes is
    observed.
  • Before carrying out your chi-square test you
    first need to tell SPSS that the numbers in your
    frequency column are indeed frequencies. You do
    this using weight cases...
  • 3. Select Weight Cases from the Data menu.
  • 4. Click the Weight cases by button.
  • 5. Select the column containing your frequencies
    and click on the across arrow.

95
  • Click Crosstabs from the Analyze - Descriptive
    Statistics menu.
  • 8. Select the first variable and click on the top
    arrow to move it into the Rows box.
  • 9. Select the second variable and click on the
    middle arrow to move it into the Columns box.
  • Click on Statistics to choose to perform a
    chi-square test on your data.
  • 11. Select the chi-square option from the
    Crosstabs Statistics dialogue box.
  • 12. Click on Continue when ready.
  • 13. Click on Cells to choose to output the
    chi-square expected values.
  • 14. Select the top left boxes to display both the
    Observed and the Expected values

96
Two way chi-square from raw data
  • 1. You will need two columns of codes. Each value
    in each column provides a code to a group or
    criteria category within the appropriate
    variable.
  • 2. Click Crosstabs from the Analyze - Descriptive
    Statistics menu.
  • 3. Select the first variable and click on the top
    arrow to move it into the Rows box.
  • 4. Select the second variable and click on the
    middle arrow to move it into the Columns box.
  • Click on Statistics to choose to perform a
    chi-square test on your data.
  • 6. Select the chi-square option from the
    Crosstabs Statistics dialogue box

97
Example
  • Suppose we want to investigate whether there is a
    relationship between the intelligence of
    employees who have through a certain job training
    program and their subsequent performance on the
    job.
  • A random sample of 50 cases from files yielded
    the following results

98
Performance
Poor fair
good
8 8 3
5 10 7
1 3 5
Below average Average Above average
IQ
Test at the 0.01 level of significance whether on
the job performance of persons who have gone
through the training program is independent of
their IQ
99
Exercise 10
  • Suppose that a store carries two different
    brands, A and B, of a certain type of breakfast
    cereal. During a one-week, 44 packages were
    purchased and the results shows below
  • brand A brand B
  • Men 9 6
  • Women 13 16
  • Test the hypothesis that the brand purchased and
    the sex of the purchaser are independent.
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