Comparing Two Populations (Seminar 5)

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    Assoc. Prof. Dr. Nagarajah Lee

    Open University Malaysia

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    Example 1 : SurveyExample 1 : Survey

    The researcher would like to test

    students is significantly differentrom e ema e.

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    Describing the samplesDescribing the samples

    Can we conclude that the mean EQ score of the

    What is the suitable test to check for this?

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    Purpose To compare differences between two populations

    Commonly Used Two Sample Test in Behavioral Science and Medical Research

    Number ofDependent Variable

    Number of cate ories

    measurement ofdependentvariables

    Interval/Ratio

    One One

    Nominal Ordinal

    One

    for comparing

    Unit of analysis

    Two or More

    Proportion Median or Mean Rank

    Mean

    Requirement Frequency per cellMore than 5

    Chi-

    Test

    Wilc

    o

    rank

    Inde

    Test

    Paire

    d

    Fish

    Test

    Frequency per cellLess than 5

    Relatedsample

    Unrelatedsample

    Mann

    Test

    Related Sample Unrelated Sample

    Statist ical t est

    quare

    on

    Sign

    est

    pen

    den

    tT-

    TT

    est

    rsEx

    act

    Whitn

    eyU

    Example Testing whether the there is any difference

    in percentage of low birth weight amongsmoking and non-smoking mothers

    Testing whether there is any differencein the median values or mean ranks

    between two groups

    Testing whether there is any difference in the

    mean values between two groups

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    NORMALITY ASSUMPTION CHECKNORMALITY ASSUMPTION CHECK

    NORMALITY:

    Ho: The data comes from a normally distributed populationH1: The data does not come from a normally distributed population

    Result: Since the p-value > .05, the null hypothesis is not rejected.

    Conclusion: The assumption of normality holds.

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    TESTING A POPULATION MEANTESTING A POPULATION MEAN

    Hypothesis:

    Ho: There is no difference in the mean EQ score between

    male and female MEd students.

    H1: There is a signif icant dif ference in the mean EQ score

    between male and female MEd students.

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    Analyze >> Compare means >>Independent t-test

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    TEST FOR A SIGNIFICANT DIFFERENCE IN MEANTEST FOR A SIGNIFICANT DIFFERENCE IN MEAN

    Result: Since the p-value > 0.05, the null hypothesis is NOT rejected.

    Conclusion: There is not enough evidence to conclude that there is a

    significant difference in the mean EQ scores between male and female MEdstudents.

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    Example 2 : MedicalExample 2 : Medical

    A st u d y w as ca r r i ed o u t t o d et er m i n e w h e th e r

    pa r t i cu la r d r ug . The depend en t va r iab le is t hen u m b er o f t r i a l s r e q u i r ed t o m ast er a g iv enas .

    A g roup o f 28 sub j ect s w ere random ly assigned.assigned t o t h e exp e r im en t a l g r oup w ere g i vent he d ru g , and t hose assigned t o t he con t ro l

    g r oup w ere g i ven p lacebo. A f te r a g i ven pe r i odo f t i m e, t h e n u m b er s o f t r i al s t o m ast er t h et ask w e re reco rded .

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    Experimental Group Cont rol Group

    17 14

    15

    5

    14

    10

    1

    12

    1

    2

    16

    11

    14

    8

    DATA SET

    13

    15

    16

    10

    2

    12

    178

    19

    112

    15

    4

    12

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    Describing the samplesDescribing the samples

    Can we conclude that the response time of thetreatment and control groups are significantlydifferent?

    What is the suitable test to check for this?

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    Purpose To compare differences between two populations

    Commonly Used Two Sample Test in Medical Research

    Number ofDependent Variable

    measurement ofdependentvariables

    Interval/Ratio

    One One

    Nominal Ordinal

    One

    Number of categoriesfor comparing

    Unit of analysis

    Two or More

    Proportion Median or Mean Rank

    Mean

    Requirement Frequency per cellMore than 5

    Chi-

    Test

    Wilc

    o

    rank

    Inde

    Test

    Paire

    d

    Fish

    Test

    Frequency per cellLess than 5

    Relatedsample

    Unrelatedsample

    Mann

    Test

    Related Sample Unrelated Sample

    Statist ical t est

    quare

    on

    Sign

    est

    pen

    den

    tT-

    TT

    est

    rsEx

    act

    Whitn

    eyU

    Example Testing whether the there is any difference

    in percentage of low birth weight amongsmoking and non-smoking mothers

    Testing whether there is any differencein the median values or mean ranks

    between two groups

    Testing whether there is any difference in the

    mean values between two groups

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    NORMALITY ASSUMPTION CHECKNORMALITY ASSUMPTION CHECK

    H0 : The data comes from a normally distributed population.

    H1 : The data does not come from a normally distributed.

    Refer to Shapiro-Wilk statistic, the significance level issmaller than .05, so reject H0.

    Conclusion : The data does not come from a normallydistributed population.

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    Purpose To compare differences between two populations

    Commonly Used Two Sample Test in Medical Research

    Number ofDependent Variable

    measurement ofdependentvariables

    Interval/Ratio

    One One

    Nominal Ordinal

    One

    Number of categoriesfor comparing

    Unit of analysis

    Two or More

    Proportion Median or Mean Rank

    Mean

    Requirement Frequency per cellMore than 5

    Chi-

    Test

    Wilco

    rank

    Inde

    Test

    Paire

    d

    Fish

    Test

    Frequency per cellLess than 5

    Relatedsample

    Unrelatedsample

    Mann

    Test

    Related Sample Unrelated Sample

    Statist ical t est

    quare

    on

    Sign

    est

    pen

    den

    tT-

    TT

    est

    rsEx

    act

    Whitn

    eyU

    Example Testing whether the there is any difference

    in percentage of low birth weight amongsmoking and non-smoking mothers

    Testing whether there is any differencein the median values or mean ranks

    between two groups

    Testing whether there is any difference in the

    mean values between two groups

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    TESTING A POPULATION MEANTESTING A POPULATION MEAN

    H0 : The drug has no effect on the number of trials.

    H1 : The drug has an effect on the number of.

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    Analyze >> Non-parametric tests

    >> 2- Independent test

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    ResultsResults

    Result: Since the p-value < 0.05, the null hypothesis is rejected.

    Conclusion: There is enough evidence to conclude that the drug has an

    effect on the number of trials needed to master the task

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    Example 3Example 3

    A r esear ch e r w o u l d l i k e t o t est w h e th e r t h e r e i s

    any d i f f e rence in pa t i en t s hea r t beat w henn u t r i en t A is g i v en i n t h r ee m eal s d u r i n g t h e

    ( t r e at m en t Y) .

    A random sam p le o f 12 pa t i en t s w as chosen .Th e t w o t r e at m en t s w er e ad m i n ist er e d o n t w o

    succeed in g occasions and pa t ien t s hear t bea tp er m i n u t e w er e r eco r d e d.

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    Heartbeat per minuteHeartbeat per minute

    1 62 54

    2 55 63

    3 80 1094 66 75

    5 84 80

    6 88 827 90 77

    8 52 89

    9 63 6610 58 71

    11 73 69

    12 67 81

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    Purpose To compare differences between two populations

    Commonly Used Two Sample Test in Medical Research

    Number ofDependent Variable

    Number of cate ories

    measurement ofdependentvariables

    Interval/Ratio

    One One

    Nominal Ordinal

    One

    for comparing

    Unit of analysis

    Two or More

    Proportion Median or Mean Rank

    Mean

    Requirement Frequency per cellMore than 5

    Chi-

    Test

    Wilco

    rank

    Inde

    Test

    Paire

    d

    Fish

    Test

    Frequency per cellLess than 5

    Relatedsample

    Unrelatedsample

    Mann

    Test

    Related Sample Unrelated Sample

    Statist ical t est

    quare

    on

    Sign

    est

    pen

    den

    tT-

    TT

    est

    rsEx

    act

    Whitn

    eyU

    Example Testing whether the there is any difference

    in percentage of low birth weight amongsmoking and non-smoking mothers

    Testing whether there is any differencein the median values or mean ranks

    between two groups

    Testing whether there is any difference in the

    mean values between two groups

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    Test of Normalit yTest of Normalit y

    0

    population.

    distributed population.

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    OUTPUT

    -level is greater than .05, so do not reject H0.

    Conclusion : The data comes from a normallydistributed population.

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    Pai r ed t t estPai r ed t t est

    H0 : There is no significant difference in the heartbeatrate between patients given nutrient A in 3 mealsduring the day and patients given nutrient A in onemeal.

    H1 : There is a significant difference in the heartbeat

    during the day and patients given nutrient A in onemeal.

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    Resu l ts

    From the table, the significance value is 0.165 (2-tailed). The

    si nificance level is reater than 0.05 so do not re ect H .

    Conclusion : There is no significant difference in theheartbeat rate between patients given nutrient A in 3 meals

    during the day and patients given nutrient A in one meal.

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    Example 4Example 4

    response time is influenced by taking a particulardrug. The dependent variable is the number of trialsrequ re o mas er a g ven as .

    A group of 28 subjects were randomly assigned to.

    to the experimental group were given the drug, andthose assigned to the control group were given

    p ace o. ter a g ven per o o t me, t e num ers otrials to master the task were recorded andcate orized as less than 10 times or 10 times andabove.

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    Groups * TRIAL_C Crosstabulation

    TRIAL_C

    4 9 13

    30.8% 69.2% 100.0%

    Count% within Groups

    experimental groupGroups

    10 times

    or more Total

    46.7% 53.3% 100.0%

    11 17 28

    39.3% 60.7% 100.0%

    % within Groups

    Count

    % within Groups

    Total

    Can we conclude that the response time of thetreatment and control groups are significantlydifferent?

    What is the suitable test to check for this?

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    Purpose To compare differences between two populations

    Commonly Used Two Sample Test in Medical Research

    Number ofDependent Variable

    Number of cate ories

    measurement ofdependentvariables

    Interval/Ratio

    One One

    Nominal Ordinal

    One

    for comparing

    Unit of analysis

    Two or More

    Proportion Median or Mean Rank

    Mean

    Requirement Frequency per cellMore than 5

    Chi-

    Test

    Wilc

    o

    rank

    Inde

    Test

    Paired

    Fish

    Test

    Frequency per cellLess than 5

    Relatedsample

    Unrelatedsample

    Mann

    Test

    Related Sample Unrelated Sample

    Statist ical t est

    quare

    on

    Sign

    est

    pen

    den

    tT-

    TT

    est

    rsEx

    act

    Whitn

    eyU

    Example Testing whether the there is any difference

    in percentage of low birth weight amongsmoking and non-smoking mothers

    Testing whether there is any differencein the median values or mean ranks

    between two groups

    Testing whether there is any difference in the

    mean values between two groups

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    Ch iChi-- Sq u ar e TestSq u ar e Test

    H0 : Treatment with the drug has no effect on the.

    H1

    : Treatment with the drug has an effect on the.

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    Analyze >> Descriptive Statistics >> Cross Tab

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    OutputOutput

    Groups * TRIAL_C Crosstabulation

    less than

    10 times

    10 times

    or more

    TRIAL_C

    Total

    30.8% 69.2% 100.0%

    7 8 1546.7% 53.3% 100.0%

    11 17 28

    oun

    % within Groups

    Count% within Groups

    Count

    exper men a group

    control group

    roups

    Total

    . . .

    Chi-S uare Tests

    .738b 1 .390

    .222 1 .638

    .745 1 .388

    Pearson Chi-Square

    Continuity Correctiona

    Likelihood Ratio

    Value df

    Asymp. Sig.

    (2-sided)

    Exact Sig.

    (2-sided)

    Exact Sig.

    (1-sided)

    .460 .320.712 1 .399

    28

    Fisher's Exact Test

    Linear-by-Linear

    Association

    N of Valid Cases

    Computed only for a 2x2 tablea.

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

    5.11.

    b.

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    nce one o e ce s as ess en o serva ons,to interpret the output from the Ch-Square test,consider the -value re orted b the Fishers ExactTest

    From the table, the p-value is 0.460(2-tailed). Thesignificance level is greater than 0.05, so DO NOTreject H0.

    onc us on : rea men w e rug as no e econ the trials needed to master the task

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