Multivariate Data. Descriptive techniques for Multivariate data In most research situations data is collected on more than one variable (usually many

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Text of Multivariate Data. Descriptive techniques for Multivariate data In most research situations data is...

  • Multivariate Data

  • Descriptive techniques for Multivariate dataIn most research situations data is collected on more than one variable (usually many variables)

  • Graphical TechniquesThe scatter plotThe two dimensional Histogram

  • The Scatter PlotFor two variables X and Y we will have a measurements for each variable on each case:xi, yixi = the value of X for case iandyi = the value of Y for case i.

  • To Construct a scatter plot we plot the points:(xi, yi)for each case on the X-Y plane.

    (xi, yi)xiyi

  • Data Set #3The following table gives data on Verbal IQ, Math IQ,Initial Reading Acheivement Score, and Final Reading Acheivement Scorefor 23 students who have recently completed a reading improvement program InitialFinalVerbalMathReadingReadingStudentIQIQAcheivementAcheivement186941.11.721041031.51.7386921.51.941051002.02.051181151.93.56961021.42.4790871.51.88951001.42.09105961.71.71084801.61.71194871.61.7121191161.73.11382911.21.81480931.01.7151091241.82.5161111191.43.01789941.61.818991171.62.61994931.41.420991101.42.02195971.51.3221021041.73.123102931.61.9

  • Chart1

    94

    103

    92

    100

    115

    102

    87

    100

    96

    80

    87

    116

    91

    93

    124

    119

    94

    117

    93

    110

    97

    104

    93

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet1

    73111

    102111

    118111

    104111

    81111

    107111

    100111

    87111

    117111

    111111

    98221

    74221

    56221

    111221

    95221

    88221

    82221

    77221

    86221

    92221

    94331

    79331

    96331

    98331

    102331

    102331

    108331

    91331

    120331

    105331

    90412

    76412

    90412

    64412

    86412

    51412

    72412

    90412

    95412

    78412

    107522

    95522

    97522

    80522

    98522

    74522

    74522

    67522

    89522

    58522

    49632

    82632

    73632

    86632

    81632

    97632

    106632

    70632

    61632

    82632

    Sheet2

    186941.11.7

    21041031.51.7

    386921.51.9

    410510022

    51181151.93.5

    6961021.42.4

    790871.51.8

    8951001.42

    9105961.71.7

    1084801.61.7

    1194871.61.7

    121191161.73.1

    1382911.21.8

    14809311.7

    151091241.82.5

    161111191.43

    1789941.61.8

    18991171.62.6

    1994931.41.4

    20991101.42

    2195971.51.3

    221021041.73.1

    23102931.61.9

    Sheet2

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet3

  • (84,80)

    Chart1

    94

    103

    92

    100

    115

    102

    87

    100

    96

    80

    87

    116

    91

    93

    124

    119

    94

    117

    93

    110

    97

    104

    93

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet1

    73111

    102111

    118111

    104111

    81111

    107111

    100111

    87111

    117111

    111111

    98221

    74221

    56221

    111221

    95221

    88221

    82221

    77221

    86221

    92221

    94331

    79331

    96331

    98331

    102331

    102331

    108331

    91331

    120331

    105331

    90412

    76412

    90412

    64412

    86412

    51412

    72412

    90412

    95412

    78412

    107522

    95522

    97522

    80522

    98522

    74522

    74522

    67522

    89522

    58522

    49632

    82632

    73632

    86632

    81632

    97632

    106632

    70632

    61632

    82632

    Sheet2

    186941.11.7

    21041031.51.7

    386921.51.9

    410510022

    51181151.93.5

    6961021.42.4

    790871.51.8

    8951001.42

    9105961.71.7

    1084801.61.7

    1194871.61.7

    121191161.73.1

    1382911.21.8

    14809311.7

    151091241.82.5

    161111191.43

    1789941.61.8

    18991171.62.6

    1994931.41.4

    20991101.42

    2195971.51.3

    221021041.73.1

    23102931.61.9

    Sheet2

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet3

  • Chart2

    94

    103

    92

    100

    115

    102

    87

    100

    96

    80

    87

    116

    91

    93

    124

    119

    94

    117

    93

    110

    97

    104

    93

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet1

    73111

    102111

    118111

    104111

    81111

    107111

    100111

    87111

    117111

    111111

    98221

    74221

    56221

    111221

    95221

    88221

    82221

    77221

    86221

    92221

    94331

    79331

    96331

    98331

    102331

    102331

    108331

    91331

    120331

    105331

    90412

    76412

    90412

    64412

    86412

    51412

    72412

    90412

    95412

    78412

    107522

    95522

    97522

    80522

    98522

    74522

    74522

    67522

    89522

    58522

    49632

    82632

    73632

    86632

    81632

    97632

    106632

    70632

    61632

    82632

    Sheet2

    186941.11.7

    21041031.51.7

    386921.51.9

    410510022

    51181151.93.5

    6961021.42.4

    790871.51.8

    8951001.42

    9105961.71.7

    1084801.61.7

    1194871.61.7

    121191161.73.1

    1382911.21.8

    14809311.7

    151091241.82.5

    161111191.43

    1789941.61.8

    18991171.62.6

    1994931.41.4

    20991101.42

    2195971.51.3

    221021041.73.1

    23102931.61.9

    Sheet2

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet3

  • Some Scatter Patterns

  • Chart3

    165.3

    70.2

    97.6

    53.8

    128.5

    98.3

    129.9

    120.5

    89.6

    102.9

    139.8

    81.9

    89.2

    155.4

    112.5

    151.8

    142.9

    69.9

    88.1

    120.4

    151.8

    107.5

    105.8

    81.9

    134.7

    74.9

    123

    156.4

    125.1

    21.2

    46.5

    100.1

    106.3

    112.6

    54.3

    112.7

    166

    131.2

    138.6

    163.6

    115.2

    113.7

    108.6

    118.4

    27.8

    89.9

    205.4

    126.3

    74

    124.3

    48.6

    90.7

    46.3

    87.1

    125.9

    109.5

    102.1

    101.4

    124.9

    138.4

    99.8

    86.1

    128.6

    115

    130.3

    106.8

    141.1

    119.1

    101.6

    86.6

    102.2

    160.1

    62.2

    41.2

    95.9

    69.4

    88.2

    126.3

    101

    118.3

    53.8

    117.3

    10.5

    99.8

    101.6

    117.5

    66.1

    129.2

    78.6

    116.2

    151.7

    100.2

    122.7

    101.1

    136.1

    49.6

    98.6

    Sheet1

    73111

    102111

    118111

    104111

    81111

    107111

    100111

    87111

    117111

    111111

    98221

    74221

    56221

    111221

    95221

    88221

    82221

    77221

    86221

    92221

    94331

    79331

    96331

    98331

    102331

    102331

    108331

    91331

    120331

    105331

    90412

    76412

    90412

    64412

    86412

    51412

    72412

    90412

    95412

    78412

    107522

    95522

    97522

    80522

    98522

    74522

    74522

    67522

    89522

    58522

    49632

    82632

    73632

    86632

    81632

    97632

    106632

    70632

    61632

    82632

    Sheet2

    186941.11.7

    21041031.51.7

    386921.51.9

    410510022

    51181151.93.5

    6961021.42.4

    790871.51.8

    8951001.42

    9105961.71.7

    1084801.61.7

    1194871.61.7

    121191161.73.1

    1382911.21.8

    14809311.7

    151091241.82.5

    161111191.43

    1789941.61.8

    18991171.62.6

    1994931.41.4

    20991101.42

    2195971.51.3

    221021041.73.1

    23102931.61.9

    Sheet2

    Verbal IQ

    Math IQ

    Scatter Plot

    Sheet3

    100100abs

    10100140

    109100.7

    109.9117.6

    88.288.2

    92.9118

    113.1149.2

    90.786.7

    117.421.3

    86.3-20.3

    84.6141.5

    91.783.6

    101.794

    105.245.1

    112.790

    94.6108.2

    109.4110.4

    93.383.7

    102.6135.9

    81115.8

    93.781.4

    97.5103.1

    114.597.7

    105.2190

    97.9120.6

    114.9140.5

    99.781.6

    115.483.2

    102120

    91.3145.9

    104.6136.6

    83.870

    12480.8

    73.294.4

    101.3121

    119108.5

    99.140.1

    101.638

    85.232.2

    98.8113.9

    108.2124.1

    106.3138.5

    99.9126.2

    101.8154

    104.590

    96.954.7

    104.159.6

    104.287.4

    104.299

    103.954

    104.4142.8

    109.248.8

    80.480.3

    109.3112.2

    97137.6

    100133.1

    95.812.4

    99.3116.5

    98.3168.1

    105.77.4

    115.7171.8

    92.848.6

    103.1149.9

    93.9132.2

    92.899.7

    106.2131.6

    91.6109.6

    99.688.7

    113.489.8

    115.4108.6

    104.5128.8

    104.278.7

    97.6112.3

    96.5106.2

    99.291.6

    88.360.3

    101.5149.7

    85.7118.3

    90.284.7

    105.7114.2

    91.5162.4

    107.4108

    85.7140.5

    98.878.4

    104.123.1

    105.1144.2

    98.8133.7

    101.9177.8

    107172.4

    83115.4

    83.2116.5

    80.490.9

    87.280.9

    97.1114.4

    106.365.2

    100.5102.2

    113.595.3

    106.363.7

    91.1115.9

    Sheet3

    165.3

    70.2

    97.6

    53.8

    128.5

    98.3

    129.9

    120.5

    89.6

    102.9

    139.8

    81.9