Menghitung Korelasi Bivariat menggunakan SPSS

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MenghitungKorelasi Bivariatmenggunakan SPSS
Pearson's correlation coefficient, Spearman's
rho, and Kendall's tau-b
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The Bivariate Correlations

• procedure computes the pair-wise associations
  for a set of variables and displays the results
  in a matrix. It is useful for determining the
  strength and direction of the association between
  two scale or ordinal variables.

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• Pairwise When computing a measure of association
  between two variables in a larger set, cases are
  included in the computation when the two
  variables have non-missing values, irrespective
  of the values of the other variables in the set.
• Scale A variable can be treated as scale when
  its values represent ordered categories with a
  meaningful metric, so that distance comparisons
  between values are appropriate.
• Ordinal A variable can be treated as ordinal
  when its values represent categories with some
  intrinsic ranking for example, levels of service
  satisfaction from highly dissatisfied to highly
  satisfied.

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Correlation

• measure how variables or rank orders are
  related.
• Before calculating a correlation coefficient,
  screen your data for outliers (which can cause
  misleading results) and evidence of a linear
  relationship.

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• Pearson's correlation coefficient is a measure of
  linear association. Two variables can be
  perfectly related, but if the relationship is not
  linear, Pearson's correlation coefficient is not
  an appropriate statistic for measuring their
  association.
• Pearson correlation coefficients assume the data
  are normally distributed.

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To Obtain Bivariate Correlations

• From the menus choose
•   Analyze  Correlate  Bivariate...
•  ? Select two or more numeric variables.

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The following options are also available

• Correlation Coefficients.
• For quantitative, normally distributed variables,
  choose the Pearson correlation coefficient.
• If your data are not normally distributed or have
  ordered categories, choose Kendall's tau-b or
  Spearman, which measure the association between
  rank orders.

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The following options are also available

• Test of Significance.
• You can select two-tailed or one-tailed
  probabilities. If the direction of association is
  known in advance, select One-tailed. Otherwise,
  select Two-tailed.

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The following options are also available

• Flag significant correlations.
• Correlation coefficients significant at the 0.05
  level are identified with a single asterisk, and
  those significant at the 0.01 level are
  identified with two asterisks.

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Result Pearsons correlation
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Result Spearmans rho correlation
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• The correlations table displays Pearson
  correlation coefficients, significance values,
  and the number of cases with non-missing values.

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Pearson correlation coefficients

• The Pearson correlation coefficient is a measure
  of linear association between two variables.
• The values of the correlation coefficient range
  from 0 to 1.
• The sign of the correlation coefficient indicates
  the direction of the relationship (positive or
  negative).

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Pearson correlation coefficients

• The absolute value of the correlation coefficient
  indicates the strength, with larger absolute
  values indicating stronger relationships.
• The correlation coefficients on the main diagonal
  are always 1.0, because each variable has a
  perfect positive linear relationship with itself.
• Correlations above the main diagonal are a mirror
  image of those below.

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• In this example, the correlation coefficient for
  Arimatika and Loneliness is 0.837.
• Since 0.837 is relatively close to 1, this
  indicates that Arimatika and Loneliness are
  positively correlated.

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Significance Values

• The significance level (or p-value) is the
  probability of obtaining results as extreme as
  the one observed.
• If the significance level is very small (less
  than 0.05) then the correlation is significant
  and the two variables are linearly related.
• If the significance level is relatively large
  (for example, 0.50) then the correlation is not
  significant and the two variables are not
  linearly related.

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• The significance level or p-value is 0.000 which
  indicates a very low significance.
• The small significance level indicates that
  Aritmatika and Loneliness are significantly
  positively correlated.

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Significance Values

• The significance level (or p-value) is the
  probability of obtaining results as extreme as
  the one observed.
• If the significance level is very small (less
  than 0.05) then the correlation is significant
  and the two variables are linearly related.
• If the significance level is relatively large
  (for example, 0.50) then the correlation is not
  significant and the two variables are not
  linearly related.

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Significance Values

• As Aritmatika increases Loneliness also
  increases. And as Aritmatika decreases,
  Loneliness also decreases.

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• N is the number of cases with non-missing values.
• In this table, the number of cases with
  non-missing values for both Aritmatika and
  Loneliness is 23.

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Notice

• Even if the correlation between two variables is
  not significant, the variables may be correlated
  but the relationship is not linear.
• So, we use Spearmans rho or Kendall Tau-b