Type: statistical procedure
Measurement level: Correlate(s): nominal, Happiness: metric.
In an ANOVA, the total happiness variability, expressed as the sum of squares, is split into two or more parts, each of which is assigned to a source of variability. At least one of those sources is the variability of the correlate, in case there is only one, and always one other is the residual variability, which includes all unspecified influences on the happiness variable. Each sum of squares has its own number of degrees of freedom (df), which sum up to Ne -1 for the total variability.  If a sum of squares (SS) is divided by its own number of df, a mean square (MS) is obtained.  The ratio of two correctly selected mean squares has an F-distribution under the hypothesis that the corresponding association has a zero-value.

NOTE:  A significantly high F-value only indicates that,  in case of a single correlate, the largest of the c mean values is systematically larger than the smallest one. Conclusions about the other pairs of means require the application of a Multiple Comparisons Procedure (see e.g. BONFERRONI's MULTIPLE COMPARISON TEST, DUNCAN's MULTIPLE RANGE TEST or STUDENT-NEWMAN-KEULS)

Type: test statistic
Range:  [0; Ne*(min(c,r)-1)], where c and r are the number of columns and rows respectively in a cross tabulation of  Ne  sample elements.

Meaning:
Chi² <=  (c-1) * (r-1) means: no or minor association
Chi² >>  (c-1) * (r-1) means: strong association

Type: statistical procedure
Measurement level: Correlate(s): nominal, Happiness: metric.
In an ANOVA, the total happiness variability, expressed as the sum of squares, is split into two or more parts, each of which is assigned to a source of variability. At least one of those sources is the variability of the correlate, in case there is only one, and always one other is the residual variability, which includes all unspecified influences on the happiness variable. Each sum of squares has its own number of degrees of freedom (df), which sum up to Ne -1 for the total variability.  If a sum of squares (SS) is divided by its own number of df, a mean square (MS) is obtained.  The ratio of two correctly selected mean squares has an F-distribution under the hypothesis that the corresponding association has a zero-value.

NOTE:  A significantly high F-value only indicates that,  in case of a single correlate, the largest of the c mean values is systematically larger than the smallest one. Conclusions about the other pairs of means require the application of a Multiple Comparisons Procedure (see e.g. BONFERRONI's MULTIPLE COMPARISON TEST, DUNCAN's MULTIPLE RANGE TEST or STUDENT-NEWMAN-KEULS)

Type: test statistic
Range:  [0; Ne*(min(c,r)-1)], where c and r are the number of columns and rows respectively in a cross tabulation of  Ne  sample elements.

Meaning:
Chi² <=  (c-1) * (r-1) means: no or minor association
Chi² >>  (c-1) * (r-1) means: strong association

Type: asymmetric standard test statistic.
Range: nonnegative unlimited

Meaning :  the test statistic is also called the "Variance Ratio" and is the ratio of two independent  estimators  of the same variance  with   n1  and   n2  degrees of freedom  respectively. The critical values of its probability distribution are tabulated extensively in almost any textbook on Statistics

Type: test statistic
Range:  [0; Ne*(min(c,r)-1)], where c and r are the number of columns and rows respectively in a cross tabulation of  Ne  sample elements.

Meaning:
Chi² <=  (c-1) * (r-1) means: no or minor association
Chi² >>  (c-1) * (r-1) means: strong association

Type: statistical procedure
Measurement level: Correlate(s): nominal, Happiness: metric.
In an ANOVA, the total happiness variability, expressed as the sum of squares, is split into two or more parts, each of which is assigned to a source of variability. At least one of those sources is the variability of the correlate, in case there is only one, and always one other is the residual variability, which includes all unspecified influences on the happiness variable. Each sum of squares has its own number of degrees of freedom (df), which sum up to Ne -1 for the total variability.  If a sum of squares (SS) is divided by its own number of df, a mean square (MS) is obtained.  The ratio of two correctly selected mean squares has an F-distribution under the hypothesis that the corresponding association has a zero-value.

NOTE:  A significantly high F-value only indicates that,  in case of a single correlate, the largest of the c mean values is systematically larger than the smallest one. Conclusions about the other pairs of means require the application of a Multiple Comparisons Procedure (see e.g. BONFERRONI's MULTIPLE COMPARISON TEST, DUNCAN's MULTIPLE RANGE TEST or STUDENT-NEWMAN-KEULS)

Type: test statistic
Range:  [0; Ne*(min(c,r)-1)], where c and r are the number of columns and rows respectively in a cross tabulation of  Ne  sample elements.

Meaning:
Chi² <=  (c-1) * (r-1) means: no or minor association
Chi² >>  (c-1) * (r-1) means: strong association