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: statistical procedure

Measurement level: Correlate: nominal, Happiness: metric

Meaning: if the correlate is measured at c levels, the c mean happiness values can be ranked from low to high. A multiple comparison procedure judges for each of the ½c(c-1) pairs whether or not they differ significantly.  A convenient way to represent the results is by ranking the c means and by underlining them in such a way that means which have a common underlining do NOT differ significantly.

When added by us, this test is performed at the 95% confidence level for all the differences together.

Type: descriptive statistic only
Measurement level: Correlate : dichotomous, Happiness level: metric
Theoretical range: unlimited.

Meaning:  effect size indicator for difference of means.
Formula: Cohen's d = (M2 - M1) ⁄ SDpooled
SDpooled = √((SD1^2 + SD2^2) ⁄ 2)

Type: descriptive statistic only
Measurement level: Correlate : dichotomous, Happiness level: metric
Theoretical range: unlimited.

Meaning:  effect size indicator for difference of means.
Formula: Cohen's d = (M2 - M1) ⁄ SDpooled
SDpooled = √((SD1^2 + SD2^2) ⁄ 2)

Type: test statistic.

Measurement level: Correlates: all metric, Happiness: metric.
Range: [-1 ; +1]

Meaning:  
beta > 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta < 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta = 0  «   no correlation.
beta = + 1 or -1  «   perfect correlation.

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)