The oneway analysis of variance function (STATS_ONE_WAY_ANOVA
) tests differences in means (for groups or variables) for statistical significance by comparing two different estimates of variance. One estimate is based on the variances within each group or category. This is known as the mean squares within or mean square error. The other estimate is based on the variances among the means of the groups. This is known as the mean squares between. If the means of the groups are significantly different, then the mean squares between will be larger than expected and will not match the mean squares within. If the mean squares of the groups are consistent, then the two variance estimates will be about the same.
STATS_ONE_WAY_ANOVA
takes two required arguments: expr1
is an independent or grouping variable that divides the data into a set of groups and expr2
is a dependent variable (a numeric expression) containing the values corresponding to each member of a group. The optional third argument lets you specify the meaning of the NUMBER
value returned by this function, as shown in Table 78. For this argument, you can specify a text literal, or a bind variable or expression that evaluates to a constant character value. If you omit the third argument, then the default is 'SIG'
.
Table 78 STATS_ONE_WAY_ANOVA Return Values
Argument  Return Value Meaning 


Sum of squares between groups 

Sum of squares within groups 

Degree of freedom between groups 

Degree of freedom within groups 

Mean squares between groups 

Mean squares within groups 

Ratio of the mean squares between to the mean squares within (MSB/MSW) 

Significance 
The significance of oneway analysis of variance is determined by obtaining the onetailed significance of an ftest on the ratio of the mean squares between and the mean squares within. The ftest should use onetailed significance, because the mean squares between can be only equal to or larger than the mean squares within. Therefore, the significance returned by STATS_ONE_WAY_ANOVA
is the probability that the differences between the groups happened by chance—a number between 0 and 1. The smaller the number, the greater the significance of the difference between the groups. Refer to the STATS_F_TEST for information on performing an ftest.
STATS_ONE_WAY_ANOVA Example The following example determines the significance of the differences in mean sales within an income level and differences in mean sales between income levels. The results, p_values close to zero, indicate that, for both men and women, the difference in the amount of goods sold across different income levels is significant.
SELECT cust_gender, STATS_ONE_WAY_ANOVA(cust_income_level, amount_sold, 'F_RATIO') f_ratio, STATS_ONE_WAY_ANOVA(cust_income_level, amount_sold, 'SIG') p_value FROM sh.customers c, sh.sales s WHERE c.cust_id = s.cust_id GROUP BY cust_gender ORDER BY cust_gender; C F_RATIO P_VALUE    F 5.59536943 4.7840E09 M 9.2865001 6.7139E17