The fifth diagnostic is the cross sectional autocorrelation test also called cross sectional dependence, the null hypothesis is that the cross sections are independent and the alternative hypothesis
is that the cross sectionals are dependent.
Caption: FIGURE 1 Mean LR test [chi square]/df statistic for N = 100, 200, 300, 400, 500, 600, 700, 800, 900, and 1,000 for k = 10, 20, 30, 40, and 50 items under the null hypothesis condition (left panel) and alternative hypothesis
condition (right panel) with 8 DIF items
Table 32 shows the hypothesis test for the 30 experiments performed for each index validation mentioned in Section 4, in order to know if there exists significant difference between the algorithms by using as the null and alternative hypothesis
the assumptions made in (15).
Since p value (0.000315) is less than a (0.05), therefore, alternative hypothesis
is accepted (Table 2).
With this operation, the identified alternative hypothesis
turns into a new null hypothesis.
For the cutoff for the alternative hypothesis
(Rouder's Bayes factor = .333), the relevant cumulative probability is greater than or equal to the cutoff.
: The content of media advertising (TV) affects the attraction of clients on Bank Mellat.
Under the alternative hypothesis
, stock returns display characteristics consistent with systemic risk (asymptotic tail dependence) and yet the nonparametric estimators remain consistent.
Heuristically, the null and alternative hypothesis
can be written as follows:
The test is divided into two categories with respect to the alternative hypothesis
. The first category is called within-dimension (panel test) in which the AR coefficient across the cross sectional units of the panel are pooled to apply unit root test on the residuals obtained by the procedure described above.
In meta-analyses, the alternative hypothesis
usually suggests that there is at least one study which differs in the effect sizes.