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.

Alternative hypothesis: 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.