For non-zero lags, IPS show that [[bar.t].sub.NT] follows a standard normal
distribution, which is as follows:
In Panel A, the weighted chi-squared distribution provides a very accurate approximation to the finite-sample behavior of ~1- In contrast, the standard normal
test leads to severe size distortions and rejects the true null hypothesis about 92% of the time at the 5% significance level.
As for possible cut scores, the standard normal
distribution of lz-ch requires the fulfillment of some conditions that can never be fulfilled with real data.
Once standard normal
variates are generated, simulated values for each of these 11 primary variables can be calculated.
For each bootstrap method of sampling, the standard normal
, percentile, and bias-corrected percentile bootstrap intervals were constructed and compared for the 1st, 5th, 10th, and 50th percentiles for the MOE and MOR for WPC.
When X random variables has standard normal
distribution, its probability density function, is to be as follows:
The mx0.025th and mx0.975th highest means then give us the 95 per cent confidence interval for the mean test statistic, and the 0.025th and 0.975th highest variances give us the 95 per cent confidence interval for the variance test statistic, under the null hypothesis that [[??].sub.k,t] is standard normal
but has the dependence structure of the fitted ARMA process.
Thus, from theorem 3.2, a testing procedure for model selection can be based on the comparison of the value of [DI.sub.n] to critical values from a standard normal
It can be shown that Yi is approximately standard normal
. Hence, we can plot [Y.sub.1], [Y.sub.2],..., on a chart with the center line CL = 0 and upper control limit at UCL = 3 and lower control limit at LCL = -3.
Where [PHI]()= the standard normal
cumulative distribution function.
IPS proved that the following standardized t-bar statistic converges to a standard normal
Assuming a standard normal
curve, the result can be interpreted that the average student's academic gain would improve from the 50th percentile to approximately the 60th percentile by implementing field trips.