Dear Parwin Jalal Jalil

Try to read the following articles. One are certified firms and the other are non certified firms. I hope that you will get the points.

Article Intellectual capital and firm performance: evidence from cer...

Article Labour productivity and firm performance: evidence from cert...

Let me know if you have further questions.

Good luck

A p-value for what?

A p-value gives the probability of a test statistic being more extreme than the one calculated from your sample under a specified statistical model.

So you need to tell us for what statistic in what kind of statistical model you like to have a p-value.

For for example. if your data are binary observations (like yes/no, present/absent, dead/alive, etc.), the interesting statistic might be an odd ratio in a logistic model and the p-value should give the probability of a more extreme odds ratio from a model assuming a true odds ratio of 1.

Or when your data are counts of events in some temporal or spatial intarval, the interesting statistic might be a rate ratio in a Poisson-model...

@jochen would you be so kind and recommend any test that would give P

Yey, cool, that's simple:

All you need is a deck of 21 cards including the queen of hearts. For any measurement you make, draw a card from the well-shuffled deck. If the card drawn is the queen of hearts, then p < 0.05.

Just make sure that you describe this correctly in the methods part ("results were considered statistically significant when after the measurement the card randomly drawn from a deck of 21 cards including the queen of hearts was the queen of hearts.")

This procedure is statistically valid. The nominal type-I error rate is 1/21 = 0.048, slightly more conservative than required. The problem is only that this procedure provides a power of only 4.8%, independent of the true effect size. But this minor disadvantage is easily compensated by the low costs (you need only a single measurement!).

Due to the low cost of an individual experiment to produce the required data, it is very cheap to repeat the experiment until you get p < 0.05. With only 14 experiments the odds are already in favour of getting p

Thanks for replying p value for age matched groups if they are matched or not. I have 20 (10 female and 10 male sample)

And

40 tested sample ( 30male and 10 female )

If "age" is a relevant covariable, then "age" should be in the model. For that small sample size there won't be much information about the functional form of the relationship between age and the response in your data. Often, assuming a linear relationship is okayish, a spline with 2 or 3 degrees of freedom would be more flexible, though.

Matching will mean to throw away 50% of your data (and it is not well defined which 50%). Further, matching will give you the average effect for your sample structure, which is not neccessarily the expected treatment effect for the population. And finally, if age is a relevant covariable, there might be an interaction with the treatment variable.

Send me your data at [email protected]. We can work it out together then concrete explanations will follow.

In experimental research, we generally compare two or more means or proportions. At times we compare the median when faced with outliers. In some instances, we even compare distributions of ranks or measure relationship.

Generally, the null hypothesis is set to test that there is no difference between the means or proportions or between the groups under comparison.

There are four possible outcomes when testing the hypothesis.

We might fail to find the true difference therefore having a false negative result also known as type II error. It is also termed beta error because we found ourselves out of the Alpha area (therefore finding ourselves in the beta area where we were not normally supposed to be) of the Gaussian curve.

We find a difference where it just happened by chance then leading to a false positive or type I error also termed alpha error because we found ourselves in the Alpha area (therefore finding ourselves out of the beta area where we were normally supposed to be) of the Gaussian curve.

In testing the null hypothesis ‘there is no significant difference between the two treatments’ IST for instance indicates a non-significant difference at the 95% CL as the P-value is equal to 0.064 assuming equal variance, which is greater than 0.05, therefore accepting the null hypothesis. The mean difference is 0.950 which is relatively high for us to assume a Type II error. In fact, there is type I error if one rejects the null hypothesis when it is true and there is type II error when one accepts the null hypothesis when it is false. This is common when the sample size is small or inadequate or the power use to estimate the sample size is weak. Let us verify this hypothesis by comparing effect sizes, using Cohen’s d .

The calculated or real effect size is 0.950/1.036, 1.036 been the standard deviation for the total group. This gives a value of 0.917.

Using Gpower, considering a sample size of 8 for a total sample of 16 which is what we have used in our experiment, a power of 85% and 80% respective at 95% CL, we obtain a theoretical effect sizes (ρ) of 1.612 and 1.507 respectively (in fact, the same precision is attained by combining higher power and higher ρ or smaller power and smaller ρ; that is the reason why when the theoretical power drops, the theoretical ρ also drops).

As seen above, the smaller the ρ, the more rigorous the test and the more the likelihood to avoid Type II error.

1.612 for instance is higher than 0.917, and we can then say that at 85% power, at 95% CL with cohort sample size of 8 or a total sample size of 16, a mean difference of 0.950 is not significant, therefore implying there was no type I error. If the real ρwas higher than the theoretical one, we would have said that the test was not rigorous enough for us not to confirm the difference or term it not obvious.

Measurement of central tendency like mean always goes with the estimation of deviation or variability that enables us to estimate the interval within which the mean is more likely to fall considering relative and systematic errors. This interval is estimated using the Standard Error of Mean when the normality assumption is significantly violated, otherwise, the 95% CI of mean is used considering t distribution. If you are comparing two means that are different, but that Confidence Intervals overlap, then your asymptotic significance might not yield a significant difference (P>0.05) at a given CL, e.g. 95% CL.