Question

The social worker performed the inferential statistical test, which produced the p-value of 0.049. Explain what this p-value means in terms of sampling error, true relationship, and testing null hypothesis (reject or fail to reject). Note that these three underlined terms should be included in your answer.

Answer 1

This is a simple question of statistical inferences of the p value on various statistical parameters.

We are given with the statistical value of 0.049 .

But what exactly is the p value we are talking about?

The P value simply indicates the degree to which the data conform to the pattern predicted by the test hypothesis and all the other assumptions used in the test (the underlying statistical model).

Let us check its meaning in light of the hypothesis testing first.

A hypothesis testing is a statistical analysis which enables us to understand if our assumption (called as null hypothesis) is valid or not with a given level of statistical significance.

Usually we take three platforms of statisitcal siginificance 99 %( 0.01), 95% (0.05) and 90% (0.10)

We compare the p value (which is an inference of the percentage complaince of the given assumption as per the given scenario)

Now in the give scenario , we have the pvalue =0.049.

The critical p value for the 95 % siginificant statement is 0.05 , (0.10 for 90% and 0.01 for 99%) .

The given p value is 0.049 <0.050

Thus this statement tells me that the p value of the given scenario is less than the cricla limit of 0.05 and hence we can say that our assumption is significant (it is slightly greater than 95 % , (100%-4.9% =95.1%) . Hence we can say that our assumption regarding the statement of hte question is signidficant and valid. (null hypothesis is validated)

Now to the sampling error and true relationship.

This is simple. A p value of 0.049 only means that given the null hypothesis thre will be a 4.9 % (0.049 expressed in percentage term) deviation from full siginificance due to error due to sampling called as sampling error.

This is so because even though the null hypothesis is correct, we’ll most likely see an effect in the sample because of random sample error. It’s an incredibly rare occurrence for the sample data to exactly match the actual population value. Therefore, the position you take for the sake of argument (null /alternate hypothesis)  is that random sample error produces the observed sample effect rather than it being a true effect.

In other words, we say that the given sample only produces 100%-4.9% =95.1 % true effect (effect of the population)