Inferential statistics & Test of significance

 

Inferential statistics & Test of significance

Inferential statistics is one of the two main branches of statistics. It uses a random sample of data taken from a population to describe and make inferences about the population. Inferential statistics are valuable when examination of each member of an entire population is not convenient or possible.

 

Difference between descriptive and inferential statistics:

1.    Descriptive statistics uses the data to provide descriptions of the population, either through numerical calculations or graphs or tables. Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question.

2.    Descriptive statistics consists of the collection, organization, summarization, and presentation of data.

Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis  tests, determining relationships among variables, and making predictions.

 

Test of significance

A test of significance may be a formal procedure for comparing observed data with a claim (also called a hypothesis), the reality of which is being assessed. It may be a statement with a few of the parameters, like the population proportion p or the population mean µ.

Once the sample data has been collected through an observational study or an experiment, statistical inference will allow the analysts to assess the evidence in favor or some claim about the population from which the sample has been taken from. 

Null Hypothesis

Every test for significance starts with a null hypothesis H₀. H₀ represents a theory that has been suggested, either because it's believed to be true or because it's to be used as a basis for argument, but has not been proved. For example, during a clinical test of a replacement drug, the null hypothesis could be that the new drug is not any better, on average than the present drug. We would write H₀: there's no difference between the 2 drugs on average.

 

Alternative Hypothesis

The alternative hypothesis, H_a, maybe a statement of what a statistical hypothesis test is about up to determine. For example, during a clinical test of a replacement drug, the choice hypothesis could be that the new drug features a different effect, on the average, compared to the current drug. We would write H_a: the 2 drugs have different effects, on the average. The alternative hypothesis may additionally be that the new drug is better, on the average than the present drug. In this case, we might write H_a: the new drug is better than the present drug, on the average.

The final conclusion once the test has been administered is usually given in terms of the null hypothesis. Either we "reject the H₀ in favor of H_a" or "we do not reject the H₀"; we never conclude "reject H_a", or maybe "accept H_a".

What is Test of Significance?

Two questions come up about any of the hypothesized relationships between the two variables:

1) what's the probability that the connection exists;

2) if it does, how strong is that the relationship

There are two sorts of tools that are required to address these questions: the primary is addressed by tests for statistical significance; and therefore, the second is addressed by Measures of Association.

Tests for statistical significance are required to address the question: what's the probability that what we expect may be a relationship between two variables is basically just an opportunity occurrence?

If we select many samples from an equivalent population, would we still find an equivalent relationship between these two variables in every sample? Suppose we could do a census for the population, we will also find that this relationship exists within the population from which the sample was taken from? Or will it be our finding due to only random chances?

 

What Tests for Statistical Significance?

Tests for statistical significance tell us what the probability is that the relationship we expected we've found is due only to random chance. They tell us what the probability is that we might be making a mistake if we assume that we've found that a relationship exists.

We can never be 100% sure that the relationship always exists between two variables. There are too many sources of error to be controlled, for instance , sampling error, researcher bias, problems with reliability and validity, simple mistakes, etc.

But using applied Mathematics and therefore the bell-shaped curve, we will estimate the probability of being wrong, if we assume that our finding a relationship is true. If the probability of being wrong is very small, then our observation of the connection can also be a statistically significant discovery.

Statistical significance means there's an honest chance that we are right to find that a relationship exists between two variables. But the statistical significance isn't equivalent as practical significance. We can have a statistically significant finding, but the implications of that finding may don’t have any application. The researcher should examine both the statistical and therefore the practical significance of any research finding.

Test of Significance in Statistics

Technically speaking, in the test of significance the statistical significance refers to the probability of the results of some statistical tests or research occurring accidentally. The main purpose of performing statistical research is essential to seek out reality. In this process, the researcher has to confirm the standard of the sample, accuracy, and good measures that require a variety of steps to be done. The researcher determines whether the findings of experiments have occurred thanks to an honest study or simply by fluke.

 

The significance may be a number that represents probability indicating the results of some study has occurred purely accidentally. The statistical significance may be weak or strong. It does not necessarily indicate practical significance. Sometimes, when a researcher doesn't carefully make use of language within the report of their experiment, the importance could also be misinterpreted.

 

The psychologists and statisticians search for a 5% probability or less which suggests 5% of results occur thanks to chance. This also indicates that there's a 95% chance of results occurring NOT accidentally. Whenever it's found that the results of our experiment are statistically significant, it refers that we should always be 95% sure the results aren't due to chance.

 

Process of Significance Testing in Test of Significance

So in this process of testing for statistical significance, the following are the steps:

1.    Stating a Hypothesis for Research

2.    Stating a Null Hypothesis

3.    Selecting a Probability of Error Level

4.    Selecting and Computing a Statistical Significance Test

5.    Interpreting the results