- We will start by applying inferential tests to psychology.
- Then we will explore the types of inferential tests in research and apply inferential tests in research.
- Throughout, we will delve into the different inferential statistics tests.
- And finally, we will take a look at an inferential statistics hypothesis testing example.

## Inferential Tests Psychology

In psychology research, researchers aim to identify if their results support their proposed hypothesis; raw data needs to be analysed to establish this. One form of analysis is called inferential testing.

**Inferential statistics** analyse data using statistical tests to determine whether the results support their hypothesis.

Data analysis in research involves performing **descriptive**,** statistical**, and **inferential tests**. The tests are necessary to create summaries, determine the relationship between **variables**, and determine if the population's findings are generalisable.

Inferential statistics can be used to identify patterns/ trends and determine if the results are generalisable to the population.

If this is not the case, then the study should be revised as it has limited use in the real world.

## Inferential Tests: Variables in Research and Chance

Before we get into the details of inferential testing, let's recap the different types of variables.

In experimental research, the independent variable (IV) is the manipulated variable, and the dependent variable is the variable measured after the IV is manipulated (and sometimes before too).

It is impossible for researchers to control external factors that may influence the IV or DV; these are known as confounding or extraneous variables, which lower the validity of the research.

When conducting research, there will always be confounding factors to some degree. The main goal of research in psychology is to identify how the IV affects the DV. However, it is impossible for researchers to say with 100% confidence that their results are due to manipulation of the IV and not external factors or due to chance.

## Types of Inferential Tests: Chance and Significance Levels

Chance is the theory that the results are not due to a fluke, e.g. the conditions during that day and a result of manipulating the IV. The probability and significance values of the research are measured to determine if the results are due to chance.

Inferential tests can be used to determine if a study's results are due to chance. Significance levels are a type of inferential test.

Significance is also known as the *p*-value. It is an inferential statistic that tells you the probability of how confidently the researchers can accept or reject the research hypothesis.

The value is best understood as a proportion. Let us look at an example that converts the p-value to a percentage.

If the p-value is 0.10, there is a 10% chance that the observed effect size is due to sampling or experimental error.

The significance value of 0.05 is the recommended alpha value (another term for significance values) in psychology. The hypothesis should be rejected if a significance level above 0.05 is found. The reason is that the results are likely due to factors other than the IV. And the hypothesis should be accepted if the significance level is below 0.05.

The lower the significance level, the more likely the results are due to the intended variables being studied. Although it's next to impossible if the study was replicated on the entire population, similar results would likely be found. Therefore, the data can be considered suitable to generalise to the population.

We can never achieve a p-value indicating 100% confidence because, in research, we collect data from a sample of people who are most likely not representative of the entire population.

## Inferential Tests in Research: Confidence Intervals

Confidence intervals are another form of inferential statistics that help researchers understand how representative their sample is of the general population.

Confidence intervals can guide how much the sample deviates from the population. If the data vastly differs, it is unlikely that it can be generalised to the population.

A 95% confidence interval indicates that you can be 95% sure that the sample consists of the average population. If the sampling method were repeated multiple times, 95% of the intervals analysed would represent the population's mean.

A larger sample size reduces the range of interval values, which means that the calculated mean is likely to be more accurate.

The variances in sampling confidence intervals and z-scores vary when different samples are used. This test differs from the previous inferential tests, z-scores, because it estimates whether the sampling procedure is representative of the population rather than the sampling distribution.

Figure 1: A distribution bell curve graph used to calculate z-scores.

## Inferential Statistics Tests: Hypothesis Testing

As mentioned earlier, errors sometimes occur when conducting experiments. These can be sampling errors, such as when the sample is not representative of the population or experimental errors.

Examples of errors include confounding variables that affect the DV, inaccuracies, or lack of precision in conducting research.

Sampling and experimental errors can affect results and cause research to draw incorrect conclusions, such as type 1 and type 2 errors.

A type 1 error is when we reject the null hypothesis even though it is true (false positive), so the researcher believes their results are significant even though they are not.

On the other hand, an type 2 error is when the researcher falsely accepts the null hypothesis and rejects the alternative hypothesis when it is true (false negative).

The null hypothesis states no differences will be found between the phenomena/groups under study.

The alternative hypothesis states that a significant relationship exists between the variables under study (i.e., the independent variable influences the dependent variable) and that this relationship did not occur by chance.

## Inferential Statistics Hypothesis Testing Examples

An example of an inferential test is the hypothesis test. The purpose of this test is to determine whether the results of the experiment are valid.

By estimating how likely the results are due to chance, we determine the validity of the results.

A null hypothesis must be stated to perform the test, and an appropriate statistical test should be chosen to perform the analysis.

If a study found a significance level of .08, the alternative hypothesis is rejected, and the null hypothesis should be accepted. The inferential test suggests the IV does not affect the DV, and the results are likely due to chance or other variables. Therefore, the results are considered inappropriate for generalisation to the population.

The statistical data analysed using the sample is likely to differ from the results that would be obtained if the entire population was tested; this difference is called sampling error. So, the analysis may show discrepancies if the study is replicated with a different sample.

In hypothesis testing, estimates of sampling error are considered to avoid errors in accepting/ rejecting the hypothesis and to reduce the likelihood of type 1 and type 2 errors.

## Inferential Testing - Key takeaways

Inferential tests are statistical tests used to determine whether the research results can be generalised to the general population.

The significance level is an inferential statistic that psychologists have agreed should be less than .05. If this is the case, it is less likely that the results are not due to chance.

Confidence intervals provide a percentage estimate of the researcher's confidence that the sample is representative of the general population. A significant percentage indicates that the data set is a reasonable and representative population sample.

Hypothesis testing is an example of inferential testing that considers sampling error.

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##### Frequently Asked Questions about Inferential Testing

What is an inferential test?

Inferential statistics are needed to test if the data collected is significant and supports a hypothesis. We can use inferential statistics to make generalisations about a data set.

What are the four types of inferential statistics?

There are different inferential tests, e.g., hypothesis testing, significance levels, confidence intervals, and probability values.

How to know what inferential test to use?

There are different inferential tests, e.g., hypothesis testing, significance levels, confidence intervals, and probability values. The inferential test used depends on what the researcher is aiming to find.

How to make an inferential test?

Inferential tests are not usually done manually. Instead, statistical packages are commonly used, such as R or SPSS.

Is a hypothesis test descriptive or inferential?

Inferential, as it is used to understand if results are generalisable rather than describing characteristics of variables,

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