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# Inferential Testing

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Inference is the process of concluding general patterns of behaviour from specific observations.

Inferential statistics are tests used to analyse data using statistical tests to determine the results that support their hypothesis.

Data analysis 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. If not, the study should be revised as it has no use in the real world. You will now learn about the different inferential statistics/tests used in research.

## Chance and significance levels in inferential testing

When conducting research, there will always be confounding factors to some degree, in addition to the effects of the independent variable on the dependent variable. For example, the results of a study may be due to chance and not the independent variables. The probability and significance values of the research are measured to determine if the results are due to chance. In this way, researchers can determine if their results are valid.

After data analysis, the hypothesis is rejected if the significance level is higher than 0.05. Results are then likely due to factors other than the independent variable. On the other hand, if the significance level is less than 0.05, the hypothesis is accepted. The results are likely to be due to the independent variable and not extraneous variables. The lower the significance level, the more likely the results are due to the intended variables being studied. Thus, if the research is conducted on the population, it is expected that similar conclusions will be drawn. Therefore, the data can be considered suitable for extrapolation to the general population.

### What are probability and significance?

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.

This 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.

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.

The significance value of 0.05 is the recommended alpha value ( another term for significance values). As mentioned earlier, if the significance level is higher than 0.05, the hypothesis is rejected. If the significance level is lower than 0.05, the hypothesis is accepted.

## Confidence intervals in inferential testing

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

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

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

Distribution bell curve graph used to calculate z-scores, Pixabay

## Accepting and rejecting the hypothesis

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 include confounding variables that affect the dependent variable, 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. The following section describes hypothesis errors that can occur and apply to hypothesis testing in inferential statistics.

### The different types of hypothesis

• The null hypothesis states that no differences can 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.

### Types of errors in hypothesis testing

• Type 1 error: rejecting the null hypothesis even though it is true (false positive) so that a researcher believes his results are significant even though they are not.
• Type 2 error: falsely accepting the null hypothesis and rejecting the alternative hypothesis when it is true (false negative).

### Hypothesis testing

An example of an inferential test is the hypothesis test. The purpose 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 chosen to perform the analysis. The null hypothesis can be accepted if a high significance level is found (more than 0.05). Therefore, the alternative hypothesis should be rejected. The independent variable does not affect the dependent variable, and the results are likely to be 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 have been obtained if the entire population had been studied. This difference is called sampling error. Thus, the analysis may show discrepancies when a study is repeated with a different sample. In hypothesis testing, estimates of sampling error are considered to avoid errors in accepting or 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 extrapolated 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 due to chance.

• Confidence intervals provide a percentage estimate of how confident the research is that the sample consists of the average 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. It is used to conclude by testing hypotheses against a representative general population sample.

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 the data set.

Inferential statistics are tests used to analyse data using statistical tests to identify their findings that support their hypothesis.

Hypothesis testing, significance levels, confidence intervals, and probability values.

• The null hypothesis states that no differences can 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.

Whether the null hypothesis can be rejected, if the alpha level is below the recommended level (.05), appropriate confidence intervals and whether a low p-value is found (results are unlikely to be a result of chance).

## Final Inferential Testing Quiz

Question

What are inferential tests?

Inferential tests are various tests such as hypothesis testing that help understand if data collected can be used to make predictions/inferences concerning generalisability to the population.

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Question

Give examples of experimental and sampling errors that may influence inferential tests.

Small sample size, confounding variables that affect the dependent variable, inaccurate or lack precision when conducting research.

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Question

How are alpha scores used as an inferential measure of analysis?

If the alpha level is analysed to be lower than 0.5, then the alternative hypothesis can be accepted. This indicates that the results are unlikely to be due to chance or a Type 1 error and can be generalised to the population.

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Question

How are p scores used as an inferential measure of analysis?

If an appropriate p-value is indicated, then the null hypothesis can be rejected, and the data is indicative of being suitable to be extrapolated to the general population.

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How are confidence intervals used as an inferential measure of analysis?

Confidence intervals can give guidelines of how much the sample deviates from the population. If the data vastly differs, then it is unlikely that the data can be extrapolated to the population.

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What does an 83% confidence interval indicate?

An 83% confidence interval indicates that researchers can be 83% confident that the sample consists of the mean population. If the sampling method were repeated multiple times, 83% of the intervals analysed would represent the population mean.

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Question

Give an example of an alternative hypothesis.

There will be a significant difference between patients who received drug therapy treatment and those randomly assigned to the placebo group.

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Question

Give an example of a null hypothesis.

There will be no observed difference between the day of an exam and time spent studying.

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Why do researchers need to form a null hypothesis when carrying out the hypothesis test inferential analysis?

To identify if there is a relationship between the variables, if the null hypothesis is accepted, then results are likely to be a result of chance.

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After carrying out hypothesis testing, a significance level of .07 was indicated. Should the researchers accept or reject the null hypothesis?

The researchers should reject the null hypothesis and accept the alternative hypothesis. This means the independent variable does affect the dependent variable, and the results are unlikely due to chance or other variables. Therefore, the results are considered appropriate to generalise to the population.

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Question

Define sample errors.

Sampling errors are the difference expected between the sample and general population, as it is challenging to obtain a truly representative sample.

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Why does hypothesis testing take into account sampling errors?

To inhibit errors of accepting or rejecting the hypothesis and decrease the likelihood of type 1 and type 2 errors occurring.

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Question

What is the definition of a non-parametric test?

Non-parametric tests are also known as distribution-free tests, these are statistical tests that do not require normally-distributed data for the analysis tests to be employed.

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Question

When is it appropriate to use non-parametric tests?

• Data is nominal (data assigned to groups, these groups are distinct and have limited similarities eg responses to "What is your ethnicity?")
• Ordinal (data with a set order / scale eg “rate your anger from 1-10”), there are outliers within the data,
• If data has been collected from a small sample.

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Question

What is the criterion of non-parametric tests?

The following criterion is required for non-parametric tests:

• At least one violation of parametric tests assumptions,
• Non-normally distributed data
• Data is random (taken from random sample)
• Data values ​​are independent from one another (no correlation between data collected from each participant)

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Question

What is the definition of nominal and ordinal data?

Nominal data is when data is assigned to groups that are distinct from each other. An example of nominal data is the response from “What is your ethnicity?”. Whereas, ordinal data is defined as data with a set scale / order. For example the response from "Rate your anger from a scale of 1-10".

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Question

Why does data need to be ranked prior to carrying out non-parametric data analysis?

Data needs to be ranked prior to statistical analysis as these ranked values ​​are used as data points for the analysis rather than the raw values ​​obtained from the experiment / observation.

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What is the 'reference value'?

The reference value is where the researchers predict / hypothesise where the median value is expected to fall.

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What do '+' and '-' ranked values ​​indicate?

Data is assigned as '+' if it is greater than the reference value and data that is '-' is lower than the reference value.

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Question

Rank the following data values and assign them with the correct sign.

Researchers hypothesised that the reference value would be 13. The dataset is: 3, 5, 3, 19, 16, 21, 14.

-3, -3, -5, +14, +16, +19, +21

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Question

What do '+' and '-' signs mean in terms of ranking data for non-parametric analysis?

Data is assigned as '+' if it is greater than the reference value and ‘-’ if it is lower than the reference value.

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Question

What are the most common non-parametric tests?

Examples of common non-parametric tests are: Wilcoxon Rank sum Test, Mann-Whitney U test, Spearman correlation, Kruskal Wallis test and Friedman's ANOVA test.

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Question

Researchers are trying to identify what would be an appropriate statistical analysis to run to identify the difference in average fitness test scores of participants during the morning, afternoon, and evening. The researchers identified that their data was skewed and there were a few extreme outliers.

Which test should they run?

The appropriate analysis test to use would be the Friedman's ANOVA test, as the data can be assumed to be non-normally distributed. The study used a within-subjects design and the analysis can help identify the difference in average scores between the morning, afternoon, and evening by comparing the ranked median values.

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Question

Is Pearson correlations a parametric or non-parametric test? What is its alternative test?

The Pearson correlation is an example of a parametric test and its non-parametric alternative is the Spearman's rank correlation.

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Question

What is the purpose of using Pearson's and Spearman's rank correlation?

The purpose of these statistical tests is to identify the association (strength and direction) between two variables.

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What are the advantages of non-parametric tests?

The advantages of non-parametric tests are:

• The shape of the distribution does not matter as these tests measure the median rather than the mean as the measure of central tendency.
• Analysis is not vastly affected by outliers.
• These tests have more statistical power than parametric tests when the assumptions of parametric tests have been violated.

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What are the limitations of non-parametric tests?

The limitations of non-parametric tests are:

• These tests are less powerful because the analysis does not take into account the entire data set (identifies the median value of the sample and compares this to the reference value).
• Data is not vastly affected by outliers, so there is an increased likelihood of having a Type 1 error.
• These tests can mostly be used for ‘hypothesis testing’ as they do not give statistical analysis findings concerning effect size and confidence intervals.

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Question

What does a .05 significance value indicate?

If a significance value of 0.05 is found then this means that there is a 95% chance the results are not due to chance or a Type 1 error.

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Question

Which of the following is a Type 1 error?

Reject the null hypothesis when it is true.

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Question

What is a significance test?

Significance tests are frequently used in psychology research to determine the probability of the results (inferential statistical data) rejecting the null hypothesis when it is true (Type 1 error).

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How is the significance value reported in research?

p

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What is another name for the significance value?

Alpha value.

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What should the researcher do if the significance value is measured as, < .08?

Accept the alternative hypothesis.

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What should the researcher do if the significance value is measured as, < .03?

Accept the alternative hypothesis.

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If a non-significant result is found, does no relationship between the independent and dependent variables exist?

No.

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Question

Correlational research on 56 people found a .63 positive relationship between time spent studying and exam results. The significance value was .05. How would this be reported?

r (56) = .63, p <.05

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Question

Correlational research carried out on 56 people found a .63 positive relationship between time spent studying and exam results, the significance value was found to be .08. How would this be reported?

r (56) = .63, p < .08 (n.s)

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Question

What can researchers infer about their data when a significant value is found?

If a significant value is found, the inferential statistic can be used to make inferences the evidence supports concerning the target population.

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What can researchers infer about their data when an insignificant value is found?

The research should not make inferences about the target population.

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What is a factor that can contribute to insignificant findings?

Occasionally, non-significant results are due to issues with the methodology used.

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How are statistical significance and probability related?

The significance value tells us the probability of how confidently the researchers can accept or reject the research hypothesis. For psychology, the significance value is 0.05.

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What is the consensus of the acceptable statistical value in research?

Researchers have a consensus about what alpha level is acceptable, which is 0.05.

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What is a type 1 error?

A type 1 error is when the researcher rejects the null hypothesis when it is true (false positive).

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What is a type 2 error?

A type 2 error is when the researcher mistakenly accepts the null hypothesis and rejects the alternative hypothesis when it is true.

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Question

Why is hypothesis testing used in psychology research?

Hypothesis testing is a statistical test used in experimental research to identify if the alternative or null hypothesis should be accepted in research.

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Question

Which hypothesis should be accepted if significant findings are found?

Significant findings mean the alternative hypothesis should be accepted and the null hypothesis rejected.

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Question

Which hypothesis should be accepted if insignificant findings are found?

Insignificant findings mean the null hypothesis should be accepted, and the alternative hypothesis rejected.

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Why is hypothesis testing used as an analysis method?

Results are more likely to be valid

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Question

Which of the following is the definition of the null hypothesis?

The researcher predicts there will be no difference in the results found between the groups (e.g., control versus experimental).

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Question

Which of the following is the definition of the alternative hypothesis?

The researcher predicts there will be no difference in the results found between the groups (e.g., control versus experimental).

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