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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.
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.
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 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.
![Inferential testing [+] Distribution bell curve graph used to calculate z-scores [+] StudySmarter](https://studysmarter-mediafiles.s3.amazonaws.com/media/1865576/summary_images/bayesian-gbc0824ed3_640.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220815%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220815T211644Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=c36588c32b7e7de7c461fa3d2dfee8945aae977cfb83328da3208e042cca1ad7)
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.
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 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).
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