# An Introduction to Statistics: Choosing the Correct Statistical Test PMC

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data. This article is a practical introduction to statistical analysis for students and researchers. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

In the absence of a consensus measurement, no decision based on measurements will be without controversy. Sometime around 1940,[11] authors of statistical text books began combining the two approaches by using the p-value in place of the test statistic (or data) to test against the Neyman–Pearson «significance level». For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical. There are no dependent or independent variables in this study, because you only want to measure variables without influencing them in any way.

One-way ANOVA is used when groups to be compared are defined by just one factor. Repeated measure ANOVA is used when groups to be compared are defined by multiple factors. For example, if we want to evaluate the effect of three different antihypertensive drugs on three different group of human volunteers, then we will use ANOVA test to evaluate about any significant difference between groups. ANOVA test does not indicate which group is significantly different from the others. Post hoc tests should be used to know about individual group differences.

## Table 1

Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling. To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process. You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure. The choice of statistical test used for analysis of data from a research study is crucial in interpreting the results of the study.

• Confidence interval is always mentioned with a particular degree of certainty, e.g. 95%.
• Dichotomous or binomial data[14] can be defined as those data which have only two outcomes such as yes or no, or male or female.
• Having this layout makes it easier for most statistical programs to deal with the data.
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• If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

The calculations are now trivially performed with appropriate software. Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not. However, Bayesian statistics https://www.globalcloudteam.com/ has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations. Type I and Type II errors are mistakes made in research conclusions.

## Key to statistical analysis

He required a null-hypothesis (corresponding to a population frequency distribution) and a sample. His (now familiar) calculations determined whether to reject the null-hypothesis or not. Significance testing did not utilize an alternative hypothesis so there was no concept of a Type II error (false negative). A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time. In theory, for highly generalizable findings, you should use a probability sampling method. Random selection reduces several types of research bias, like sampling bias, and ensures that data from your sample is actually typical of the population.

This contrasts with other possible techniques of decision theory in which the null and alternative hypothesis are treated on a more equal basis. Suppose the mean systolic blood pressure in a sample population is 110 mmHg, and we want to know the population systolic blood pressure mean. Although the exact value cannot be obtained, a range can be calculated within which the true population mean lies. This range is called confidence interval[20] and is calculated using the sample mean and the standard error (SE).

## Advantage and Disadvantages of Nonparametric Methods over Parametric Methods and Sample Size Issues

Although it is difficult to know about the details of every statistical test, a biomedical researcher must have the basic knowledge of inferential statistics. Selection of wrong statistical test can lead to false conclusions which can compromise the quality of research. Similarly, a wrong interpretation will also lead towards a wrong conclusion.

A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false. A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding. There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate. If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

Any discussion of significance testing vs hypothesis testing is doubly vulnerable to confusion. A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. It is a simplified table only to crudely demonstrate how to select a test for statistical analysis of data.

Various online and offline software like SPSS, Minitab, RStudio, and GraphPad Prism are available for statistical analysis which ease the process of data analysis. The test chosen to analyze data will depend on whether the data are categorical (and whether nominal or ordinal) or numerical (and whether skewed or normally distributed). Parametric tests are more powerful and have a greater ability to pick up differences between groups (where they exist); in contrast, nonparametric tests are less efficient at identifying significant differences. Time-to-event data requires a special type of analysis, known as survival analysis. Sometimes, a study may just describe the characteristics of the sample, e.g., a prevalence study.

Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure is based on how likely it would be for a set of observations to occur if the null hypothesis were true. This probability of making an incorrect decision is not the probability that the null hypothesis is true, nor whether any specific alternative hypothesis is true.

The final step of statistical analysis is interpreting your results. Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population. It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship. From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable.

The confidence level which is commonly used is 95%, but 90 and 99% confidence levels can also be calculated. Studies may be conducted to test a hypothesis and derive inferences from the sample results to the population. Studies may also look at time to a particular event, analyzed using survival analysis.

The form of data will affect the kinds of statistical approach you take. Today statistics provides the basis for inference in most medical research. Yet, for want of exposure to statistical theory and practice, it continues to be regarded as the Achilles heel by all concerned in the loop of research and publication – the researchers (authors), reviewers, editors and readers. Science primarily uses Fisher’s (slightly modified) formulation as taught in introductory statistics.

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