How do you compare means of groups or conditions? (2024)

Why and why not we compare means?1 In RWE studies, comparing means can involve analysing the average ages of patients experiencing adverse events (AEs) from two different medications. By comparing the means, one can examine if, for a particular medication, AEs occur in significantly older patients, potentially revealing age-related risks.2 In one of our longitudinal observation studies, we compared the mean values of age, weight and BMI of two groups of participants using two-sample t-tests to see how those who responded to the questionnaire differed from those who didn't.3 In the RCT, comparing means of the baseline characteristics of groups is not of much use since allocation is randomised; any comparison would be deemed superfluous.

In my experience i have come to understand that at the heart of many research , business questions and solutions finding is a “Comparison”: -Does one teaching method produce better results than another? -Does a new drug reduce symptoms more than a placebo? Comparing means can provide answers to these questions by determining if observed differences are statistically significant.

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Depending on data/group of independent samples, one can use T-Test (independent samples T-Test, paired samples T-Test, one-sample T-Test) or ANOVA (one-way ANOVA or two-way ANOVA).A handy mnemonic to memorise:T-test: Tea is meant for 2Example: Comparing the average blood pressure levels of patients before and after a new treatment using paired t-test. This assesses if the treatment caused a significant change in BP within group.ANOVA: 3 words: ANalysis Of VarianceExample- One-Way-ANOVA: Analysing the mean cholesterol levels across three different dosage groups of medication.Example- Two-Way-ANOVA: Comparing effectiveness of two drugs across different age groups to find if drug and age have a significant impact on the outcomes.

In my experience, ensuring the assumptions of these tests, like hom*ogeneity of variances for ANOVA, is crucial. If not met, results can be misleading.An example of a situation where a standard t-test might not be apt is with paired data, like pre-test and post-test scores from the same students. Here, a paired t-test, which accounts for the paired nature of the data, is more suitable.I agree with the distinction between t-tests and ANOVA based on group numbers. However, when ANOVA indicates a significant difference, post-hoc tests are needed to pinpoint which specific groups differ.But, it's vital to remember that statistical significance doesn't always mean practical significance

T-test assumptions mnemonic: TWIN1. T- Two Independent Samples: The data should come from independent samples randomly sampled from the population.2. W- Within-Group Normality: The data within each group should follow a roughly normal distribution.3. I- Identical Variances: The variances of the two groups should be roughly equal.4. N- Numerical Data: The dependent variable should be continuous variable.ANOVA mnemonic: Infinity, Numbers, Have, Random, NormsIndependence: Observations in groups are separate.Normality: Residuals follow a normal distribution.hom*ogeneity of Variance: Residual variability is consistent across groups.Random Sampling: Samples are randomly selected.No Multicollinearity: Covariates are minimally correlated.

Before using t-tests or ANOVA, it's important to check if the data meets certain assumptions to ensure the validity and reliability of the results. These assumptions include normality, where the data should exhibit a bell-shaped curve and be symmetric around the mean; hom*ogeneity of variance, indicating that the data should have similar spreads or variability; and independence, ensuring that data points don't influence or affect each other. If your data doesn't meet these assumptions, alternative methods or data transformations may be necessary

When you do tests like t-tests or ANOVA, you get two main results: a p-value and an effect size.The p-value is like a reality check. If it's a small number (usually below 0.05), it means the difference you found in your study probably isn't just a random fluke.The effect size tells you how big or important that difference is. If it's a large number (often more than 0.5), it means the difference is pretty significant.Now, some extra thoughts:For example, imagine you're comparing the heights of two groups of people. Even if one group is just a tiny bit taller and it shows a small p-value, the effect size can tell you if that height difference is just an inch or a whole foot!

When you're sharing results from comparing averages, it's good to mention:What test you used and who or what you compared.The average score and how spread out the scores were for each group.The p-value (a reality check number) and effect size (how big the difference is).For example, we wanted to see who did better on tests: online students or those who learn in-person. Online students score of 85.6, with scores mostly within 10 points of this average. In-person students had an average score of 78.4, with scores mostly within 10 points of this average too. It showed that online students did better, and the difference wasnt by chance. The difference was also big enough to matter, showing online students really had an edge in this case.