Yes,normality and homogeneity is necessary before we conduct parametric test.(t-test,ANOVA,Pearson correlation )

But for non parametric test no need.

Yes, you need to check normality and homogeneity of variance separately for each group or condition relevant to each t-test and ANOVA, not just the overall distribution of your variables. This ensures the validity of your hypothesis tests.

You have to check normality and Homogeneity of variance for all the variables that will be used for each T-test and ANOVA. So the answer is yes, you have to check for each separately before conducting any further analysis. The whole point is to validate your data quality and check if the data is normally distributed as this could affect the rest of your analysis.

Yes, you have to check the assumptions every time you run a parametric test. If you are using jamovi software, in the ANOVA and t-test menus your have the options to check the assumptions directly por each analysis you do.

No, you do NOT have to check such assumptions, = not at all, as parametric procedures are very robust against ‘violations’. Verify this yourself. Do a two-group t-test as well as the corresponding Mann-Whitney U test (on the same cases and variables of course), and see how small the difference is. It is very rare that one is ‘significant’ (p=0.05). Also notice that these conditions apply only to ‘significance’ as such. They are no conditions for computing means and SD’s etc. In fact, p-values are highly over-rated. They are more determined by the N (small = n.s. and large = sign.), and much less by what you as a researcher (or journalist, policymaker, doctor) are really interested in: How large is the effect size, i.e. do the groups substantially differ, does the policy to be evaluated ‘work’, is this new medicine really effective (and not just slightly effective yet ‘significant’ due to N=10.000). In the end, Cohen’s d is more important than ‘p’, and its conditions and assumptions.

No, since ttest assumes normality of the distribution of samle means, not of rvs. And is quite robust even if not satisfied.

Preferably should be performed.

But from what as a researcher you really interested in, answer may differ- as "significance" not differ a lot by the nature of test but robustness (in simple terms, p-value in t-test and MW U test or BM test may not differ much), but parametric tests thought to be more statistically sound. But from a clinical or practice point of view effect size is of more importance. Now, you will find effect size calculation for normal distribution is easier, but there are way around for non-parametric data as well (even excluding difficult statistics, but we have apps to handle those as well).

So, you need to take a call with justification, or feel free flow common practice of testing the assumptions (often considered good practice, but if you see literature it may no be commonly reported) as well.

You should check normality and homogeneity of variances for each specific t-test or ANOVA separately. Each test requires that the data meet these assumptions individually for the groups or conditions being compared. Checking these assumptions for the overall distribution of your three variables is not sufficient.

4o mini

These procedures assume normality of the errors in the regression (t tests and ANOVAs are just special cases of regression). Looking at the raw data may or may not give you a sense of that - depending on the model.

e.g., an independent t test:

y_i = b0 + b1*x_i + e_i [here x is a binary grouping variable coded 0 and 1 or simialr)

the errors: e_i is assumed to be sampled from a normal distribution (with constant variance and mean 0)

In this case plotting the residuals of the model (which are used to estimate the variance of e_i in the population) is essentially equivalent to plotting the raw scores of the two groups separately as the group means are constant and the raw scores are simply the group means plus e_i. (If you plot the two groups combined the distribution would be bimodal - not normal).

So in this case looking at the raw data within each group is fine.

However, it isn't like that for all models. For instance a paired t test is:

y_i = b0 + b1*x_i + e_i

but here y_i is not the raw data but the difference between groups i.e.,

y_i = y1_i - y2_i

Thus the e_i term relates to the differences between groups and plotting the raw scores may by very misleading. In effect the residuals of this model strip out the individual differences which may be any old distribution - so the raw scores could be approximately normal and the residuals not (or vice versa).

So general advice is to check normality of the residuals for these models - as this works for any model of this type (regression type models that assuming normality of residuals). Graphical methods are best for this as you are looking for major departures from normality rather than the existence of a departure (no sample is perfectly normal). It follows that you check normality after running the analysis in most cases.

There are other reasons to look at the distribution of raw scores - but not specifically to test whether a normal parametric regression model is a good idea.

Homegeneity of variance is slightly difference and here I'd usually just look at the SDs of each group in an independent analysis to see if they are similar and not wildly different (a ratio comfortably below 2:1 for the largest and samllest Sd might be a good rule of thumb). There are also corrections (Welch-Satterthwaite fot t tests and ANOVA) that can be used if there any concerns (or just as a default). For repeated measures - you need to check sphericity instead (though for comparisons of 2 conditions or any ANOVA with 2 levels on each factor e.g., a 2x2 ANOVA, sphericity can not be violated).

Finally, are ANOVA and t tests robust against violations of normality? Not really. Historically it was thought to be the case, because they tested robustness in a very limited way. If you also consider statistical power (Type Type II error) they are not robust. In particularly high excess kurtosis (of residuals) is very problematic for these models/tests. This is often but not always also reflected in the raw scores. Robust including robust regression and rank based methods might be appropriate in these cases, although they typically don't involve comparing the means of the groups (which might matter depending on research question.)

you should check normality and homogeneity for each group or sample involved in your hypotheses tests, rather than over the overall distribution of the three variables. This ensures that the assumptions are met for each specific test, leading to more reliable results.

yes,we have to check it. Because,Normality tests are tests of whether a set of data is distributed in a way that is consistent with a normal distribution. Typically, they are tests of a null hypothesis that the data are drawn from a normal population, specifically a goodness-of-fit test. Hence, while it is possible to reach a definitive conclusion that a set of data is not normally-distributed (by rejecting the null hypothesis), the most one can say if the null hypothesis is not rejected is that the data could possibly come from a normally distributed population.So we have to check it before

actually anova does this. the normality is asked for error term of the regression. when doing a linear regression you measure the normality of error with mean zero and variance constant.

Hi Sarthik,

In your case, you need to check for normality and homogeneity of variance for each hypothesis test, not just over the overall distribution of the three variables.

Here’s why:

How to Proceed:

• For t-tests: Test the normality assumption separately for the groups you're comparing in each t-test (e.g., using the Shapiro-Wilk test or Q-Q plots).
• For ANOVA: Use tests like Levene’s test or Bartlett’s test to check for homogeneity of variances before running the ANOVA.

By checking these assumptions for each hypothesis, you'll ensure that the results of your t-tests and ANOVAs are valid.

Good luck with your analysis!

Yes, it is generally necessary to check normality and homogeneity before conducting hypothesis testing, especially for parametric tests.

• Normality ensures that the data follows a normal distribution, which is a key assumption for many parametric tests (e.g., t-tests, ANOVA).
• Homogeneity of variance (equal variances) is important for tests like ANOVA and t-tests to ensure the validity of results.

If these assumptions are violated, you may need to use non-parametric tests or transform the data.

You can of course use ANOVA without doing any testing at all, since it is basically an analysis of variance and the estimated variances can be interpreted directly.