You might post some descriptive statistics and the histogram you are looking at.

How obvious a skew of, say, 0.5 would be on a histogram may depend on the underlying distribution and how the histogram is plotted.

Sampling from a normal distribution, in my experience, having a skew of, say 0.5 shouldn't be overwhelmingly obvious.

But, for example, I've attached a histogram with the following statistics. The underlying distribution isn't normal, the skew is only 0.45, but it's obvious in the histogram that the data are skewed.

I'm assuming you have some reason to assess if the data are approximately normal in distribution. My advice is always to look at the plotted data (histogram, q-q plot, etc.), and be honest (but not overly strict) with your assessment. I never look at skewness or kurtosis values, and I would advise ignoring tests like Shapiro-Wilks unless you have some good reason to use them. Nothing in the world is perfectly normally distributed, and Shapiro-Wilks telling you this is usually not very useful. That being said, reporting those statistics is fine if that's what is expected of you.

vars n mean sd median trimmed mad min max range skew kurtosis se

X1 1 59 0.79 0.53 0.7 0.77 0.58 0.01 2.18 2.17 0.45 -0.63 0.07

Data:

0.35413371 1.68959815 0.99514623 1.48202976 0.38421182 1.32614370 0.33727989

1.08865241 0.42953434 0.04150355 0.27831112 1.44127895 1.15146418 0.30463362

0.64814624 0.28888104 0.77370215 0.95144935 0.63953619 0.99151999 0.39245106

0.38181037 0.05838689 0.89725551 0.44784163 1.40651014 0.30006070 0.01321383

0.66427643 1.37140310 0.67991174 0.40983357 0.69609083 1.93781075 0.97787845

1.32761945 1.16026266 0.18456459 0.07817183 0.77305539 1.17658876 0.47839017

2.17841493 1.30465697 0.39117613 1.11343780 0.01460299 0.67951644 0.82541950

0.12158178 0.44750388 0.87319621 1.28090276 0.66369301 0.15145645 1.55074821

1.51167092 1.60119962 0.70884880

I have attached my histograms and descriptives tables. I have been taught that we have to test normality via Shapiro-wilks, histograms and Q-Q plots in order to determine if data is parametric or not and therefor determine what inferential test to use.

when describing normality I have put :

"Tests of normality were conducted for each variable. As per the data in Table 1, Reaction Time demonstrated conference with normality amongst both groups where data was non-skewed (SE = .24) and mesokurtic (SE = .48). This was confirmed by a Shapiro-Wilks test for group 1 where W(100) = .99, p < .414 (one tailed) and for group 2 where W(99) = .99, p < .342 (one tailed)."

would this be un-necessary? Thank you for your help, as you probably can tell I am still new to this and learning.

Based on the histograms, I wouldn't consider those data to be normally distributed. For me, the skewness, kurtosis, and Shapiro-Wilks don't really help me with this assessment.

But it's fine what you wrote as a description for Reaction Time.

If you can present some of the informatin in the table you included, that's a good approach, since it gives the reader all the information. Presenting the data as two box plots together, or two histograms together also tells the reader a lot about the data.

Since you have two groups, I assume you are considering using a t-test. In this case, it makes sense to look at the distribution of each of the groups. But also note that the t-test has an assumption about the groups having equal variance, unless you are using a t-test which doesn't have this assumption (Welch's t-test).

Also note that with a sample size of c. 100 in each group, the t-test may be robust

to reasonable deviations of normality. Especially since in the histograms you present, the distributions among the groups are relatively similar. You can look up the central limit theorem (CLT) as it applies in the case of t-tests.

I know this is getting complicated, and requires some judgement.

For more complex analyses, my advice is to start with whatever statistical analysis you are planning on conducting, and looking up the assumptions of that analysis in a real statistics textbook. I've attached two pages from Montgomery, Design and Analysis of Experiments, 4th ed. It's specifically discussing analysis of variance (anova), but these assumptions apply to other general linear models. Note that the assessment is made on the residuals of the analysis, not the raw data, and it considers both the normality of the residuals and the equal variance (homoscedasticity) of the residuals.

One other note: data can't be parametric or not parametric. That terminology doesn't make sense there. Instead it's the statistical tests that can be classified as parametric or not parametric.