# Normal Distribution Curve

I understand that if a graph is close to the shape of a bell shape (and the mean tends to zero, and the SD is close to 1), then we can say it is normally distributed. Visually inspecting a normal curve can be subjective as well. How should I confirm if the residuals of the curve below is normally or approximately normally distributed? I am using this judgment to as a pre-determination of ANOVA assumptions.

• Can you give some context, why do you need an approximate normal distribution? How to judge the approximation depends on purpose. Sep 24, 2017 at 18:38
• I am inspecting my data to ensure that they do not violate the assumptions for conducting an ANOVA and a Regression Analysis
– Vyas
Sep 24, 2017 at 18:41
• "if a graph is close to the shape of a bell shape (and the mean tends to zero, and the SD is close to 1), then we can say it is normally distributed" -- (i) the mean and standard deviation are irrelevant to whether or not it's normally distributed; (ii) many things that are very much not normal may look more or less bell-shaped, so merely looking bell shaped is not a means to assert normality; (iii) that doesn't look at all bell-shaped anyway; it's clearly bimodal. What's your response? (iv) are those residuals from the actual model you want to assess the assumptions of? Sep 25, 2017 at 4:48
• Consider trying to identify the two groups that seem to have accounted for two distributions here. You might conduct a separate analysis on each group. Sep 25, 2017 at 15:46
• What do you mean by two groups? Why do you say it is bimodal? I see the term "conservative approach" is used. If the normality test says that the distribution is not normal, how should I proceed to conduct the ANOVA and Regression, apart from reporting that the sample is not normally distributed?
– Vyas
Sep 26, 2017 at 2:47