#### Rachyxxx

##### New Member
I am conducting research on the effects of social media usage (frequency of checking and duration) on body image and self esteem n = 264. Every ANOVA is not significant however Boxplots have revealed a good number of outliers. When I removed 5 "moderate outliers" (between the mild and extreme range) some of the results become significant. However how do I justify this?.. it changes the p value. Should I just remove all outliers (like 20)? There is only one extreme outlier. Also I am examining difference between gender. Should I split the file before I check for outliers or after? Does that many outliers warrant log transformation? The skewness stat is fine.

Pleaseee help I'm in a mireee

Thankyou

#### obh

##### Well-Known Member
Hi Rachy,

What method did you use to define the outliers? Tukey Fence?

Generally, I think you should remove outliers only if you suspect a mistake.
If you have n=264, you expect to have some extreme values ...

If for example, you use +- 2 standard deviations to calculate the outliers, with normal distribution
around 5% of the valid data will be outliers ...

#### Rachyxxx

##### New Member
Hi obh,

Thankyou for replying so quickly. I used the method which uses boxplots with 1.5 (mild) 3 (extreme) x interquartile range. There are many mild outliers using this method so I thought I should just use moderate ones (between these ranges) maybe that was silly...I have just used the standard deviation method as you said and there are 23 outliers.

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#### obh

##### Well-Known Member
Hi Rachy,

Do you mean you used the Tukey fence? k=1.5, 3
Lower = Q1 - k * IRQ.
Upper = Q3 + k * IRQ.

I didn't say the say one method is better than other, also I prefer the Tukey fence.
So if it was normal you would expect to get around 12 outliers, and you have 23 outliers?

ps what ANOVA test do you run? what is the sample size?

#### Rachyxxx

##### New Member
Thankyou, 23 outliers yep I know mostly mild but 5 are "moderate" I did it manually with a calculator and a ruler but I have just carried out the actual Tukey and there are outliers as I'd thought. Sample size is 264. The groups are not equal so that might be affecting things? I am carrying out 4 between groups ANOVAs frequency x self esteem, duration x self esteem, frequency and body image, duration and body image. I am also putting gender in as a independent variable.

#### obh

##### Well-Known Member
Hi Rach,

I didn't understand exactly what are you doing. how many IVs?
I would check outliers separately for each group.
So n1+n2+n3+n4= 264?

#### Rachyxxx

##### New Member
The sample size overall is 264, the independent variables are duration of use (of social media), frequency of checking (social media) and gender (male and female). The dependent variables are body satisfaction and body image. I want to know if there's any sig difference.

#### Miner

##### TS Contributor
There are a number of different tests for outliers (see below). Tukey's fence, used with the box plot, is very sensitive and will flag many potential outliers. The larger your sample size, the more it will flag. I recommend using a more selective test from the ones below. Outliers should only be removed if you can find a reason such as a measurement error or transposing numbers. Otherwise, you should use methods that are robust to outliers.

#### katxt

##### Active Member
A couple of thoughts -
Perhaps you might be better off using a non parametric test.
If you have several anovas in your analysis, have you thought of the implications of multiple p values? Perhaps you should be using a more stringent critical value for significance.

#### obh

##### Well-Known Member
There are a number of different tests for outliers (see below). Tukey's fence, used with the box plot, is very sensitive and will flag many potential outliers. The larger your sample size, the more it will flag. I recommend using a more selective test from the ones below. Outliers should only be removed if you can find a reason such as a measurement error or transposing numbers. Otherwise, you should use methods that are robust to outliers.

View attachment 2291
Hi Miner,

Nice table! but probably also confusing one as there are too many options
I assume usually using the 2 standard deviation method or Tukey fence with k=1.5 will do the job.

If I understand correctly, Rachy also runs the 2 standard deviation method for outliers and has 23 outliers, while if it was a normal distribution without outliers you would expect to get ~12 outliers.

So if the distribution and the outliers are reasonably symmetrical, probably ANOVA should still be OK, I assume there is no final agreement what is too many outliers ...

But of course, it will be safe also to run a non-parametric test, and since the test power should be strong (of course it depends on the required effect size), even a bit weaker non-parametric test should be strong enough.

A smaller significance level is probably a good idea, as suggested by katxt
Anyway Rachy, you should also look at the effect size.

#### Rachyxxx

##### New Member
Hi guys, firstly I just want to say thankyou so much for all your help and replies I am new to stats and currently doing an MSc (Psychology) and my supervisor is on holidays so I am on my own. So all your help is really appreciated. Atm I have decided to leave the outliers because I can't justify removing them, they are not data errors. I have checked the distribution of residuals - body satisfaction x frequency of checking the skewness z score is - 2.22 and body satisfaction x duration the skewness z score is -2.28 which indicates skewness however the self-esteem residuals are okay. Also given that I have loads of outliers am I justified in running a non-parametric test?
Thanks again,

Rach

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#### obh

##### Well-Known Member
The Shapiro test is a normality test ... not anon parametric test instead of ANOVA ...

#### Rachyxxx

##### New Member
Sorry misspoke! Meant to say I will have a look at shapiro then perhaps run a non para if that is advisable?

#### obh

##### Well-Known Member
Probably SW will not be normal especially with a sample size of 264 (no data is really normal)
You can just look at the histogram and decide.
Maybe ANOVA will still be okay with n=264 despite the fact that ANOVA is sensitive to outliers.
If you have any doubt you may try both ANOVA and a non-parametric test.

#### Rachyxxx

##### New Member
You are correct the SW is not normal. I think the fact that I have so many outliers, the skewness is over 1.96 for body satisfaction means I should run a non-parametric test for this one perhaps a Kruskal Wallis. Then just report both in the results?
Thanks again

#### Karabiner

##### TS Contributor
I have the same problems with my son's homework. thanks.
Exactely the same problems, and all of them?