Seeing if data is normally distributed in R

Question

Can someone please help me fill in the following function in R    data is a single vector of decimal values normally distributed  lt - function data    if data is normal  return TRUE  else return NO

User · Answer

library DnE  x lt -rnorm 1000 0 1  is norm x 10 0 05

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I would also highly recommend the SnowsPenultimateNormalityTest in the TeachingDemos package   The documentation of the function is far more useful to you than the test itself  though   Read it thoroughly before using the test

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Normality tests don t do what most think they do  Shapiro s test  Anderson Darling  and others are null hypothesis tests AGAINST the the assumption of normality  These should not be used to determine whether to use normal theory statistical procedures  In fact they are of virtually no value to the data analyst  Under what conditions are we interested in rejecting the null hypothesis that the data are normally distributed  I have never come across a situation where a normal test is the right thing to do  When the sample size is small  even big departures from normality are not detected  and when your sample size is large  even the smallest deviation from normality will lead to a rejected null   For example    gt  set seed 100   gt  x  lt - rbinom 15 5  6   gt  shapiro test x       Shapiro-Wilk normality test  data   x  W   0 8816  p-value   0 0502   gt  x  lt - rlnorm 20 0  4   gt  shapiro test x       Shapiro-Wilk normality test  data   x  W   0 9405  p-value   0 2453   So  in both these cases  binomial and lognormal variates  the p-value is   0 05 causing a failure to reject the null  that the data are normal   Does this mean we are to conclude that the data are normal   hint  the answer is no   Failure to reject is not the same thing as accepting  This is hypothesis testing 101    But what about larger sample sizes  Let s take the case where there the distribution is very nearly normal    gt  library nortest   gt  x  lt - rt 500000 200   gt  ad test x       Anderson-Darling normality test  data   x  A   1 1003  p-value   0 006975   gt  qqnorm x       Here we are using a t-distribution with 200 degrees of freedom  The qq-plot shows the distribution is closer to normal than any distribution you are likely to see in the real world  but the test rejects normality with a very high degree of confidence   Does the significant test against normality mean that we should not use normal theory statistics in this case   another hint  the answer is no

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SnowsPenultimateNormalityTest certainly has its virtues  but you may also want to look at qqnorm   X  lt - rlnorm 100  qqnorm X  qqnorm rnorm 100

User · Answer

In addition to qqplots and the Shapiro-Wilk test  the following methods may be useful   Qualitative    histogram compared to the normal cdf compared to the normal ggdensity plot ggqqplot   Quantitative    nortest package normality tests normtest package normality tests   The qualitive methods can be produced using the following in R   library  ggpubr   library  car    h  lt - hist data  breaks   10  density   10  col    darkgray    xfit  lt - seq min data   max data   length   40   yfit  lt - dnorm xfit  mean   mean data   sd   sd data    yfit  lt - yfit   diff h mids 1 2     length data   lines xfit  yfit  col    black   lwd   2   plot ecdf data   main  CDF   lines ecdf rnorm 10000   col  red    ggdensity data   ggqqplot data    A word of caution - don t blindly apply tests  Having a solid understanding of stats will help you understand when to use which tests and the importance of assumptions in hypothesis testing

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The Anderson-Darling test is also be useful   library nortest  ad test data

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when you perform a test  you ever have the probabilty to reject the null hypothesis when it is true   See the nextt R code   p function n     x rnorm n 0 1    s shapiro test x    s p value    rep1 replicate 1000 p 5   rep2 replicate 1000 p 100   plot density rep1   lines density rep2  col  blue   abline v 0 05 lty 3    The graph shows that whether you have a sample size small or big a 5  of the times you have a chance to reject the null hypothesis when it s true  a Type-I error

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Consider using the function shapiro test  which performs the Shapiro-Wilks test for normality   I ve been happy with it

[r] Seeing if data is normally distributed in R

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