Thread Subject: Histogram and Normality test

Dear all,

I have a 2^18-length data, sampled at 48 kHz with a 16-bit
ADC. The histogram is very close to the normal
distribution, but the data always fails the normality
hypothesis tests.
When plotting the histogram with 1000 bins, there are
various spikes in the figure. I know reducing the number of
bins help get a smoother curve, but am I correct in
assuming that these spikes are the reason the tests fail? I
mean, the test needs to average the spike amplitudes to get
the estimated distribution, so the result doesn't have the
same moments as the original sample.

Thanks for any explanation,
Mastaneh

"Mastaneh " <mtorkama@iupui.edu> wrote in message
<g7cmca$a2c$1@fred.mathworks.com>...
> Dear all,
>
> I have a 2^18-length data, sampled at 48 kHz with a 16-bit
> ADC. The histogram is very close to the normal
> distribution, but the data always fails the normality
> hypothesis tests.
> When plotting the histogram with 1000 bins, there are
> various spikes in the figure. I know reducing the number of
> bins help get a smoother curve, but am I correct in
> assuming that these spikes are the reason the tests fail? I
> mean, the test needs to average the spike amplitudes to get
> the estimated distribution, so the result doesn't have the
> same moments as the original sample.


I would investigate the source of the spikes in the original
data and not in the histogram bins. There are some scripts
to remove outliers and this may be all you need.
>
> Thanks for any explanation,
> Mastaneh

"Mastaneh " <mtorkama@iupui.edu> wrote in message <g7cmca$a2c$1@fred.mathworks.com>...
> Dear all,
>
> I have a 2^18-length data, sampled at 48 kHz with a 16-bit
> ADC. The histogram is very close to the normal
> distribution, but the data always fails the normality
> hypothesis tests.
> When plotting the histogram with 1000 bins, there are
> various spikes in the figure. I know reducing the number of
> bins help get a smoother curve, but am I correct in
> assuming that these spikes are the reason the tests fail? I
> mean, the test needs to average the spike amplitudes to get
> the estimated distribution, so the result doesn't have the
> same moments as the original sample.
>
> Thanks for any explanation,
> Mastaneh
 
Testing the normality of data through the histogram shape would not be enough. You need to run more tests. Here is some of them you can apply using Matlab Statistics Toolbox:

QQ-Plot (qqplot(x))
Skewness and Kurtosis
Kolmogorov-Smirnov Test(kstest)
Chi Square Test
Lilliefors test for goodness of fit (lilitest)
Jarque–Bera test(jbtest)

Sajjad