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Normal Distributions, Standard Deviations, Modality, Skewness and Kurtosis: Understanding concepts - YouTube
Channel: NurseKillam
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The normal distribution is a theoretical concept
of how large samples of ratio or interval
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level data will look once plotted.
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Since many variables tend to have approximately
normal distributions it is one of the most
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important concepts in statistics.
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The normal curve allows for probabilities
to be calculated.
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In addition, many inferential statistics require
that data are distributed normally.
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If your data is not normal be careful what
statistical tests you use with it.
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In a normal distribution, measures of central
tendency including the mean, median and mode
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all fall at the same midline point.
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The mean, median and mode are all equal.
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The calculation of these measures of central
tendency are covered in another video.
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Normal distributions share several key features.
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They are unimodal, meaning that there is only
one peak in the distribution.
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When divided at the mean a normal distribution
takes the form of a symmetrical bell-shaped
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curve.
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Standard deviations are used to measure how
much variation exists in a distribution.
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Low standard deviations mean values are close
to the mean whereas high standard deviations
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mean that values are spread out over a large
range.
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In a normal distribution approximately 34%
of scores fall between the mean and 1 standard
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deviation above the mean.
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Therefore, based on it's symmetry, approximately
68% of scores fall between 1 standard deviation
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above and 1 standard deviation below the mean;
approximately 95% of scores fall between 2
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standard deviations above and 2 standard deviations
below the mean;
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approximately 99.7% of scores fall between
3 standard deviations above and below the
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mean.
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Z scores are used to measure how many standard
deviations above or below the mean a particular
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score is.
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These scores allow for comparison and probability
calculations.
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Not all samples approximate a normal curve.
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To understand more about distributions it
is important to understand modality, symmetry
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and peakedness.
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A distribution can have more than one peak.
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The number of peaks contained in a distribution
determines the modality of the distribution.
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Most distributions are normally distributed
and have only one main peak, meaning they
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are unimodal.
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However, it is possible to have distributions
with two or more peaks.
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Distributions with two peaks are bimodal.
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Distributions with more than two peaks are
multimodal.
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Symmetry and modality are independent concepts.
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If two halves of a distribution can be superimposed
on each other where each half is a mirror
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image of the other, the distribution is said
to be symmetrical.
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Sometimes data are not symmetrical.
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If the peak is off centre one tail of the
distribution will be longer than the other,
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meaning it is skewed.
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Skewness is a measure of the symmetry of distributions.
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Pearson's skewness coefficient provides a
non-algebraic, quick estimation of symmetry.
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Recall that Normal distributions are symmetrical
and bell shaped.
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In a perfect distribution the skewness coefficient
will be equal 0 because the mean equals the
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median.
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Positive skewness means there is a pileup
of data to the left leaving the tail pointing
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to the right side of the distribution.
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The tail has been pulled in the positive direction.
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The data is skewed to the right.
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In this case the Mean is to the right of the
median.
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Interestingly, positive skews are more common
than negative ones.
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Negative skewness means there is a pileup
of data to the right with a long tail on the
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left side.
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The tail has been pulled in a negative direction.
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In this case the Mean is to the left of the
median.
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To remember the meaning of a positive and
negative skew think of pulling on tails.
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Remember that the tail points towards the
direction of the skew.
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The mean is also pulled in the direction of
the long tail of the skew.
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Kurtosis is a measure of the shape of the
curve.
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It measures if the bell of the curve is normal,
flat, or peaked.
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Since it's calculation is tedious it is typically
done by a computer.
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Using Fisher's measure of kurtosis a normal
distribution would receive a coefficient of
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0 and be called mesokurtic.
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If the calculation of excess Kurtosis results
in a large positive number the distribution
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is too peaked to be considered normal.
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This type of data is called leptokurtic.
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The curve is taller and skinnier than a normal
distribution.
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The beginning of the word kind of sounds like
leapt so think of a skinny guy who leapt high
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in the air.
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If the calculation of excess Kurtosis results
in a negative number it is too flat to be
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normal.
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It would be called platykurtic.
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The curve is shorter and fatter than a normal
distribution.
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One way to remember this is that the beginning
of the word kind of sounds like a flat plateau.
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If a distribution is skewed there is no need
to calculate kurtosis since the distribution
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is already not normal.
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Thank you for watching.
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Please subscribe and explore more of my videos.
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Let me know what you found helpful and what
other information you may need.
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I look forward to reading your comments.
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