# The Naked Scientists Forum

### Author Topic: Statistics  (Read 10475 times)

#### 4getmenot

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##### Statistics
« on: 14/08/2006 18:07:28 »
Is anyone good with statistics??? I had a choice between that or calculus...i am thinking i should have taken the latter cause i can not figure this out...grrrrrrrr.

k

#### 4getmenot

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##### Re: Statistics
« Reply #1 on: 14/08/2006 18:09:20 »
What are the characteristics of the normal distribution? Why is the normal distribution important in statistical analysis? Find three real-life examples of a continuous variable. Which do you think may be normally distributed? Justify your answers.

This is an example of many, many, many....questions my instructor puts out to us on a daily basis......

k

#### another_someone

• Guest
##### Re: Statistics
« Reply #2 on: 14/08/2006 19:19:58 »
Ah, but statisticians are better paid (actuaries get paid ridiculous sums of money).

http://en.wikipedia.org/wiki/Normal_distribution
quote:

The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. It is a family of distributions of the same general form, differing in their location and scale parameters: the mean ("average") and standard deviation ("variability"), respectively. The standard normal distribution is the normal distribution with a mean of zero and a standard deviation of one (the green curves in the plots to the right). It is often called the bell curve because the graph of its probability density resembles a bell.

The fundamental importance of the normal distribution as model of quantitative phenomena in the natural and behavioral sciences is due to the central limit theorem (the proof of which requires rather advanced undergraduate mathematics). A variety of psychological test scores and physical phenomena like photon counts can be well approximated by a normal distribution. While the mechanisms underlying these phenomena are often unknown, the use of the normal model can be theoretically justified if one assumes many small (independent) effects contribute to each observation in an additive fashion. The normal distribution also arises in many areas of statistics: for example, the sampling distribution of the mean is approximately normal, even if the distribution of the population the sample is taken from is not normal. In addition, the normal distribution maximizes information entropy among all distributions with known mean and variance, which makes it the natural choice of underlying distribution for data summarized in terms of sample mean and variance. The normal distribution is the most widely used family of distributions in statistics and many statistical tests are based on the assumption of normality. In probability theory, normal distributions arise as the limiting distributions of several continuous and discrete families of distributions.

http://www.le.ac.uk/bl/gat/virtualfc/Stats/normal.htm
quote:

The term 'normal distribution' refers to a particular way in which observations will tend to pile up around a particular value rather than be spread evenly across a range of values (the Central Limit Theorem). It is generally most applicable to continuous data and is intrinsically associated with parametric statistics (e.g. ANOVA, t tests, regression analysis). Graphically the normal distribution is best described by a 'bell-shaped' curve. This curve is described in terms of the point at which its height is maximum (its 'mean') and how wide it is (its 'standard deviation').

In the above example, the most common measurement (i.e. 9)is the same in curves A and B but there is a greater range of values for A than for B. Curve C has the same distribution as A but the most common measurement (i.e. 18) is twice that of curve A. All of these distributions are normal and can be described by:

#### Example

The antennae lengths of a sample of 32 woodlice were measured and found to have a mean of 4 mm and standard deviation of 2.37 mm. Using these parameters and the equation above, the expected frequency at each of the lengths encountered was calculated.
Code: [Select]
`Measurement  Observed    Cumulative  Estimated  Estimated              frequency   observed    frequency  cumulative                         frequency               frequency      0         2           2           1.3         1.3      1         3           5           2.4         3.7      2         4           9           3.8         7.5      3         3          12           4.9        12.4      4         4          16           5.4        17.8      5         7          23           4.9        22.7      6         3          26           3.8        26.5      7         3          29           2.4        28.4      8         2          31           1.3        30.2      9         1          32           0.6        30.8`When the observed frequencies (bars) are plotted against the predicted normal distribution (red line) it can be seen that there is a rough agreement between the two. When the cumulative frequencies are plotted against each other the resulting straight line suggests that this sample may have a distribution close enough to normal to allow the use of parametric statistics. To test for normality properly you would have to use something like a Kolmogorov-Smirnoff test (see below).

### Deviations from Normality

The above describes the normal distribution that are found occassionally
##### Tests for Normality

The simplest method of assessing normality is to look at the frequency distribution histogram. The most important things to look at are the symetry and peakiness of the curve. In addition be aware of curves that indicate two or more peaks this would show a bimodal distribution and are not very friendly in statistics.
Visual appraisals must only be used as an indication of the distribution and subsequently better methods must be used. Values of skew and kurtosis as found in Excel's Function Wizard (SKEW and KURT respectively) are another good indicator, but can be over optimistic regarding the data's match with normality. Before the advent of good computers and statistical programs, users could be forgiven for trying to avoid any surplus calculations. Now that both are available and much easier to use, tests for normality (and homogeneity of variance) should always be carried out as a best practice in statistics. SPSS and Minitab contain the Kolmogorov-Smirnov test, which is the principal goodness of fit test for normal and uniform data sets. Alternatively, if you are a whizz on the calculator or in Excel and have a day or two spare or have access to UNISTAT, you may wish to use the Shapiro-Wilk test which is more reliable when n<50.
Both of the above tests use the same hypotheses:
HO: there is no difference between the distribution of the data set and a normal one
HA: there is a difference between the distribution of the data set and normal
The P-value will be provided by SPSS or Minitab, if below 0.05 reject the HO.

George

#### another_someone

• Guest
##### Re: Statistics
« Reply #3 on: 14/08/2006 19:21:50 »
Like the antennae lengths of woodlice mentioned above, most biologically inherited traits (such as IQ) are subject to normal distribution.

George

#### neilep

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##### Re: Statistics
« Reply #4 on: 14/08/2006 20:19:56 »
My brother chose statistics over calculus.......he did really well but always said it was so damn mundane !!..I think he wished he had done calculus instead. But don't let this sway your decision  or have you change your mind...speak to your tutors.

Men are the same as women, just inside out !

#### 4getmenot

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##### Re: Statistics
« Reply #5 on: 23/08/2006 14:24:26 »
well...i should have gone with calculus also, cause this is really really hard....it is more prabability than numbers and i can do much better with real numbers than this stuff....geeezzz.

k

#### moonfire

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##### Re: Statistics
« Reply #6 on: 23/08/2006 14:32:30 »
I prefer statistics....you mean you have a choice between the two???  What is your major?

"Lo" Loretta

#### 4getmenot

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##### Re: Statistics
« Reply #7 on: 23/08/2006 14:24:26 »
well...i should have gone with calculus also, cause this is really really hard....it is more prabability than numbers and i can do much better with real numbers than this stuff....geeezzz.

k

#### moonfire

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##### Re: Statistics
« Reply #8 on: 23/08/2006 14:32:30 »
I prefer statistics....you mean you have a choice between the two???  What is your major?

"Lo" Loretta

#### 4getmenot

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##### Re: Statistics
« Reply #9 on: 23/08/2006 14:24:26 »
well...i should have gone with calculus also, cause this is really really hard....it is more prabability than numbers and i can do much better with real numbers than this stuff....geeezzz.

k

#### moonfire

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##### Re: Statistics
« Reply #10 on: 23/08/2006 14:32:30 »
I prefer statistics....you mean you have a choice between the two???  What is your major?

"Lo" Loretta

#### 4getmenot

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##### Re: Statistics
« Reply #11 on: 25/08/2006 01:09:17 »
yeah, i HAD to take one of them.....My Major is Technical Management/ minor in Project Management. At least I only have two more weeks of it....unfortanatly I got my first grade under an A !!! I WAS at a 4.0 gpa...i am sure that blew that real quick.

k

#### moonfire

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##### Re: Statistics
« Reply #12 on: 25/08/2006 01:59:28 »
With Statitistics? Think outside the box of numbers and like you said probability..visualize...statistics can be played with on both sides of the spectrum which can make it a bit confusing or fun....depending on some of us warped minds think...hehe

"Lo" Loretta

#### 4getmenot

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##### Re: Statistics
« Reply #13 on: 25/08/2006 05:58:29 »
I like the idea of it and in some cases i can understand it, when it is explained it seems simple, but when i am trying to answer the test questions i blank and forget how i got the answers to my struggling 4 hours of homework or how i got it....grrr

k

#### moonfire

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##### Re: Statistics
« Reply #14 on: 25/08/2006 06:17:47 »
OH Boy...slapping my head with Philosphy...trying to remember the philosophers with their thoughts...aaagggghhh!  I was nutso!  I made up lyrics to sing to remember, cassette tapes playing over and over, index cards taped to everything...Who is Plato? etc...all of the other crazy greats...yes, crazzzzzzzzzzzzyyyyyyyyyyy!

"Lo" Loretta

#### 4getmenot

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• Posts: 138
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##### Re: Statistics
« Reply #15 on: 23/08/2006 14:24:26 »
well...i should have gone with calculus also, cause this is really really hard....it is more prabability than numbers and i can do much better with real numbers than this stuff....geeezzz.

k

#### moonfire

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• Posts: 4597
• Can't stand the heat, step away from the fire!
##### Re: Statistics
« Reply #16 on: 23/08/2006 14:32:30 »
I prefer statistics....you mean you have a choice between the two???  What is your major?

"Lo" Loretta

#### 4getmenot

• Sr. Member
• Posts: 138
• Life is one big adventure
##### Re: Statistics
« Reply #17 on: 25/08/2006 01:09:17 »
yeah, i HAD to take one of them.....My Major is Technical Management/ minor in Project Management. At least I only have two more weeks of it....unfortanatly I got my first grade under an A !!! I WAS at a 4.0 gpa...i am sure that blew that real quick.

k

#### moonfire

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##### Re: Statistics
« Reply #18 on: 25/08/2006 01:59:28 »
With Statitistics? Think outside the box of numbers and like you said probability..visualize...statistics can be played with on both sides of the spectrum which can make it a bit confusing or fun....depending on some of us warped minds think...hehe

"Lo" Loretta

#### 4getmenot

• Sr. Member
• Posts: 138
• Life is one big adventure
##### Re: Statistics
« Reply #19 on: 25/08/2006 05:58:29 »
I like the idea of it and in some cases i can understand it, when it is explained it seems simple, but when i am trying to answer the test questions i blank and forget how i got the answers to my struggling 4 hours of homework or how i got it....grrr

k

#### moonfire

• Neilep Level Member
• Posts: 4597
• Can't stand the heat, step away from the fire!
##### Re: Statistics
« Reply #20 on: 25/08/2006 06:17:47 »
OH Boy...slapping my head with Philosphy...trying to remember the philosophers with their thoughts...aaagggghhh!  I was nutso!  I made up lyrics to sing to remember, cassette tapes playing over and over, index cards taped to everything...Who is Plato? etc...all of the other crazy greats...yes, crazzzzzzzzzzzzyyyyyyyyyyy!

"Lo" Loretta

#### daveshorts

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##### Re: Statistics
« Reply #21 on: 25/08/2006 11:16:58 »
I think the question mostly boils down to how much maths you are intending on doing in the future, calculus is very useful for doing other stuff, huge swathes of maths, physics etc depend on it (including most of statistics if you get a little deeper), however in itself it is not so useful directly. So if you are intending on taking any more maths courses in the future (including stats) the calculus will be very useful, however if not, a more vocational stats course may make more sense as you will probably end up directly applying its contents.

#### moonfire

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##### Re: Statistics
« Reply #22 on: 25/08/2006 14:14:10 »
So true Dave, but I had to take both!  If only I had a choice...K, what is your major?

"Lo" Loretta

#### 4getmenot

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##### Re: Statistics
« Reply #23 on: 26/08/2006 03:55:18 »
My major is Technical Management with a focus in Project Management. I do not plan to take anymore math classes after this, supposedly this is the last one i need to get my degree so...i can only hope for the best at this point, i think i should have gone with calculus though...i guess i will know once i am in project management at work and see what we use more....hmmm (pulling on LAST hair in my head) grrrr

k

#### moonfire

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##### Re: Statistics
« Reply #24 on: 26/08/2006 04:36:22 »
I remember that...slapping hand to forehead...40's something moment..yikes!  I wanted to go back for masters and may still do it...I stare at my GRE book all the time...open it and then shut it, open it and then shut it...aagghh!

"Lo" Loretta

#### The Naked Scientists Forum

##### Re: Statistics
« Reply #24 on: 26/08/2006 04:36:22 »