Statistics

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Statistics

• BIOL 151 Laboratory
• Winthrop University

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Why do we do statistics?

• It is in our nature as human beings to include
  personal bias when we evaluate situations.
  
• Science shouldnt be clouded by the observers
  point of view.
  
• Statistics allow us to make an objective
  judgement about what we discover.
  

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Why do we do statistics?

• What does objective mean (as opposed to
  subjective)?
  
• Something that can be measured.
• Not open to interpretation or opinion.
• Removes the influence of personal bias.

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The Scientific Method

• Remember that your hypothesis is an attempt to
  predict the outcome of your experiment.
  
• Support.
• Reject.
• You NEVER prove a hypothesis!
• There are at least two hypotheses in all
  experiments.
  
• The null hypothesis.
• Alternative hypothesis (or hypotheses).

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The Null Hypothesis

• The null hypothesis says that there is no
  difference between the things that you are
  comparing.
  
• For example, our null hypothesis in the leaf
  exercise would state that there was no difference
  in size between the inner leaves and the outer
  leaves on the tree.
• The null hypothesis is always a possible
  outcome!

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Alternative Hypotheses

• There always has to be at least one alternative
  hypothesis in experiments.
  
• This states that the test groups are different.
• For example, in our leaf experiment, two
  alternative hypotheses could be
  
• The outer leaves are larger because they receive
  more sunlight.
  
• The inner leaves are larger because they get
  less sunlight, and need more surface area to
  carry out photosynthesis.

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More on the Scientific Method

• Once you have a working hypothesis, you design
  the experiment.
  
• Experimental design includes variables.
• Independent variable this is what you vary.
• These variables have an effect on the dependent
  variable.
  
• Dependent variable What you measure.

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Variables

• What were some of the independent and dependent
  variables weve looked at so far?
  
• Disinfectant experiment?
• Leaf survey?
• You can keep them straight in your head by
  thinking the phrase, What is the effect of _____
  on _____?
  
• Blank one is the IV, and blank two is the DV.

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Variables

• Variables have different forms that we call
  levels in statistics.
  
• For example, if you were conducting an
  experiment that looked at baby gender and its
  effect on birth weight, gender would be the
  variable.
• Then, male and female would be the levels of our
  gender variable.

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Variables

• The independent variable must have at least two
  levels.
  
• We need to have some variance to have an
  experiment!

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A Few Examples

• What is the effect of tree species on heat
  output when wood is burned?
  
• DV ______________
• IV _____________
• Levels ?

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A Few Examples

• What is the effect of city population size on
  gas prices in the United States?
  
• DV ______________
• IV _____________
• Levels ?

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A Few Examples

• What is the effect of dog breed on dog
  lifespan?
  
• DV _______________
• IV ______________
• Levels ?

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Data and Data Types

• Once we have our hypothesis and experimental
  design, we collect data.
  
• There are two types of dependent variable data
• Discrete.
• Continuous.
• Data is either one or the other it cant be
  both discrete and continuous.

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Data and Data Types

• Discrete data is data sorted by characteristics
  or attributes, or something you count.
  
• Example Color.
• Colors are either red, blue, green, magenta.
• Example Gender.
• Male, female.
• Example Number of children in a household.
• You cant have 3.5 children.
• Discrete data is either/or.
• Something is either red or greenthere is no
  red and a half.

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Data and Data Types

• Continuous data is data that you obtain by
  measurement.
  
• Various tools are used to generate continuous
  data
  
• Rulers
• Scales
• Speedometers
• Etc.
• Since you got this data from measuring
  something, continuous data has units associated
  with it.
  
• Kilometers
• Grams
• Liters
• Etc.

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Using Statistics

• Statistics are used to answer our questions about
  our data, while keeping personal biases out.
  
• We rely on math in order to do this.

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Using Statistics

• What do we need in order to run good
  statistics?
  
• Large sample sizes need to be able to have a
  good representation of what is going on in the
  situation we are investigating.
  
• Random sampling again, we need to keep out
  personal bias (as much as we possibly can)!
  

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Using Statistics

• There are two types of statistics we are going
  to talk about in this lab
  
• Descriptive statistics.
• Statistical tests.

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Descriptive Statistics

• Descriptive statistics include mean, variance,
  and standard deviation.
  
• Descriptive stats are used mainly to summarize
  data.
  
• This is usually the first step in data analysis.

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Descriptive Statistics

• The mean is the average of the numbers in a data
  set.
  
• Tells us how things differ, on average, or what
  is typical.
  
• Variance measures how much variability there is
  around the mean.
  
• In other words, how the samples are dispersed.
• Standard deviation is derived by taking the
  square root of the variance.

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Descriptive Statistics

• Classic example of standard deviation is the
  bell-shaped curve.
  
• This graphically depicts a normal
  distribution.

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Statistical Tests

• Statistical tests are used to detect
  statistically significant differences in data
  sets.
  
• We will be using the t-Test and the X2 test.
• But first, lets talk about why we do statistical
  tests.

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Statistical Tests

• You may have two means that appear to be
  different from each other.
  
• However, if there is a lot of overlap between
  the two data sets, there may not be a
  statistically significant difference between the
  two.
• See the board for an example!

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The t-Test

• We use the t-Test on data that is continuous.
• Remember, continuous data is data that is
  measured (volume, length, weight, etc.)
  
• We use the t-Test to determine if there is a
  statistically significant difference between
  means.

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The t-Test

• To run the t-Test, you must know the following
  _
  
• The means of your samples (X).
• Sample size (n).
• The variance of your samples (Var).
• The equation is found in your book.
• You can use your calculator to figure out the
  means and the variances of your samples.
  

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The t-Test

• Once you get your t value, you need to look at
  the degrees of freedom table in your lab manual
  (page 34).
  
• Degrees of freedom, in general, is a number
  related to the sample size that accounts for the
  number of observations made.
  
• Larger sample sizes will give more degrees of
  freedom.

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The t-Test

• From the degrees of freedom table, you find the
  critical value associated with that number.
  
• If your t value is greater than the critical
  value, you have a statistically significant
  difference between your means.
  
• This means you would REJECT your null hypothesis
  and ACCEPT your alternate hypothesis.

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The t-Test

• If the critical value is greater than your t
  value, there is no statistically significant
  difference between your means.
  
• Therefore, you would REJECT your alternate
  hypothesis, and ACCEPT your null hypothesis.

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The Next Test The X2 Test

• We use the X2 test when the dependent variable
  is composed of discrete data.
  
• Recall the difference between discrete and
  continuous data.
  
• Continuous data is data we gathered by
  measuring.
  
• Discrete data is based on characteristics or
  counts of something.
  
• It is either/or.

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The X2 Test

• So, we use the X2 on discrete data, and
  furthermore, we are interested in how objects are
  distributed through time or spatially.
  
• Remember, the t-Test tests for difference
  between means. The X2 test tests for differences
  in distribution!
  
• The example your book gives looks at beer sales
  over a period of time.
  

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The X2 Test

• The X2 test uses observed values and expected
  values in an equation.
  
• Observed values are the data that you
  collected.
  
• In the beer example, they are 27, 41, and 21,
  for Blitz, Grog, and Zowie respectively.

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The X2 Test

• The expected values are what you would expect to
  see if each of the samples were equivalent.
  
• In other words, what you would see if your null
  hypothesis were supported (no difference between
  samples)!
  
• For the beer example, the expected value is
  29.33 for each brand of beer.

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The X2 Test

• Expected value is calculated by taking the sum
  of all samples, and dividing it by the number of
  levels.
  
• So, 27 41 20 88
• 88 / 3 29.33
• (Basically, you are taking the average.)

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The X2 Test

• What does that sigma (?) mean?
• For each of your levels (in the beer example,
  Blitz, Grog, and Zowie), you get a value for
  
• (o-e)2 e.
• The sigma means that you add up all of these
  values that you find for each level.

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The X2 Test

• So what happens after you have your X2 value?
• Essentially same thing as with the t-Test, with
  some minor differences.
  
• You find your degrees of freedom, find the
  corresponding critical value on the table (page
  34), and make a comparison
  
• To find degrees of freedom for the X2 test, you
  take the number of levels of the independent
  variable and subtract one.
  
• So, for the beer example, degrees of freedom
  would be 3 -1 2

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The X2 Test

• If your X2 value is higher than the critical
  value, you REJECT your null hypothesis and state
  that there is a significant difference between
  the samples (you accept your alternate
  hypothesis!).
• If lower, you accept the null.
• Make sure you use the right degrees of freedom
  table (the t-Test and X2 Test have different
  tables)!

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Statistics Exercises

• You are going to run a t-Test on your
  disinfectant labs zone of inhibition data.
  
• You will also do a t-Test on your leaf
  measurement data.
  
• Finally, you will be doing a X2 test on M Ms.
• Directions for using your calculators is on the
  board.