Transcript File - Groby Bio Page

Match up definitions
1. Hypothesis
A. The value that occurs most
often in a data set
2. Mean
B. A statistical test used to
determine the significance of an
association between categories of
data
3. Mode
C. The sum of the data divided by
the number of data entries (n)
4. Median
D. A graphical representation of
the variability of data.
5. Range Bars
E. The number that occurs in the
middle of a set of sorted numbers.
6. Chi-squared χ2
F. A tentative explanation of an
observation, capable of being
tested by experimentation
Evaluative Prep
Mussel shell length
A student investigated the variation in the length of mussel
shells on two locations on a rocky shore, the results are
shown in the table below.
Location
Mean length
(mm)
Median length
(mm)
Length Range
(mm)
Lower shore
9.67
9.00
8.00 to 12.00
Upper shore
6.00
6.00
6.00 to 7.00
1) Plot the two mean length values on a bar chart
2) Add range bars to the bar chart
3) Indicate with a small cross the median value on the range
bar
Graph skills
Rules for graph drawing
PA
The graph should be of an appropriate size to make
good use of the paper.
There should be an informative title, and axes scaled
appropriately with ascending scale and equidistant
intervals should be fully labelled with units.
Bar charts – made up of blocks of equal width, which do
not touch.
Range bars – upper and lower range values connected
by a line
Median value accurately plotted with a cross
Question – Using the table and the bar chart describe
one similarity and one difference in the range of
mussel lengths for both shores
(3 marks)
KARL PEARSON
(1857-1936)
(Pearson’s)
British
mathematician,
‘father’ of modern
statistics and a
pioneer of
eugenics!
Chi-squared (χ2) test
• Chi-squared is used to test if the observed
frequency fits the frequency you expected or
predicted.
• The theory is used to predict a result – this is
called the expected result
• The experiment is carried out and the actual
result is recorded – this is called the observed
result
How do we calculate the expected
frequency?
• You might expect the observed frequency of
your data to match a specific ratio. e.g. a 3:1
ratio of phenotypes in a genetic cross.
• Or you may predict a homogenous distribution
of individuals in an environment. e.g. numbers
of daisies counted in quadrats on a field.
Note: In some cases you might expect the observed
frequencies to match the expected, in others you
might hope for a difference between them.
What is the null hypothesis (H0)?
To see if the results support the theory you make a
hypothesis called the null hypothesis
H0 = there is no statistically significant difference
between the observed frequency and the expected
frequency
Your experimental result will always be a bit different
but you need to know if the difference is just due to
chance, or because the theory is wrong
Χ2 is carried out and the outcome either supports or
rejects the hypothesis
Calculating χ2
χ2
=

(O – E)2
E
O = the observed results
E = the expected (or predicted) results
You have been wandering about on a seashore and you have
noticed that a small snail (the flat periwinkle) seems to live only
on seaweeds of various kinds. You decide to investigate
whether the animals prefer certain kinds of seaweed by
counting numbers of animals on different species. You end up
with the following data:
Write a hypothesis for this investigation
Seaweed
serrated
wrack
bladder
wrack
egg
wrack
spiral
wrack
other
algae
TOTAL
Observed
45
38
10
5
2
Expected
O-E
(O – E)2
(O – E)2/E
How do we calculate expected values?
Expected results = 45 + 38 + 10 + 5 + 2 = 100 = 20
5
5
In the question you may be given a calculation for how to work out your
expected values
Answers
Seaweed Observed
serrated
45
wrack
bladder
38
wrack
egg
10
wrack
spiral
5
wrack
other
2
algae
TOTAL
Expected
O-E
(O – E)2
(O – E)2/E
20
25
625
31.3
20
18
324
16.2
20
-10
100
5.0
20
-15
225
11.3
20
-18
324
16.2
80.0
Compare your calculated value of χ2 with the critical value
in your stats table
Our value of χ2 = 80.0
Degrees of freedom = no. of categories - 1 = 4
D.F.
Critical Value
(P = 0.05)
1
2
3
4
5
3.84
5.99
7.82
9.49
11.07
Our value for χ2 exceeds the critical
value at 5% (p = 0.05) probability
level, so we can reject the null
hypothesis.
There is a significant difference
between our expected and observed
results at the 5% level of probability.
In doing this we are saying that the
snails are not scattered about the
various sorts of seaweed but seem to
prefer living on certain species.
P Values
• If the P value is less than 0.05 (an arbitrary, but well
accepted threshold), the results are deemed to be
statistically significant.
• All it means is that, by chance alone, the difference (or
association or correlation..) you observed (or one even
larger) would happen less than 5% of the time.
• It’s an estimate of how likely we are to observe our result
by chance.
• If p = <0.05, there is a 5% probability of making our
observation purely by chance.
• This means we can reject the null hypothesis.
Plenary
SA statistic sheet