Recall:
Mean
Standard deviation
Variation
Continuous variation
Normal distribution
THE X 2 AND T TESTS
Use statistical methods to analyse ecosystems (t-test, x2)
T-TEST
• Used to assess whether or not the means of two sets of data with
roughly normal distributions, are significantly different from one
another.
• Steps
1. Identify hypotheses (null vs. alternative)
II. Compute for the mean and standard deviation of the two sets
of data
III. Apply the t-test formula
IV. Determine the degree of freedom (v)
V. Identify the t value
https://www.graphpad.com/quickcalcs/ttest1/?Format=50
T-test calculator
CHI-SQUARED TESTS
• To determine if there is a statistically significant association
between the distribution of two species.
• Steps
1. Identify hypotheses (null vs. alternative)
II. Construct a table of frequencies (observed vs. expected)
III. Apply the chi-squared formula
IV. Determine the degree of freedom (v)
df = (m – 1) (n – 1)
V. Identify the p value
Where:
m = number of rows
;
n = number of columns
SAMPLE PROBLEM
Two species of fir tree are found along the coast of Southern
California.
These two tree species are the Grand Fir (Abies grandis) and the
Noble Fir (Abies procera). Their distribution patterns were established
via 150 quadrat samples, yielding the following results:
25 = both present
30 = Noble Fir only
45 = Grand Fir
50 = neither present
STEP 1: IDENTIFY THE HYPOTHESES
• Null hypothesis (H0): There is no significant difference
between the distribution of two species (i.e. distribution is
random)
• Alternative hypothesis (H1): There is a significant difference
between the distribution of species (i.e. species are
associated)
STEP 2: CONSTRUCT A TABLE OF
FREQUENCIES
Expected frequency = (Row total x column total) / Grand total
STEP 3: APPLY THE CHI-SQUARED FORMULA
STEP 4: DETERMINE THE DEGREE OF
FREEDOM
STEP 5: IDENTIFY THE P VALUE
df = (m – 1) (n – 1)
Where:
m = number of rows
;
n = number of columns
T TEST VS. X 2 TEST
IDENTIFY THE FOLLOWING FORMULAS:
Question
2(a) two (for one mark) from
number of ields tudied ;
(width of) the headland/strip ;
(type of) cer al/crop ;
Answer
Total: 19
Mark
1
Ad it onal Guidance
A length if qualifed by 6m
2(b)(i dat is nominal/categoric
1 A dat can be grouped/is discret
or
testing the dif er nce betwe n observed (O) and expected (E) results ;
2(b)(i) ther is no signifcantdifer nce betwe n umber of but erflies of each 1 A without herbicde/not reated/control for not sprayed
species when headland sprayed and when ot sprayed ; A with erbicde/treated for sprayed