Mathematics, Practicals, Flashcards
what is ACCURACY
a measure of the closeness of agreement between an individual test result and the true value
if accurate, it is close in agreement with the true value- can be an accepted reference value, though usually not known

what is PRECISION
the closement of agreement between a number of independent measurements obtained under the same conditions in the experiment
it depends only on the distribution of random errors- i.e. the spread of measurements- and does not relate to the true value

what is ERROR of measurement
the difference between an individual measurement and the true value or accepted reference value of the quantity being measured

what are the two types of error and what is the difference between them
- RANDOM ERROR- errors in measurement caused by factors which vary from one measurement to another
- SYSTEMATIC ERROR- errors whose effects are not reduced when observations are averaged/the mean
what is the formula for the volume of a sphere
V = 4/3 π r3
which is RQ
(give formula)
respiratory quotient is the ratio of carbon dioxide produced and oxygen consumed per unit time by an organism
RQ = volume of CO2 produced/ volume of oxygen used
per unit of time
eg. if glucose, 6 CO2 molecules are produced and 6 O2 molecules are consumed; 6/6 = 1.0
what are the RQ values of different respiratory substrates
glucose = 1.0
triglycerides = 0.7
protein = 0.9
what is the equation for the Simpson’s Index of Diverisity (D)
D = 1 - Σ (n/N)²
n = number of individuals in one population
N = number of individuals in the whole community
what does the result of the Simpson’s Index of Diversity equate to
value of D is 0-1
0 = N0 diversity (where only 1 species exist)
near 1 = high diversity

how can you measure these abiotic factors:
- Temperature
- pH
- Light intensity
- Depth of water
- Flow rate
- O2 concentration
- Turbidity
- Type of substrate
- Dissolved solids (conc. of ions eg. Ca2+)
Thermometer or temperature probe
Universal indicator or pH probe
Light meter
Metre ruler
Flow meter or timing how long a floating object takes to travel a set distance
O2 probe
Colorimeter or arbitrary scale (0-10)
Visual description eg. rock, mud, sand
Conductivity metre
give the formulae for NITRIFICATION
Oxidation of ammonia to nitrite
2 NH3 + 3 O2 → 2 NO2- + 2H+ + 4 H2O + release of energy*
- ammonia+oxygen → nitrite+protons+water (*energy released used by bacteria for chemosynthesis)*
- Oxidation of nitrite to nitrate*
2 NO2- + O2 → 2 NO3- + release of energy*
nitrite+oxygen → nitrate+energy
when should you use the STUDENT’s T-TEST
how does it work
> when there are two strata eg. a woodland habitat and grassland habitat and how many bluebells in each
- State the null hypothesis
- Calculate the t value, using the difference between the means and SD of the two sets of data.
- Compare t with the critical value for the appropriate degrees of freedom at a p value of 0.05
- If t > critical value, the difference is significant
- Reject the null hypothesis
what are the types of line transect
CONTINUOUS LT = count all species that touch the transect
I N T E R R U P T E D LT = count species that touch the line at fixed intervals
how is productivity measured
kJ/m2/yr

due to seasons
what is standard deviation
how is it better than range
Spread from the mean i.e. distribution
The wider the spread, the larger the SD.
Range can include outliers.
how is % efficiency of biomass transfer between trophic levels measured
- biomass at higher trophic level*
- ——————————————– x100*
- biomass at lower trophic* level
eg. 250/1250 x 100 = 20%
how to make sampling more accurate
USE MORE QUADRATS/LARGER SAMPLE SIZE, to
- reduce effect of outliers
- find a running mean/one closer to true value/find more consistent measure of mean
PLACE QUADRATS RANDOMLY eg. using random number generator/coordinates
or randomly within stratified sampling PROPORTIONALLY TO AREA SIZE
when should you use chi-squared test
Finding if there is a difference between observed and expected values
eg. dihybrid crosses & ratios of expected vs. studied
IF x2 value calculated IS GREATER THAN THE CRITICAL VALUE, ACCEPT/SUPPORT NULL HYPOTHESIS
what is a plan diagram

when is the CHI-SQUARED stats test used
To assess the significance of differences between expected and observed results.
NULL HYPOTHESIS = no significant deviation between E and O results.
The larger the deviation, the larger the x2
IF x2 EXCEEDS p=0.05, THE O RESULTS DIFFER SIGNIFICANTLY
when sampling, what is important to keep in mind for the method
- REPEATS! in each area, with the same technique in each area
- Use number of quadrats/sampling sites proportional to area’s size
- Classify + count species, using identification key
- Tape measure, quadrat, sweep net/pitfall traps,
what is the null hypothesis in a Spearman’s Rank stats test
and what can we say about the null hypothesis if rs = 0.075 and the critical value at p = 0.05 is 0.564
There is no correlation between (factor A) and (factor B).
The critical value is larger than R. The correlation between factor A and factor B is not significant at the 95% confidence level.
Therefore there is a greater than 5% probability that the relationship is due to chance, so we accept the null hypothesis: no correlation.

why can the STUDENT’s TEST not be used to analyse a set of observed + expected results
- t-test compares two or more means
- no mean in this data/cannot calculate mean/standard deviation from it
why might observed results differ from expected results
RANDOM FERTILISATION
Calculate rs for the following values
SOIL MOISTURE 0% 20% 40% 60% 80%
RANK (R1)
NUMBER OF SEEDLINGS GERMINATED 0 8 15 42 33
RANK (R2)
d (R1-R2)
critical value at p = 0.05 is 1.0

(R1) 1 2 3 4 5
(R2) 1 2 3 5 4
d (R1—R2)
0 0 0 1 1 d = 2 (no negatives)
d2 = 2 (i.e. 12 + 12)
rs = 1 - (6 x 2 / 5(25-1))
rs = 0.9
Critical value > rs , the correlation between soil moisture (%) and number of seedlings germinated is not significant.
A farmer crossed an ash red male (XX) with a brown female (XY).
Ash red XCr is dominant to brown XCbr is dominant to blue XCbl
Pigeons are kept in small mixed flocks but tend to be monogamous- each season the female produces two eggs.
The offspring of the same pair of birds:
Year 1 : brown male, blue female
Year 2 : ash red male, ash red female
Year 3 : ash red male, blue female (etc. etc.)
x2 in Chi-squared test = 1.6 critical value at p=0.05 is 7.81
(a) What can be concluded about the observed results collected by the breeder? 1 mark
(b) Explain why the observed results did not exactly match the predicted results. 1 mark
(c) In Year 4 two brown females were produced. The breeder had not expected any, so had left the category out of the results table. What effect would adding this unexpected results have on the value of chi-squared? 1 mark
(d) Assuming the breeder had made an accurate prediction about the ratio of of offspring, what might the breeder have concluded about the parents of the chicks in Year 4? 1 mark
(e) Explain how you have reached this conclusion. 2 marks
(a) There is no significant difference between the expected & observed results.
(b) RANDOM FERTILISATION (not random mating)
(c) The value would increase to infinity.
(d) They were not monogamous- there was another bird involved.
(e) In female offspring the allele for feather colour comes from male parent. Original male bird did not have allele for brown feathers. Brown feathers allele in female would not produce brown female offspring.
Heterozygous male x heterozygous female
TtDd x TtDd
offspring phenotypes: curly/pink, curly/black, straight/pink, straight/black
- What is the phenotypic ratio?
- Describe in words how this phenotypic ratio might be different if the two genes were autosomally linked.
- 9 : 3 : 3 : 1
- There would be a higher proportion of heterozygous (curly/pink) / more phenotypes like parents.