Maths skills for A-level Biology Flashcards
magnification uncertainties
what is the uncertainty of a piece of equipment?
half of its resolution
how to find the uncertainty of something you’ve had to add values to find?
if you add 2 readings together, you add the 2 uncertainties
what is the margin of error?
the area between the 2 uncertainties on either side of the reading, the true reading lies within this area. e.g. 50 cm with uncertainty of ± 0.5 the margin of error will lie between 49.5 and 50.5
its the size of the resolution
what is the percentage error?
uncertainty/ reading X 100
what is magnification?
size of image / size of real object
what will the null hypothesis always be?
there will be no significant difference between what’s being measured / no correlation
what does it mean if p≤0.05?
it is unlikely that the difference/ correlation is due to chance.
you can reject the null hypothesis. so the result is significant
what does it mean if p>0.05?
insufficient proof to reject null hypothesis, still relatively high chance difference / correlation is due to chance
What does it mean if your chi-squared value ≥ critical value at p = 0.05?
probability that difference in results is due to chance is
the difference between observed and expected values is significant and there is insufficient evidence to reject null hypothesis
What does it mean if your chi-squared value < critical value at p = 0.05?
probability that difference in results is due to chance is > 5%
the difference between observed and expected values is not significant and there is sufficient evidence to reject the null hypothesis
when can chi-squared be used?
when the data is about frequencies for different categories
the data is independent
what is the chi-squared equation?
what are the different correlation coefficients?
Pearson’s correlation coefficient
Spearman’s rank correlation coefficient
what does Pearson’s correlation coefficient allow you to do?
work out the degree to which 2 sets of continuous data are correlated. using data that isn’t ranked
what does Spearman’s rank correlation coefficient do?
it involves ranking variables in size order. this means you can only use it when both variables can be put in size order
what is the formula for Spearman’s rank correlation coefficient?
n = number of observations
d = difference between ranks
how to work out d for spearmen’s rank?
rank the 2 sets of variables being compared from 1 to n, with the smallest being ranked the same in both sets.
how to determine whether a spearman’s rank correlation is significant?
find the critical value using the probability level (p) and number of observation (n). if Rs ≥ critical value then the correlation is significant and the null hypothesis can be rejected.
what does an unpaired student’s t-test tell you?
if the difference between the means of 2 groups of different individuals is significant
what is the formula for an unpaired student’s t-test?
x̄ = mean
s = standard deviation
n = number of values in data set
when can an unpaired student’s t-test be used?
when the data is:
in 2 categorical groups
from different individuals (independent)
interval data - data measured on the same scale, where each unit is the same size
how to work out the degrees of freedom for an unpaired t-test?
df = n1 + n2 - 2
How can you tell if a t value is signifcant?
t ≥ critical value, the difference between the 2 means is significant, the null hypothesis can be rejected
what does a paired t-test tell you?
whether the means of 2 sets of data that have come from the same individuals are significantly different
when can a paired t-test be used?
the 2 categorical groups should include the same individuals
each measurement in 1 group is paired with a measurement in the other group
both groups shouls be the same size
how to find the degrees of freedom for a paired t-test?
df = n-1
what is the formula for a paired t-test?
t = (-d- √n)/sd
d= mean of the differnces between each pair of measurements
n= number of pairs
sd = standard deviation of the differences between each pair of measurements
Formula for the index of diversity?
N = total number of organisms in area of all species
n = numer of organisms in a particular species
what do the results of the index of diversity show?
what is simpson’s index of diversity?
n = number of organisms of a particular species
N= number of organisms of all species
what do the results of simpsons index of diversity show?
a number between 0 and 1 is given, 0 meaning all the species are the same
the closer to 1, the more diverse an area is
what is resolution?
the smallest interval of a measuring instrument
how to use a calibration curve to identify the concentration of an unknown glucose sample?
make known concentrations of glucose + benedicts test
use colorimeter to measure absorbance
plot graph of absorbance against concentration
use graph to measure the concentration of an unknown substance from its absorbance
what is a reading?
a value found from an instrument using a single judgement
e.g. themometer, balance, pH meter, measuring cylinder, flask, voltmeter
what is a measurement?
a value taken using 2 judgements
e.g. ruler, vernier calliper, micrometer, protractor, stop watch, burette
in this case the uncertinty is double as uncertinties for the 2 judgements must be added
what is the uncertainty of the mean?
1/2 x range of measured values
what happens to uncertinty when you multiply or divide values?
add the percentage uncertainties
what happens to uncertainty when you have values to the power of one another?
multiply the percentage uncertainty by the power
a = bc
%a = c x %b
what is a simple dilution?
done when diluting a concentrated stock solution
how to carry out a simple dilution?
C1V1 = C2V2
C1= concentration of stock
C2= desired concentration
V1= volume of stock needed to make new concentration
V2= final volume
Then make up rest of solution with V2 - V1 of distilled water
what is a serial dilution?
the stepwise dilution of a substance of solution
when are serial dilutions used?
when a solution contains too many bacterial colonies to count, by diluting the solution, the number of colonies in a small concentration of the solution can be found
how to carry out a serial dilution?
take 1 part of the stock and mix with 9 parts growth medium and mix to form a 10-1 dilution
take 1 part of this solution and add to 9 parts of growth medium and mix to form a 10-2 dilution
repeat to get 10-3 dilutions and so on
eventually you can inoculate a petri dish with the diluted sample to estimate how many colonie were on the original plate by multiplying by 10number of times diluted
how to find standard deviation on a calculator?
mode
stat
1-var
enter values
M+
on
shift
stat
var
sx
M+
what is the equation for cardiac output?
stroke volume x heart rate
what is the equation for pulmonary ventilation rate?
tidal volume x breathing rate
what is a statistic?
a single number that describes a set of data
what does it mean if a statistic exceeds the critical value?
if a statistic exceeds the critical value of a particular probability level, then we can say the probability of the data occuring as a result of chance is less than or equal to that level
