Download Programmed Text onData Analysis (Appendix B)

APPENDIX B
Programmed Text on Data Analysis (Membrane Potential)
STATISTICS
When data are collected, it is advisable to make more than one measurement of a
variable x. The mean x of the n measurements can then be calculated by the
formula_________
Sx
n
This mean is a measure of central tendency; it provides a single summary figure that
best describes the central location of the entire set of observations.
It is also useful to have a measure of the spread or variability in the observations,
i.e. the extent to which they are clustered around the mean or scattered more
widely. The variance can be calculated by the formula ______________
 (x  x)
2
n
where the numerator is the sum of the squares of the deviation from the mean.
From this is calculated the standard deviation, given by___________________
variance
 (x  x)
2
n
When the variable falls on a normal distribution, 95% of
within_____________with the remaining 5% lying outside these limits.
the
values
±2 standard deviations of the mean,
If a series of samples, each of size n, are drawn from the population, these sample
means will also be normally distributed about the population mean. The standard
deviation of these means is ____________________, and 95% of the sample means will
again lie within_____________________________.
the standard error of the mean, ± 2 standard deviations of the mean.
Standard error of the mean is obtained by calculating ___________________.
standard deviation
n
When two sets of data are being compared with a view to deciding whether they are
significantly different, it is usual to assume that the variations between them are
due to measurement (random sampling) error.
This assumption is called
________________.
lie
the Null Hypothesis.
If one calculates the probability of these variations arising purely by chance, and
finds it to be very low (usually less than 1 in 20 or 5%), one can then reject the null
hypothesis and accept that the differences did NOT arise randomly, but are in fact
real.
Examples of such data sets are the sample means mentioned earlier. By performing
Student’s
t-test (using the difference between the means and the standard error
of this difference), and taking into account the number of degrees of freedom, one
obtains a number which indicates whether or not there is a real difference between
the two samples.
GRAPHS
When considering experimental observations it often appears that two variables
being measured in a population are somehow inter-related. For example, the
MEMPOT program is based on an equation, which gives one variable, membrane
voltage, in terms of a second variable, electrolyte concentration. However, as this
equation is fairly complex, it is useful to start with a relationship, which can be
expressed by a simple linear equation.
What is the general form of a linear relationship? __________________.
y = mx + b.
When does the straight line represented by this equation pass through the origin?
___________.
when b = 0.
What does m represent?_____________________________
the slope of the line.
When is this equal to the ratio of y to x i.e. when is y proportional to
x?__________________
only when b = 0.
Considering a simplified version of the equation in the MEMPOT program, when only
one cation is assumed to be contributing to the membrane voltage, one obtains the
following relationship_______________________________
[K]o
RT
Vm =
ln
F
[K]i
Describe in words the variable on the x-axis when Vm is plotted on the yaxis?________________________________________________________________________________
__.
x is the natural logarithm of the ratio of the outside to the inside concentration of K+
ions.
What are the units of x? _____________________________.
it is a ratio, i.e. a number without any units.
If linear graph paper
have?_________________
is
used
for
this
plot,
what
shape
will
the
curve
exponential.
What is the mathematical explanation for this?
___________________________________________
The equation can be rewritten with voltage as a power of e.
To produce a straight line, rather than a curve, we use semi-log graph paper. What
is another advantage of plotting data on a logarithmic scale?
___________________________________________________________________________________
___________________________________________________________________________________
To compress data which would otherwise be spread out over a very wide range of
values.
There is a very important question one should ask about the relationship between
two variables: how well do the data points on the graph “hug” the straight line
expressing the relationship between them?
To ascertain this, one calculates
the________________________
correlation coefficient, r
which, if the “fit” is poor, will approach a value of _____________,
zero,
but if the “fit” is excellent, will approach close to _____________.
one.
Note that a high degree of correlation does not imply anything about a causal
relationship between x and y, but what it does do is enable one to predict values of y
from x with a high degree of probability that they will be correct. Of course, some
variables will be positively correlated, with r having a value between 0 and +1,
whereas others will be negatively correlated, with r falling between 0 and -1; see if
you can think of examples of these differences from everyday life.
In the MEMPOT program you are given the opportunity to test the goodness of fit of
different lines to a certain set of data you have generated, by varying one of the
“constants” in the relevant equation. The mathematical method of doing this is to
calculate the sum of the squares of the deviations of the experimental points from
the predicted curve; the smaller this sum, the better the fit, since the calculation of r
(which involves this term being subtracted from 1) will result in a higher value.