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Chapter 4

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Biology

BIOL 180

H E R R O N, J O N

Spring

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BIOL 180 - Reading 4-1:
Bioskill 3:
Standard Error Bars:
Standard error for a the mean is a quantity that indicates the uncertainty in a calculated
mean (I-Beams on graphs)
Quantiﬁes how conﬁdent you are that the mean you’ve calculated is the mean
you’d observe if you did the experiment under the same conditions an
extremely large number of times
Measure of precision
Sometimes, error bars represent conﬁdence interval of the mean mean
Conﬁdence interval gives an estimated ranged of values that is like to include the
population parameter being studied, such as the survival rate of animals after exposure
to a pathogen
Calculated from a given set of sample data
A conﬁdence level of 95 percent means that 95 percent of the conﬁdence
intervals would include the population parameter
Related to standard deviation, which doesn’t change as a sample size increases
Standard error of the mean (SEM) depends on both standard deviation (SD) and
sample size
Calculated by device standard deviation by square of the sample size
SEM decreases as the sample size increases, because the extend of chance
variation is reduced
To come to an objective (instead of subjective) conclusion about what data may show,
you must use a statistical test to determine whether the data in two diﬀerent trials is
signiﬁcant
If he diﬀerence is found to be statistically signiﬁcant, then it is not likely to have
occurred by chance - it’s likely to be attributable to an actual facto
Using Statistical Tests:
Three common statistical tests are:
Chi-square test
T-test
Analysis of variance
Chi-square tests:
Used to compare observed data with data you would expect to obtain according
to a speciﬁc hypothesis
For example, if according to Mendel’s law you expected equal number of male
and female oﬀspring from a cross but you observed 9 males and 23 males, you
might want to know whether the diﬀerence between the observed and expected
number was due to chance or to other factors
Chi-square test always tests the null hypothesis, which states that there is no
signiﬁcant diﬀerence between the observed and expected results. T-tests:
Used to determine if there is a signiﬁcant diﬀerence between the mean values of
two groups
Can help support hypothesis or null hypothesis
Analysis of variance (ANOVA):
Compares the means of two or more sets of data by calculating how widely
individual values in each data set vary
If they vary greatly from the mean, the variance is large, and vice-versa
When applied to only two data sets, ANOVA will give the same results as a t-test
ANOVA is a powerful statistical test because it allows you to test for each factor
while controlling for others and to detect whether one variable aﬀects another
As an example, if you were comparing the activity of a particular enzyme in
mainland and island tortoises, you might want to determine whether sex aﬀects
enzyme activity, so you could also separate the data sets by sex
Regression and correlation analyses:
Are done when a researcher wants to know whether there is a relationship or
correlation between to variables
If positive, there is a positive slope, if negative, there is a negative slope
For example, when patients are given increasing amounts of a drug, does their
blood pressure increase or decrease proportionally?
Correlation is a way to express the relationship between two variables, whereas
linear regression is about the best ﬁt line in a graph
Interpreting P Values and Statistical Signiﬁcance:
There is a three-step process to determine if diﬀerence are signiﬁcant:
1. Specify the null hypothesis:
1. Reactant concentration has no eﬀect on reaction rate
2. Calculate a test statistic
1. Compares the actual diﬀerences in reaction rates at the three reactant
concentrations to to the diﬀerence predicted by the null hypothesis. The
null hypothesis predicts that there should be no diﬀerence
3. Determine the probability of getting by chance a test statistic at least as large as
the one calculated. This probability, called the P value, comes from a reference
distribution - a mathematical function that speciﬁes the probability of getting
various values of the test statistic if the null hypothesis is correct. The P value is
the estimated probability of rejecting the null hypothesis when the hypothesis is
correct.
1. A P value of 0.01 means that there is a 1 percent chance that the null
hypothesis has been reject when it is actually correct. On percent is
considered a very small chance of making such an error, thus, very small
P values indicate that researchers have high conﬁdence in the signiﬁcance
of diﬀerences in their data
Most researchers consider a diﬀerence among treatment groups to be statistically
signiﬁcant if there is less a 5 percent probability of observing by chance, or P < 0.05
When presenting P values in the scientiﬁc literature, researchers often use an asterisk ratio system as we’ll as quoting P values
Examples:
Statistical
P Value

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