Common Statistical Methods Used in Transgenic Fish Research
Session #6:
Common Statistical Methods Used In Transgenic Fish Research
M.Afifi
M.Sc., Biostatistics(Joint Supervision with ISSR, Cairo University) Ph.D., Candidate (AVC, UPEI, Canada)
E-mail: [email protected]
Tel: +201060658185
Before gene transfer After gene transfer
Statistics role
Before gene transfer
Experimental Design: CRD, CBD
Experimental unit: Single Fish or Fish tank, Replicates homogenous, same exper. condition
Sample Size: 3, 6, 8, 12????
Basic Experimental Design for Transgenic Fish Research:
1. Setting experimental questions >>>> statistical questions
2. Setting hypotheses and then statistical null hypotheses
4. Statistical consideration (treatment groups, sample size, true replication, confounding factors etc.)
5. Sampling design (independent, random, samples)
6. Data collection & measurement (Quality Control and Quality Assurance Procedures)
7. Data analysis–Too few data: cannot obtain reliable conclusions–Too many data: extra effort (time and money) in data collection
pseudoreplication
True replication
Fish
The transgenic fish used in this experiment were produced and raised in a biosecure facility at the DFO/UBC Centre for Aquaculture and Environmental Research (CAER) in West Vancouver, B.C., Canada.
Due to differences in growth rate, which produces fish of large size differences at each age, control fish used were 1 year older than transgenic fish in order to match fish to the same developmental stage and size.
Fish were cultured in filtered, aerated, flow-through well water at approximately 10 °C prior to and during the experiment. Since the two types of salmon reach smolt size at different times of the year (the normal time of May/June in their second year for non-transgenic fish, and in August/September of their first year for the growth accelerated fish).
After gene transfer
Qualitative QuantitativeCold-tolerance growth reproductive traits
Salinity-tolerance Massbiomass
food consumedspecific growth rate (SGR), Protein efficiency ratio (PE)
Food conversion efficiency (EC)Q-PCR
Comparative Biochemistry and Physiology journalImpact Factor: 1.551
Introduction to Two of Basic Statistical Techniques:
Group comparison methods for selection of appropriate tests
Correlation based methods
Flowcharts for selection of appropriate tests
Basic rules of any statistical test
Assumption Hypothesis testing
Basic rules of hypothesis testing Hypothesis:
• Null hypothesis, H0:
• Difference in (means, proportions, medians) is not actual (non-sig),
• Difference not due to treatment effect but due to any other reasons (Chance , Error)
• Alternative hypothesis HA : VS H0
Test statistic- value: value calculated from the data (an algebraic expression particular to the
hypothesis we are testing),
t-test >>>> t-value
F-test >>>> F-value
χ2-test >>>>>> χ2 value
P-value: probability value (0-1) (Sig): Attached to each value of the test statistic It
the probability of getting the observed effect (or one more extreme) if the null hypothesis is true
Comparison of Means
2-Independent sample Means
Two-sample t-test (unpaired t-test) Compare the means in two independent groups of observations using representative
samples.
Assumptions
Two samples must be independent unrelated
Normality A small departure from Normality is not crucial and leads to only a marginal loss in power
Homoscedastic (equal variances) >>>> Checked by Levene’s test
Aquaculture International Journal, IF:1.878
Figure 2. Growth performance in F1 transgenic and full sibling non-transgenic zebrafish. Fifty-four zebrafish of
F1 fry were randomly selected and grown individually under similar conditions. At the beginning of the
experiment, they were four week old. Zebrafish were weighed weekly during 6 weeks to monitor growth
performance. In the course of the experiment, fin DNA was extracted and assayed for transgene identification.
Weight of transgenic and non-transgenic full siblings was compared employing a Student t-Test (*, P < 0.05).
Welch's t-test
(Unequal variances t-test) widely used modification of the t-test,
adjusts the number of degrees of freedom when the variances are not equal to
each other.
If the sample sizes are not large,
equal variances not assumed
non-parametric method,
Mann–Whitney U test
Paired (dependent) t-test
FreezingRefrigeration
Methods of pairing: Self-pairing: each animal used as its own control (Before and After)
Natural pairing: each pair of animals is biologically related (e.g. litter mates).
Artificial (matched) pairing: each animal is paired with an animal matched with
respect to one or more factors that affect response.
To avoid allocation bias in an experiment when there is self-pairing, each animal is
randomly allocated to receive one of the two treatments initially; it then receives
the other treatment later.
If there is natural or matched pairing, one member of the pair is randomly allocated
to one of the two treatments and the other member receives the second treatment.
Paired Vs. Independent Test
If the sample sizes are not large,
equal variances not assumed
non-parametric method,
Wilcoxon rank test
F-test
ANOVA
Comparing more than two means
Suppose, for example, we have four groups. >>>>> compare using a two-
sample t-test) for every combination of pairs of groups >>> six possible t-tests
Principle
Total variability in a data set is partitioned into a different source of variation.
The sources of variation comprise one or more factors, each explained by the
levels or categories of that factor (e.g. the two levels, ‘male’ and ‘female’, defining
the factor ‘sex’, or three dose levels for a given drug factor), and also unexplained
or residual variation which results from uncontrolled biological variation and
technical error.
We can assess the contribution of the different factors to the total variation by
making the appropriate comparisons of these variances.
The variation is expressed by its variance
The analysis of variance encompasses a broad spectrum of experimental
designs ranging from the simple to the complex.
One-way analysis of variance Single factor with several levels or categories where each level comprises a group
of observations.
For example, the levels may be:
Feed formula for dogs: dry feed formula, a tinned feed and a raw meat
Different treatment dose levels of a drug, one of which is a placebo representing
simply the drug vehicle, while the others are, say, 50%, 100% and 200% of the
presumed effective dose. Consider the simple case >>> only one factor , 2 sources of variation:
Between the group means
Within the groups
In the experimental situation, the animals should be randomly allocated to one of
the levels of the factor, i.e. to one of the groups, in order to avoid allocation bias
Assumptions:
results are reliable only if the assumptions on which it is based are satisfied
samples representing the levels are independent
Observations in each sample come from a Normally distributed population with
variance σ2; this implies that the group variances are the same. Approximate
Normality may be established by drawing a histogram; moderate departures
from Normality have little effect on the result.
Constant variance, the more important assumption, may be established by
Levene’s test
Post-hoc testMultiple Comparisons of Means
Which group means Differs?????
Post-hoc Test
Multiple Comparison
Multiple comparisons
Conducting a number of tests, but the more tests that we perform, the more
likely it is that we will obtain a significant P-value on the basis of chance alone.
We have to approach this problem of multiple comparisons in such a way that
we avoid spurious P-values.
Adjusted p-values are simply the unadjusted p-values multiplied by the number of possible comparisons (six in this case);
If multiplying a p-value by the number of comparisons produces a value greater than one, the probability is given as 1.00.
Most Common Multiple comparisons
Least significant difference (LSD)
Duncan’s multiple range test, (DMRT)
Tukey’s (HSD)
Newman–Keuls tests,
Bonferroni’s correction
Scheffe’s
. Be aware: they often produce slightly different results!
Example Fig. 1. Growth rates and hormone profiles of wild-type (W),
domesticated (D), and GH transgenic (T) salmon. (A)
Specific growth rates (SGR).
(B) Plasma IGF1 levels. n = 10 per genotype.
Letters above bars denote significant differences among
groups (1-way ANOVA, P < 0.05).
Error bars represent standard SEM.
Example 2 .
Example Fig. 1. Plasma concentrations of growth hormone (A) in non-
transgenic and transgenic salmon fed full rations and inration-
restricted transgenic coho salmon (pair fed with controls).
GH values (A) are pooled from samples (N = 23) taken on Sept.
11, 2002 and Oct. 11, 2002, which did not differ significantly.
Statistical relationships between groups are indicated by letters
where significant differences occur.
Bars are means ± SE, letters denote significant differences.
TABLE 2.—Sample size (n), mean body weight, mean fork length, and mean condition factor (CF) for
all fish sampled.
Different lowercase letters indicate statistically significant differences between populations (ANOVA).
The letters H, T, and N represent hatchery, transgenic, and cultured nontransgenic fish, respectively.
Detailed statistical analysis
by category of analyzed data
and sex of coho salmon.
Asterisks indicate statistically
significant values.
Abbreviations are as follows:
GSI 5 gonadosomatic index,
H 5 hatchery fish, T
5transgenic fish, and N 5
cultured nontransgenic fish.
2-way ANOVA
Enzyme activities were measured before (pre-diet treatment, n=8) and after a 12-week feeding trial (post-
diet treatment, n=3 replicates, n=4 fish/replicate). Differences between C and T pre-diet treatment
(p<0.05) are indicated by on the larger value, and differences between fish (F) and diet (D) groups post-⁎diet treatment are indicated by differing letters (a, b, c).
Reporting results in table:
If the sample sizes are not large,
equal variances not assumed
non-parametric method,
Kruskal-wallis test
Correlation and regression
Correlation (r)
measure the degree of association by calculating Pearson’s product moment
correlation coefficient, usually just called the correlation coefficient or, sometimes, the
linear correlation coefficient.
take any value from −1 to +1.
Correlation (r)
(a) perfect positive association,r = +1;
(b) perfect negative association, r = −1;
(c) positive association, r = +0.86;
(d) negative association, r = −0.85;
(e) no association, r = 0;
(f) no linear association, r = 0.
Above hatched cells includes analysis with all groups combined (non-transgenic, full-ration
transgenic and ration-restricted transgenic fish). Below hatched cells displays correlations for non-transgenic and full-ration transgenic fish
only. Correlation coefficients are shown for significant correlations only. aLiver GH correlations do not include non-transgenic fish in which expression was
undetected.
Regression linear relationship between two numerical variables with a change in one variable
being associated with a change in the other, we may be interested in determining the
strength of that relationship.
Are the points in the scatter diagram close to this line or are they widely dispersed
around it? Provided a linear relationship exists between the two variables, the closer
the points are to the line, the stronger the linear association between the two variables.
Linear regression lines
Body composition and energy content in relation to wet body weight of growth enhanced transgenic
Linear regression lines
Atlantic salmon >>>open triangles
controls >>>solid circles. fed to satiation three timesrday on a commercial diet.
Each data point represents a subsample of five fish. Data is presented with fitted regression lines solid lines. surrounded by 95% confidence intervals (dashed lines).
Regression coefficients for the relation between body composition and energy content per fish wet weight of growth enhanced transgenic Atlantic salmon and controls fed to satiation three timesrday on a commercial diet: Y=b0+b1×BW where ‘Y ’ is absolute nutrient or energy content, ‘b0’ and ‘b1’ are regression coefficients, ‘BW’ is wet body weight
Nonlinear regression
Second degree polynomial
Nonlinear regression
second degree polynomial
Nonlinear regression
Chi-square test
χ2
International Journal of Molecular Sciences
The genotype frequencies in HWE
Statistical analysis
The genotype frequencies were calculated and HWE was tested using a chi-
square test of
The population genetic indexes including He, Ho, effective allele numbers (Ne)
and PIC were calculated by Nei’s method [25]. Generally, polymorphism
information content (PIC) is classified in to the following three types: low
polymorphism (PIC value < 0.25), median polymorphism (0.25 < PIC value <
0.5) and high polymorphism (PIC value > 0.5). The LD structure measured by
D’ and r2 was performed with the HAPLOVIEW software (Ver.3.32) [26].
Association analyses between genotypes or haplotypes of GH gene and four growth
traits were performed using general linear model (GLM) procedure with SPSS 17.0
software (IBM, Armonk, NY, USA). We used the following statistical model:
Y = u + G + e where Y is the phenotypic value of each trait;
u is population mean value of 4 growth traits,
G is the fixed genotype effect of each SNP, and
e is the random error effect.
Multiple comparisons between different genotypes were tested using the LSD
method with Bonferroni correction adjustment [27].
How would these results be reported in a scientific journal article?
Tabular Presentation.
Mean ± SD or SEM with Both t-value and P-value
Mean ± SD or SEM with only P-value
Representing P-values with astrikes
Representing P-values with superscripts
Graphical presentation
Simple Bar Box plots
Report your results in words
Your Formal sentence must includes:
Dependent , independent variable
Exact p-value (unless the p value is less than .001). < 0.000 Or < 0.0001
The direction of the effect as evidenced by the reported means, as well as a
statement about statistical significance,
Symbol of the test (t), the degrees of freedom (6), the statistical value (2.95)