The best way to do the proper statistical analysis and interpretation of experimental results is to plan analysis step-by-step.
The first step is to specify biological question which has to be answered during analysis.
The second step is to choose appropriate type of analysis and criteria which will answer our question. We will see that the same dataset can be processed by different statistical criteria depending on formulated question.
And the third step is to interpret results of statistical analysis directly towards our data. This is achieved better by using methods of graphical visualization together with statistical tests.
We will discuss the main principles of planning statistical analysis on two examples based on the study of antibacterial activity of two plant essential oils (thyme and tea tree) against 24 clinical isolates of two bacterial species (Escherichia coli and Enterococcus faecalis) alone and in the combination with antibiotic gatifloxacin.
Data of Example 1 contain the results of the disk diffusion method with values of inhibition zones around the disks containing either oil alone or oil mixed with sub-inhibitory concentration of gatifloxacin.
Data of Example 2 contain results of microdilution method with values of minimal inhibitory concentrations (MICs) of also either oil alone or oil mixed with gatifloxacin in sub-inhibitory concentration. Looking forward, the first example requires application of parametric tests, the second example – of non-parametric tests. Most biological data have non-normal distribution and require use of non-parametric tests, like our second example which represents fragment of real research. Among our bank of microbiological datasets we did not find data with normal distribution and because of this, data for the first example were artificially generated by the Random Number Generator for the Normal Distribution (v1.0.8) software (http://www.wessa.net/rwasp_rngnorm.wasp/).
In our examples general biological question can be formulated as “Does the activity of essential oil change in the presence of antibiotic gatifloxacin”. Very commonly, the study is conducted to investigate simultaneously several effects; and the same can be seen in our example. From data of this small experiment we may answer simultaneously several research questions, some of them are the following:
1. Is the activity of tea tree oil different against E. coli and E. faecalis (data are presented in 4th column, with taking into account also data of 3rd column);
2. Is the activity of thyme oil different against E. coli and E. faecalis (data are presented in 6th column, with taking into account also data of 3rd column);
3. Is the activity of tea tree oil changed in presence of gatifloxacin against all tested strains (data of 4th and 5th columns),
Therefore, although the experiment was planned in general to study influence of antibiotic gatifloxacin on activity of essential oils, several biological questions can be formulated during processing of its results.
Getting answers on the formulated biological questions is possible only after defining statistical concepts – defining types of studied variables, groups to be compared and determining criteria which should be used in each situation.
Example 1. Activity of tea tree and thyme essential oils alone and in the combination with gatifloxacin against E. coli and E. faecalis
|
№
|
Strain №
|
Species
|
Diameters of inhibition zones, mm
|
|
Tea tree oil alone
|
Tea tree oil
in the presence
of gatifloxacin
|
Thyme oil alone
|
Thyme oil
in the presence
of gatifloxacin
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
1
|
1580
|
E.coli
|
21.01
|
15.93
|
14.78
|
20.46
|
|
2
|
635
|
E.coli
|
11.61
|
19.87
|
16.94
|
20.41
|
|
3
|
1298
|
E.coli
|
13.83
|
11.62
|
18.74
|
16.39
|
|
4
|
1295
|
E.coli
|
20.89
|
18.85
|
9.13
|
25.94
|
|
5
|
1299
|
E.coli
|
13.11
|
20.36
|
15.97
|
20.90
|
|
6
|
1690
|
E.coli
|
13.39
|
17.07
|
12.06
|
23.22
|
|
7
|
1307
|
E.coli
|
17.00
|
15.66
|
19.08
|
20.14
|
|
8
|
1689
|
E.coli
|
15.97
|
14.72
|
15.34
|
24.42
|
|
9
|
1050
|
E.coli
|
16.80
|
18.06
|
13.61
|
21.30
|
|
10
|
1496
|
E.coli
|
11.65
|
17.57
|
16.12
|
22.28
|
|
11
|
1681
|
E.coli
|
14.31
|
19.09
|
13.94
|
26.32
|
|
12
|
801
|
E.coli
|
16.27
|
15.13
|
13.33
|
19.88
|
|
13
|
1714
|
E. faecalis
|
6.78
|
16.80
|
20.48
|
27.87
|
|
14
|
626
|
E. faecalis
|
9.98
|
9.47
|
24.05
|
32.26
|
|
15
|
1692
|
E. faecalis
|
11.19
|
11.62
|
16.14
|
36.20
|
|
16
|
1690
|
E. faecalis
|
13.56
|
11.96
|
13.19
|
33.76
|
|
17
|
751
|
E. faecalis
|
11.22
|
17.52
|
15.96
|
26.85
|
|
18
|
1682
|
E. faecalis
|
8.91
|
8.03
|
21.24
|
13.21
|
|
19
|
724
|
E. faecalis
|
10.62
|
12.01
|
20.31
|
29.86
|
|
20
|
723
|
E. faecalis
|
14.43
|
14.03
|
18.91
|
27.17
|
|
21
|
1681
|
E. faecalis
|
10.99
|
10.07
|
15.52
|
35.58
|
|
22
|
799
|
E. faecalis
|
13.29
|
13.52
|
14.02
|
29.56
|
|
23
|
801
|
E. faecalis
|
11.45
|
17.61
|
16.71
|
21.60
|
|
24
|
1576
|
E. faecalis
|
11.76
|
11.64
|
16.54
|
31.95
|
Example 2. Activity of tea tree and thyme essential oils alone and in the combination with gatifloxacin against E. coli and E. faecalis
|
№
|
Strain №
|
Species
|
Minimal inhibitory concentration, % (vol./vol.)
|
|
Tea tree oil alone
|
Tea tree oil
in the presence
of gatifloxacin
|
Thyme oil alone
|
Thyme oil
in the presence
of gatifloxacin
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
1
|
1580
|
E. coli
|
1
|
0.5
|
0.25
|
0.06
|
|
2
|
635
|
E. coli
|
1
|
0.1
|
0.5
|
0.03
|
|
3
|
1298
|
E. coli
|
0
|
0
|
2
|
0.06
|
|
4
|
1295
|
E. coli
|
0
|
0.1
|
2
|
0.5
|
|
5
|
1299
|
E. coli
|
1
|
1
|
1
|
0.06
|
|
6
|
1690
|
E. coli
|
1
|
0.1
|
0.5
|
0.06
|
|
7
|
1307
|
E. coli
|
1
|
2
|
0.06
|
0.12
|
|
8
|
1689
|
E. coli
|
0
|
0
|
0.06
|
0.01
|
|
9
|
1050
|
E. coli
|
4
|
2
|
1
|
0.06
|
|
10
|
1496
|
E. coli
|
1
|
0.1
|
0.25
|
0.02
|
|
11
|
1681
|
E. coli
|
1
|
0.1
|
0.5
|
0.03
|
|
12
|
801
|
E. coli
|
4
|
0.3
|
0.5
|
0.03
|
|
13
|
1714
|
E. faecalis
|
4
|
0.5
|
0.5
|
0.06
|
|
14
|
626
|
E. faecalis
|
8
|
8
|
0.25
|
0.03
|
|
15
|
1692
|
E. faecalis
|
2
|
0.3
|
0.5
|
0.06
|
|
16
|
1690
|
E. faecalis
|
1
|
0.3
|
0.25
|
0.06
|
|
17
|
751
|
E. faecalis
|
1
|
8
|
0.06
|
0.03
|
|
18
|
1682
|
E. faecalis
|
4
|
0.5
|
0.5
|
0.03
|
|
19
|
724
|
E. faecalis
|
4
|
2
|
2
|
0.06
|
|
20
|
723
|
E. faecalis
|
1
|
0.5
|
4
|
0.12
|
|
21
|
1681
|
E. faecalis
|
2
|
0.3
|
0.5
|
0.03
|
|
22
|
799
|
E. faecalis
|
1
|
0
|
0.12
|
0.12
|
|
23
|
801
|
E. faecalis
|
2
|
0.5
|
1
|
0.06
|
|
24
|
1576
|
E. faecalis
|
4
|
0.5
|
0.25
|
0.02
|
