# Qstat

The qstat calculator returns the Q statistic for an OTU definition. This calculator can be used in the summary.single, collect.single, and rarefaction.single commands.

$Q=\frac{\frac{1}{2}n_{R1} + \sum n_r + \frac{1}{2}n_{R2}}{\ln\left(\frac{R_2}{R_1}\right)}$

where,

$R_1$ = the number of individuals in an OTU when at least 25% of the least abundance OTUs are sampled

$R_2$ = the number of individuals in an OTU when at least 75% of the least abundance OTUs are sampled

$n_{R1}$ = the number of OTUs that belong to the OTU where the 25% cutoff is found

$n_{R2}$ = the number of OTUs that belong to the OTU where the 75% cutoff is found

$\sum n_r$ = the total number of OTUs that lie between the 25% and 75% cutoffs

Open the file 98_lt_phylip_amazon.fn.sabund generated using the Amazonian dataset with the following commands:

mothur > read.dist(phylip=98_lt_phylip_amazon.dist, cutoff=0.10)
mothur > cluster()


The 98_lt_phylip_amazon.fn.sabund file is also outputted to the terminal window when the cluster() command is executed:

unique	2	94	2
0.00	2	92	3
0.01	2	88	5
0.02	4	84	2	2	1
0.03	4	75	6	1	2
0.04	4	69	9	1	2
0.05	4	55	13	3	2
0.06	4	48	14	2	4
0.07	4	44	16	2	4
0.08	7	35	17	3	2	1	0	1
0.09	7	35	14	3	3	0	0	2
0.10	7	34	13	3	2	0	0	3


The first column is the label for the OTU definition and the second column is an integer indicating the number of sequences in the dominant OTU. The Q statistic is then calculated using the values found in the subsequent columns. For demonstration we will calculate the Q statistic for an OTU definition of 0.10. There are 55 OTUs so the 25% cutoff would occur at 13.75 and the 75% cutoff at 41.25:

Abundance Number of OTUs Cum. Num. of OTUs Quartile
1 34 34 <-- R1
2 13 47 <-- R2
3 3 50
4 2 52
5 0 52
6 0 52
7 3 55

Therefore we have $n_{R1}$ and $n_{R2}$ equalling 34 and 13, respectively and R1 and R2 are 1 and 2, respectively. Finally, $\sum n_r$ equals zero.

$Q=\frac{\frac{34}{2} + 0 + \frac{13}{2}}{\ln\left(\frac{2}{1}\right)}=33.90$

Running...

mothur > summary.single(calc=qstat)


...and opening 98_lt_phylip_amazon.fn.summary gives:

label	qstat
unique	69.249362
0.00	68.528014
0.01	67.085319
0.02	62.035887
0.03	58.429149
0.04	56.265107
0.05	49.051631
0.06	44.723546
0.07	43.280851
0.08	37.510071
0.09	35.346029
0.10	33.903333 <---


These are the same values that we found above for a cutoff of 0.10.