Two-stage sampling to measure Grass Diversity

The survey area can be partitioned into three types of land-use categories. Thus three strata have been made according to the land uses. The total area of land-use 1 is 25 x 40 sq. mt. It has 1000, 1x1 sq. mt. quadrates. The total area under land use 2 and 3 are 25 x 40 sq. mt. and 49 x 40 sq. mt respectively.In the first stage of sampling, 15 quadrates have been selected from each type of land use.

First-stage sampling from land-use 1(strata 1)

# generating sample from 1000 quadrates
set.seed(11)
sample(1000,15)

##  [1] 762  34 696 921 144 113 549 572 374 908 213 214  62 478 734

---

set.seed(11)
strata1_sample=sample(1000,15)
row_postions<-floor(strata1_sample/40)+1
column_position<-strata1_sample%%40
quadrates<-data.frame(strata1_sample,row_postions,column_position)
quadrates

##    strata1_sample row_postions column_position
## 1             762           20               2
## 2              34            1              34
## 3             696           18              16
## 4             921           24               1
## 5             144            4              24
## 6             113            3              33
## 7             549           14              29
## 8             572           15              12
## 9             374           10              14
## 10            908           23              28
## 11            213            6              13
## 12            214            6              14
## 13             62            2              22
## 14            478           12              38
## 15            734           19              14

First-stage sampling from land-use 3(strata 1)

# generating sample from 1000 quadrates
set.seed(1111)
sample(49*40,15)

##  [1] 1836  438   50  794 1316  497  326 1510  986  991  111   63  551 1601  205

set.seed(1111)
strata1_sample=sample(49*40,15)
row_postions<-floor(strata1_sample/40)+1+50
column_position<-strata1_sample%%40
quadrates<-data.frame(strata1_sample,row_postions,column_position)
quadrates

##    strata1_sample row_postions column_position
## 1            1836           96              36
## 2             438           61              38
## 3              50           52              10
## 4             794           70              34
## 5            1316           83              36
## 6             497           63              17
## 7             326           59               6
## 8            1510           88              30
## 9             986           75              26
## 10            991           75              31
## 11            111           53              31
## 12             63           52              23
## 13            551           64              31
## 14           1601           91               1
## 15            205           56               5