Two phase sampling is a method where a first phase sample is selected and observed to obtain variable x. Then a second phase subsample is selected from the first phase sample where the selection probability depends on x. This allows collecting more detailed data from a smaller subsample while using the first phase to guide the selection. An example is capture-recapture estimation of animal populations where some are marked in the first phase to guide selection in the second phase. The method reduces data collection time while maintaining accuracy by focusing effort where most needed.

1. TWO PHASE
SAMPLING
BY
UMME SALMA SHAIK
SAPTAMI RJ

2. INTRODUCTION
• Neyman (1938)
• double sampling
• sample selection- X-Y
• Two-phase sampling is particularly useful when the cost for observing x is
relatively cheap compared with the cost for observing Y

3. • To formalize, two-phase sampling can be described as follows:
• [Step 1] - From the finite population, select a first-phase sample A1 of size
n1 and observe x.
• [Step 2] - Treat the first-phase sample A1 as the population and select a
second phase sample A2 of size n2.
• In this case, the selection probability for the second-phase sample is often
determined by the value of x obtained from the first-phase sample

4. • Since the second-phase sample selection probability depends on the
observed value of the first-phase sample, the sample inclusion probability
for the second phase sample is a random variable in the sense that its value
is changed as the first-phase sample changes

5. Population of X (N units)
first phase
Sample (Large) n 'units
second phase
Subsample (small) n units

6. Example :
Capture-recapture estimation
• A lake has N fish.
• Catch and mark 200 fish; then release them.
• Later catch 100 fish
• Suppose 20 of the fish in the second sample are marked
• We estimate that 20% (20/100) of the fish in the lake are marked.

7. • marked
• 100 - 20
• (N)? – 200
• N*20 =200*100
N=200*100 20 =1000

8. ASSUMPTIONS
• Population is closed. (N stays the same.)
• The two samples are independent.
• Application :
• The double sampling method is designed to determine
biomass by sampling in quadrats. It can be applied to a wide variety of
vegetation types, particularly grasslands and shrublands.
• This method can reduce time for taking sample , but still fairly accurate
• Clipping and weighing vegetation is expensive and tedious

9. • With this method ocular estimates of biomass are made for a small number
of quadrats
• And vegetation on the quadrats is clipped and weighed
• For the remaining quadrats only the ocular estimates are performed

10. ADVANTAGES
• Less time consuming than the harvest method ( since estimating is faster
than the clipping )
• And more accurate than the estimation method ( since estimating
production can be subjective and cause error )
• How ever it still requires a lot of training which involves weighing
representative units of a plant

11. DISADVANTAGES
• Formulae for data analysis and sample size estimation are much more
complex than for some other method

12. THANK YOU