Define ALLOCATION and Types[Equal , Proportional , Optimum (Neymann's)] #allocation #neymaan's #bsc

Define ALLOCATION and Types[Equal , Proportional , Optimum (Neymann's)] #allocation #neymaan's #bsc #allocationtype
#allocationanditstypes

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In statistics, allocation refers to the process of distributing samples or resources among different groups, strata, or treatments in an experiment or survey to ensure effective data collection and analysis. Proper allocation is crucial for achieving accurate and reliable results.

Types of Allocation in Statistics

1. Equal Allocation

Each group or stratum receives an equal number of samples.

Example: In an experiment with two groups, each group is assigned 50 participants out of 100 total participants.
Use Case: When variability is assumed to be the same across groups.

2. Proportional Allocation

The sample size for each group is proportional to the size of that group in the population.

Formula: , where:
= population size of group ,
= total population size,
= total sample size.

Example: If Group A has 60% of the population and Group B has 40%, the sample is split in the same proportion.

3. Optimal Allocation (Neyman Allocation)

Allocates samples based on both group size and variability (standard deviation) within each group.
Formula: , where is the standard deviation of group .
Use Case: When there are significant differences in variability across groups.

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