# Statistical concepts

# Confidence level

## The interval of values in which we can observe a difference between groups that is not due to chance and that reflects the reality.

# Margin of error

## The margin of error refers to how precise you want your estimate to be. The larger the sample size, smaller the margin of error. If you have a confidence level of 95%, your margin of error will be 5%.

# Power

## The power of a study refers to the ability of finding a difference between groups when that difference exists. Power increases with a larger sample size.

# Effect size

## Magnitude of the effect under the alternative hypothesis. The larger the effect size, the easier it is to detect an effect and require fewer samples.

# Variation

## When we are calculating sample size, we need to consider data variation (variance and standard deviation).

## Variance represents the squared deviation of a variable from its populatin or sample means. The variance of a proportion is p*q where p is the proportion of interest and q is 1-p.

## Standard deviation is the squared root of variance. If the standard deviation has a high value, that means that data are wider spread and tend to be far from the mean.

# Family Oral Fluids

## Family oral fluids are an aggregate sample type shown to be cost efficient and convenient. The outcome is the number of litters to test to have a given confidence that the disease would be detected in an infected herd.

### Input

### Output

## Sample size - number of litters to be sampled to detect disease:

fieldepi.org

# Family Oral Fluids

## Family oral fluids are an aggregate sample type shown to be cost efficient and convenient. This sampling tool considers pooling factors on the probability of sampling at least one positive litter.

#### Example: Assuming that the room has 3 positive litters and that the total number of litters in the room is 60. If we collect 3 pools each with 5 individual FOF, then the probability of sampling at least one positive litter would be 58.53%.

### Input

### Output

## Probability of sampling at least one positive litter (%):

fieldepi.org

# Family Oral Fluids

## Family oral fluids are an aggregate sample type shown to be cost efficient and convenient. This sampling tool considers pooling factors on the probability of having a positive animal and detecting it through PCR

#### Example: Assuming a total number of 5 positive litters in a room with 60 litters. If we collect 3 pools, each with 3 FOF samples, then the probability to sample and detect a positive litter would be 56.5%.

### Input

### Output

## Probability of sampling and detecting a positive litter (%):

##### (Margin of error +/- 1%)

fieldepi.org

# Sample size to detect disease: Serum and Swabs

## The outcome is the number of animals to test to have a given confidence that the disease would be detected in an infected herd.

### Input

### Output

## Sample size - number of pigs to be sampled to detect disease:

Number of Serum samples required or number of swabs required

fieldepi.org

# Sample size to Compare two means

## The outcome is the number of animals to test if we are comparing the difference between means for two groups.

#### Example: To detect a difference of 0.03 in Average Daily Gain with margin of error of 5% and power of 80%, let us compare two groups, one with ADG of 1.47 and the other with ADG of 1.50. The difference between means is of 0.03, the standard deviation is of 0.03. For a two sided test and a confidence level of 95%, the number of animals in each group to detect a difference of 0.03 in ADG should be 16 animals per group.

## Input

### Output

## Sample size to compare means:

fieldepi.org

# Power of test (comparison between two groups)

### Output

## Power of test:

fieldepi.org

# Sample size to Compare two proportions

## The outcome is the number of animals to test if we are comparing the difference between proportions for two groups.

#### Example: To detect a difference of 1% in mortality between two groups of animals, with a 95% confidence interval and 80% power, average mortality is 7%. The expected proportion for the treatment group is 0.06 and the expected proportion for the control group is 0.07. For this example, the number of animals needed in each group would be 9540 to detect a difference of 1% in mortality.

## Input

### Output

## Sample size to compare proportions:

fieldepi.org