Standard Deviation Index Calculator

Many techniques can help us identify test models, but one of the simplest is the standard deviation index. So, through this article and the application of our calculator, you can learn more about it. You can find out how to calculate the standard deviation index using the laboratory environment and many other questions below.

What is the SDI standard deviation index?

The SDI standard deviation index is a method of measuring the variability of returns for a given investment. We use this index to compare different investments and decide which is more suitable for an assigned portfolio. The SDI standard deviation index results from the difference between yield and means yield square.

This index helps determine the volatility of an investment. The SDI standard deviation index measures variation in the return on an equity portfolio, mutual fund, or other investment. We use this calculator to compare two or more means to see which has less risk and avoid possible errors.

If the SDI is number 1.7, this indicates a bias of number 1.7 standard deviations from the mean value of the group, which cannot be favorable. In this example, the value is positive, and therefore the consensus group is smaller than the laboratory environment.

If the value of SDI is number 1.7, it means that the laboratory means and the mean of the consensus group is at a distance of number 1,7 standard deviations. In that case, the value of the mean consensus group is much higher than the laboratory mean.

Standard deviation index formula

The standard deviation index measures bias (how close your target value is). Using the following formula, you can calculate the SDI:

SDI = \frac{L_{m} - Cg_{m}}{CgSD}

L_m – Laboratory Mean
Cg_m – Consensus Group Mean
CgSD – Consensus Group Standard Deviation

The Laboratory Mean means there is the model’s mean. In contrast, the population’s mean is the mean of the consensus group, and the standard deviation is the standard deviation of the consensus group.

The standard deviation ratio of the consensus group is presented as the difference between the laboratory mean of the consensus group mean.

If we look at the formula of the standard deviation index calculator, we see how close or far the mean of the test is actually from the mean of the population.

How to calculate SDI?

Since we have given the formula for calculating SDI in the previous text, through the example, you will best understand and see the application of the standard deviation index calculator:

If we have a date, for example, that the laboratory mean is number 10, the mean value of group number 9, while the standard deviation of the consensus group is number 3. When we enter the specified values ​​in our standard deviation index calculator, we will get the following:

SDI = \frac{10 - 9}{3} = 0.33

The value 0.33 gives us the answer that the mean values ​​are 0.33 of the standard deviation. The magnitude or absolute value and the sign can be positive or negative. Also, it can provide insight into how this can improve the testing model.

We use standard population deviation(σ)  when necessary to measure the entire population. It represents the square root of the variance of a given data set. You can apply the following equation to find the standard deviation of the entire population.

\sigma = \sqrt{\frac{1}{N}\cdot \sum_{i=1}^{N}\left ( x_{i}-\mu \right )^{2}}

xi  – an individual value
μ  – the mean / expected value
N – the total number of values

Correction of the standard deviation of the sample

In most cases, you cannot sample each member within a population. The above equation must be modified so that the standard deviation can be measured through a random population sample. There are many ways to calculate the standard deviation of the sample. The standard deviation of the sample does not have an estimator that can be unbiased and has the maximum probability as opposed to the mean value of the sample.

The equation below is the “corrected standard deviation” of the “sample.” This is a corrected version of the equation. It is obtained by modifying the standard deviation equation of the population using sample size as population size but as such removes some.

Therefore, we say that the “correction standard deviation of the sample” is the most commonly used estimator for the population’s standard deviation.

s = \sqrt{\frac{1}{N-1}\cdot \sum_{i=1}^{N}\left ( x_{i}-\bar{x} \right )^{2}}

How to interpret the SDI values?

The target FDI is 0.0, indicating that the mean is the same as the mean of the consensus group. The bias compared to the mean value of the consensus group from this group of statistics may have a positive or negative deviation. With the help of signs and data (+; -;), we can identify any exceptions in the observation.

If the laboratory means the value is higher than the mean value of the consensus group, we will mark it with a plus sign (+). Based on that, there may be an extraordinary value on the left side (negative side) of the mean value of the consensus group.

In contrast, with a minus sign (-), we indicate that the laboratory means the value is less than the mean value of the consensus group. In this case, there may be an extraordinary value but on the right side (positive side).

If we cannot deviate, the next step is to check the variables that could cause the mean value of the consensus group to be higher or lower than the laboratory mean.

Example of interpretation SDI

The following text will explain which variables can cause the mean value of the consensus group to be higher or lower than the laboratory mean. If there is a variable or more that reduces the mean value of the consensus group, it means that the SDI has a positive value.

Variables change in many ways depending on the specific case. This is true of the model. So, the variables are adjusted in this way. You need to be careful when performing this step. Any mistake can throw you out of your flow and show you the error. Sometimes some variables may be completely unrelated and therefore have to be discarded.

By analyzing data the values of the standard deviation, we can determine whether our model is acceptable or not. This is the best indicator for understanding the model’s bias and taking appropriate and necessary measures to correct them if shown the error.

• SDI = 0 explains that the laboratory means and the mean of the consensus group are the same and equal. That tells us the bias is 0.

• SDI > 0 but <= 1 shows that the laboratory means and the mean of the consensus group are closer to each other, and it shows less bias, and we can say that it is a favorable condition.

• SDI is greater than 1, but =< 1.25. This shows us an acceptable limit within which the laboratory value is.

• The SDI value is more significant than 1.25, but =< 1.49. This value is acceptable but must go through model testing.

• When the SDI is between numbers 1.50 and 1.99. This case indicates bias and should be investigated.

• FDI >= 2. If this case occurs, you should know that corrective action is needed and that performing this test is certainly unacceptable.

The above example gives a value of 0.33 and in this category will be within the second pass and belongs to values between 0 and 1 and indicates a lower bias.

Which index is based on SD values?

As we have already stated through our calculator, the standard deviation index measures bias. The target FDI is 0.0 means that there is no difference between the laboratory mean and the mean of the consensus group.

FAQ