STANDARD ERROR.pptxnnsnsnskssjddjdndjjjdjd

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1. STANDARD ERROR by G.Arivukkarasi

2. In statistics, the standard error is the standard deviation of the sample distribution. The sample mean of a data is generally varied from the actual population mean. It is represented as SE. It is used to measure the amount of accuracy by which the given sample represents its population. SE=Original value -Estimated value

3. The mean and deviation of sampling distributions of statistics can be computed as in the case of probability distributions based on individual observations. The standard deviation of sampling distribution of a statistic is called the standard error. Generally standard error decreases as the sample size increases.

4. Statistics is a vast topic in which we learn about data, sample and population, mean, median, mode, dependent and independent variables, standard deviation, variance, etc. Here we will learn the standard error formula along with SE of the mean and estimation.

5. Standard Error : The standard error is one of the mathematical tools used in statistics to estimate the variability. It is abbreviated as SE. The standard error of a statistic or an estimate of a parameter is the standard deviation of its sampling distribution. We can define it as an estimate of that standard deviation.

6. Standard Error Formula : The accuracy of a sample that describes a population is identified through the SE formula. The sample mean which deviates from the given population and that deviation is given as;

7. Standard Error of the Mean (SEM) : The standard error of the mean also called the standard deviation of mean, is represented as the standard deviation of the measure of the sample mean of the population. For example, normally, the estimator of the population mean is the sample mean. But, if we draw another sample from the same population, it may provide a distinct value.

8. Thus, there would be a population of the sampled means having its distinct variance and mean. It may be defined as the standard deviation of such sample means of all the possible samples taken from the same given population. SEM defines an estimate of standard deviation which has been computed from the sample. It is calculated as the ratio of the standard deviation to the root of sample size.

9. The standard error of the mean shows us how the mean changes with different tests, estimating the same quantity. Thus if the outcome of random variations is notable, then the standard error of the mean will have a higher value. But, if there is no change observed in the data points after repeated experiments, then the value of the standard error of the mean will be zero. Variane should be one.

10. Standard Error of Estimate (SEE) The standard error of the estimate is the estimation of the accuracy of any predictions. It is denoted as SEE. The regression line depreciates the sum of squared deviations of prediction. It is also known as the sum of squares error. SEE is the square root of the average squared deviation. The deviation of some estimates from intended values is given by standard error of estimate formula.

11. How to calculate Standard Error Step 1: Note the number of measurements (n) and determine the sample mean (μ). It is the average of all the measurements. Step 2: Determine how much each measurement varies from the mean.

12. Step 3: Square all the deviations determined in step 2 and add altogether: Σ(xi – μ)² Step 4: Divide the sum from step 3 by one less than the total number of measurements (n-1). Step 5: Take the square root of the obtained number, which is the standard deviation (σ).

13. Step 6: Finally, divide the standard deviation obtained by the square root of the number of measurements (n) to get the standard error of your estimate

14. Calculation for SE Give the SE of mean length for a sample of 25 fishes from a population with variance 4cm? Given : variance = 4cm SD =2cm Sample size( n =25 ) Formula : SE =SD\ √n

15. Sol : = 2\ √25 =2\5 SE =0.4

16. Importance of Standard Error Standard errors produce simplistic measures of uncertainty in a value. They are often used because, in many cases, if the standard error of some individual quantities is known, then we can easily calculate the standard error of some function of the quantities.

17. Also, when the probability distribution of the value is known, we can use it to calculate an exact confidence interval. However, the standard error is an essential indicator of how precise an estimate of the sample statistic’s population parameter . Precision is a statistic(measuring) To fix confidence limit

18. If sample size increases error value will be less. To compare the test statistics. To determine the size of the sample required to ahieve the desired precision.