Question

How does R calculate “Std. Error”? How can I do it by hand?

Max Call: glm(formula = cbind(damage, 6 - damage) - temp, family - binomial(link = "probit"), data = orings) Deviance Residuals: Min 10 Median 3Q -1.0134 -0.7761 -0.4467 -0.1581 1.9983 Coefficients: Estimate Std. Error z value Prizl), (Intercept) 5.59145 1.71055 3.269 0.00108 ** temp -0.10580 0.02656 -3.984 6.79e-05 *** signif. codes: 0 ***** 0.001 **** 0.01 *' 0.05 0.1 * 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 38.898 on 22 degrees of freedom Residual deviance: 18.131 on 21 degrees of freedom AIC: 34.893 Number of Fisher Scoring iterations: 6

Answer 1

How to find 'Standard Error by hand? t of all you need to know, rohat the standard erron is. Standard error tells you how well your sample mean estimates the true population wan. A lange Standard error means a lot of variability in the population. A small standard error implies the population is more uniform, ie Sample mean is close to the population mean. Now let give the steps to find it :- Step 1: Record the number of measurements (1) and calculate the sample mean (Ml. This is just the average of all measurements. Step 2 Calculate how much each measurement deviates from the mean. (subtract the sample mean from the measurement)ne (xi-M Step 3: Square all the deviations calculated in step 2. Now, add these together. F(Xi-M)(-M) +(XEM)?.... Step 4: Divide the sum from step 3 by one less than the total no. of measurements (n-1) ie nu (xi-M) Step 5: Now, find the square root of the measurement you got in step-4. This is known as the standard deviation (o) 0 / Încki-M) Step 6: Finally divide the standard deviation from step 5 by the square root of the number of measurements (n) to get the standard error of your estimate. Standard Error Now, let us do an example by hand Player Number / Height (inches) f s= Mean - Measurement ! 75 70 on m wwwNAD eil II 0 - - JJ OS W-N- + 75 (74 -2.48" Standard Ewo ES=74 2.48 6 = 0.69 inches 0.ga 13

In this picture, I have tried my level best to illustrate the importance of Standard Error in statistics. Firstly, I define what the standard error is. Secondly, I have discussed the steps for finding standard error. Thirdly, I have given an example of height of students where standard error is calculated. Hope, you will understand now.