![]() We worked out in Chapter 1 that the mean was 10.27, the standard deviation 4.15, and there were 11 sportspeople in the sample. In Chapter 2 (Task 8) we looked at an example of how many games it took a sportsperson before they hit the ‘red zone’ Calculate the standard error and confidence interval for those data. If you use these exact values you’d get, for the singing group: Note: these values will look slightly different than the graph because the exact means were 10.00147 and 10.01006, but we rounded off to 10 and 10.01 to make life a bit easier. If you did the tasks in Chapter 1, you’ll know that the mean is 32.19 seconds: Discovering Statistics Using R Andy Field, Jeremy Miles, Zoë Field Published: April 2012 From 58. Calculate standard error and 95% confidence interval for these data. Large values, therefore, indicate that a statistic from a given sample may not be an accurate reflection of the population from which the sample came. the mean) it tells us how much variability there is in this statistic across samples from the same population. The standard error is the standard deviation of the sampling distribution of a statistic. The standard error tells us not about how the sample mean represents the sample itself, but how well the sample mean represents the population mean. The standard deviation tells us how much observations in our sample differ from the mean value within our sample. What’s the difference between the standard deviation and the standard error? The standard deviation is a measure of how much error there is associated with the mean: a small standard deviation indicates that the mean is a good representation of our data. We use the variance, or standard deviation, to tell us whether it is representative of our data. A hypothetical estimate of the ‘typical’ score. The mean is a simple statistical model of the centre of a distribution of scores. What is the mean and how do we tell if it’s representative of our data? We are usually interested in populations, but because we cannot collect data from every human being (or whatever) in the population, we collect data from a small subset of the population (known as a sample) and use these data to infer things about the population as a whole. See the full license terms at the bottom of the page. You can use this material for teaching and non-profit activities but please do not meddle with it or claim it as your own work. This document contains abridged sections from Discovering Statistics Using R and RStudio by Andy Field so there are some copyright considerations.
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