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Standard error of the mean

Standard error of the mean
When you take a sample of observations from a population, the mean of the sample is an estimate of the parametric mean, or mean of all of the observations in the population. If your sample size is small, your estimate of the mean won't be as good as an estimate based on a larger sample size. Here are 10 random samples from a simulated data set with a true (parametric) mean of 5. The X's represent the individual observations, the red circles are the sample means, and the blue line is the parametric mean. As you can see, with a sample size of only 3, some of the sample means aren't very close to the parametric mean. You'd often like to give some indication of how close your sample mean is likely to be to the parametric mean. Here's a figure illustrating this. Usually you won't have multiple samples to use in making multiple estimates of the mean. This figure is the same as the one above, only this time I've added error bars indicating ±1 standard error. Similar statistics Example Web pages Related:  Statistics

Statistics Notes: Standard deviations and standard errors 6 BASIC STATISTICAL TOOLS There are lies, damn lies, and statistics......(Anon.) 6.1 Introduction 6.2 Definitions 6.3 Basic Statistics 6.4 Statistical tests 6.1 Introduction In the preceding chapters basic elements for the proper execution of analytical work such as personnel, laboratory facilities, equipment, and reagents were discussed. It was stated before that making mistakes in analytical work is unavoidable. A multitude of different statistical tools is available, some of them simple, some complicated, and often very specific for certain purposes. Clearly, statistics are a tool, not an aim. 6.2 Definitions 6.2.1 Error 6.2.2 Accuracy 6.2.3 Precision 6.2.4 Bias Discussing Quality Control implies the use of several terms and concepts with a specific (and sometimes confusing) meaning. 6.2.1 Error Error is the collective noun for any departure of the result from the "true" value*. 1. * The "true" value of an attribute is by nature indeterminate and often has only a very relative meaning. 6.2.2 Accuracy 6.2.4 Bias 1.

Tutorials, Calculators, Consulting and Statistics Help Maintaining a laboratory notebook » Colin Purrington Some gratuitous advice on why and how to keep a written log detailing your science. Why you might want to keep a laboratory notebook To provide yourself with a complete record of why experiments were initiated and how they were performed. You’ll forget if you don’t. What to use as a laboratory notebook Purchase a notebook that possesses a stitched binding. What to put on the outside of your notebook Put your full name and year of use on the front of notebook. Tips on how to keep your notebook Devote pages 1 and 2 to a Table of Contents (which you will fill in as time passes). What to write with You should use a pen that can stand up to the dangers of the laboratory and also to time itself. hazardous conditions, but I only gave myself a day for the experiment since it’s not really earth-shattering science. Here are some conclusions: What should go into your notebook: Include detailed notes on all discussions and thoughts on the experimental goals. Using this page Purrington, C.B. Like this:

Statistical significance of correlations Statistical significance of correlations The chart below shows how large a correlation coefficient must be to be statistically significant. The chart shows one-tailed probabilities, so multiply the probabilities along the top row of the chart by 2 to get 2-tailed probabilities. In other words, the columns labeled .05, .025, .01, .005, .0005 (for one-tailed probabilities) should be changed to .10, .05, .02, .01, and .001 (for two-tailed probabilities). For our purposes, we will always be using two-tailed probabilities. Here is an example of how to read the chart. After finding that row, look across the table. Reading this way you will see that your correlation of .44 is significant at the .025 (one-tailed) level, which is .05 two-tailed. If you had 20 participants and a correlation of -0.53, what could you say? If you had 14 participants and a correlation of .49, what could you say?

CONFIDENCE - Docs editors Help Calculates the width of half the confidence interval for a normal distribution. Sample Usage Syntax CONFIDENCE(alpha, standard_deviation, pop_size) alpha - One minus the desired confidence level. Notes CONFIDENCE calculates the width of half the confidence interval such that a value picked at random from the data set has 1-alpha probability of lying within the mean plus or minus the result of CONFIDENCE. See Also ZTEST: Returns the two-tailed P-value of a Z-test with standard distribution. Examples Share this: Mary is a Docs & Drive expert and author of this help page. Was this article helpful?

Applets This page contains applets from McClelland's Seeing Statistics, which have been integrated with material in Fundamental Statistics for the Behavioral Sciences, (5th edition) by David C. Howell. You merely need to click on the appropriate link to open the applet, and then follow the directions on the page. These applets will run best if you have Sun's Java Virtual Machine installed on your computer. Chapter 4: Brightness Matching Experiment Chapter 5: Why Divide by N-1? Chapter 6: Normal Distribution and z- Scores Chapter 8: Testing a Simple Null Hypothesis Chapter 9: Correlation Construction of scatter diagrams: CorrelationPoints allows user to click on a scatter diagram to add data points with the correlation coefficient automatically updated with each new point. Chapter 17: Factorial Analysis of Variance Graphing interactions illustrates main effects and interactions, and shows how one can change without the other. Comments to: Return to index

Statistics Tutorial - Choosing a T-Test Explanation Paired or Independent t-test?There are two types of t-test, the paired t-test and the independent t-test. This page tells you how to pick the right one for your data. We have already seen that when comparing two samples, it is important to know whether or not the samples are paired. With paired (dependent) samples, it is possible to take each measurement in one sample and pair it sensibly with one measurement in the other sample. One of the reasons that you need to identify the type of experimental design that you are dealing with is that you need to use the right t-test for the right design: The paired t-test is used when you have a paired designThe independent t-test is used when you have an independent designThat's easy enough. The other thing you need to decide at this point is easy to decide, but can be slightly harder to understand. Level 3 of this topic explains why you need to make this choice.

Comparing the slopes for two independent samples | Real Statistics Using Excel In this section we test whether the slopes for two independent populations are equal, i.e. we test the following null hypothesis: H0: β1 = β2 i.e. β1 – β2 = 0 The test statistic is If the null hypothesis is true then where If the two error variances are equal, then as for the test for the differences in the means, we can pool the estimates of the error variances, weighing each by their degrees of freedom, and so Now Since we can replace the numerators of each by the pooled value , we have Note that the while the null hypothesis that β = 0 is equivalent to ρ = 0, the null hypothesis that β1 = β2 is not equivalent to ρ1 = ρ2. Example 1: We have two samples, each comparing life expectancy vs. smoking. Figure 1 – Data for Example 1 Figure 1 – Data for Example 1 As can be seen from the scatter diagrams in Figure 1, it appears that the slope for women is less steep than for that of men. Figure 2 – t-test to compare slopes of regression lines Figure 2 – t-test to compare slopes of regression lines

GraphPad - FAQ 1327 - The Mann-Whitney test doesn't really compare medians. You'll sometimes read that the Mann-Whitney test compares the medians of two groups. But this is not always correct (1) Consider this example: The graph shows each value obtained from control and treated subjects. It is also not entirely correct to say that the Mann-Whitney test asks whether the two groups come from populations with different distributions. The Mann-Whitney test compares the mean ranks -- it does not compare medians and does not compare distributions. If you make an additional assumption -- that the distributions of the two populations have the same shape, even if they are shifted (have different medians) -- then the Mann-Whiteny test can be considered a a test of medians. The Kruskal-Wallis test is the corresponding nonparametric test for comparing three or more groups. 1. Need to learn Prism 6? These guided examples of common analyses will get you off to a great start!