Inferential Statistics

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Population – a complete group or set of items that have similar characteristics. Sampling Error is the fluctuation of the value of a statistic from one sample to another drawn from the same population. Researchers compute statistics with only one sample. Inferential statistics assume random sampling from populations. Inferential statistics is a mental task of obtaining more than one sample. If we took 25 students from the 50,000 calculate the mean and then draw a new sample and repeat the process; each mean is considered one datum. If this was done 10,000 times we would have 10,000 data points. This distribution is a sampling distribution of the mean. standard deviation of a sampling distribution of the mean is called the standard error of the mean (SEM). The smaller the SEM the more accurate are the estimation of the population values. The equation for the SEM is: . ±1 SD=68%, ±2SD=95%, ±3SD=99.7%. Anything outside +3SD is not statistically significant. SD is the samples standard deviation and the N is the sample size. To increase the accuracy of the estimations, increase the sample size. WE can now calculate the SEM using the example and table shown. In our example, if we use this formula to calculate the SEM for an SD of 100.0 with a sample of 25 students the answer is 20. The standard deviation of the sampling distribution in our example is 20.0 With a sample size of 25 and a population mean of 500.0, the chances are about 95 out of 100 that any sample mean will fall between 460 and 540 (i.e., 2 SDs above and below the mean).