Significant tests are used to find the likelihood that the null hypothesis isn’t correct. However, if you end up accepting H this doesn’t mean it’s true because it’s still a hypothesis. The same can be said for accepting H1.
Standard error and 95% confidence limits
Most data comes from samples taken from a bigger population. You can then draw conclusions from your results about that population. A statistic taken from a sample, like the mean or the standard deviation, will have a sampling distribution which shows how far from the population value the sample statistic is most likely to be. The standard error is the standard deviation of the sampling distribution.
The standard error of the mean can be calculated using:
SE? = s
?n
Where s is the sample standard deviation and n is the number of samples taken.
The mean you take from your sample is one value called a point estimate. It’s an estimate because you don’t know what the exact population mean is. You figured out how much it’s likely to differ by calculating the standard error. Now you can work out the limits in which the population mean is likely to lie between. This interval is called the confidence interval.
You can’t calculate a useful interval estimate which you know will always contain the population mean because there’s a small chance that your sample contains a lot of very small or very large values. However, you can calculate an interval so that most of the intervals you calculate will contain the population value.
A confidence interval is more informative than the null hypothesis because it provides a number of plausible values for your unknown parameter.
CI = x +/- t x s
?n
Where x is the sample mean, t is the test statistic (retrieved from the t table), s is the standard deviation and n is the number of samples.
To find the correct t value from the t table:
- find 95% in the CI column (at the bottom of the table)
- find the degrees of freedom (the number of samples you have minus 1)
- where these two values meet in the table is your t value
You can be 95% confident that the true popular mean lies between the two values you calculate.