Data analysis methods and applications

Stat Notes

Sampling error and standard error of the mean (SEM) measure the error in assuming the sample accurately represents the population; the smaller the error, the more closely the sample can be assumed to match the population.

Confidence intervals (CIs) are ranges in which a value might fall and are limited by the confidence level -- the higher the confidence level (the degree of certainty desired), the larger the confidence interval will be to ensure the data point falls within it.

Null hypothesis is always that there is no effect of an intervention/variable -- that measured groups do not differ significantly on the measured area(s).

Alternative hypothesis states that there is an effect of the measured intervention(s)/variable(s).

Probability Sampling is used to obtain a study sample that is representative of the population. This rarely occurs with fully randomized sampling; reducing sampling error is key in yielding reliable and valid results. Because of the relationship between sample size and the standard error of the mean (SEM), a larger sample size means a smaller error.

Statistical inference refers to both an estimation of parameters such as the mean and other basic summary statistics of a data set/population, and to hypothesis testing.

Interval estimation is an estimated confidence interval.

Hypothesis testing includes the objective means of determining if a null hypothesis should or should not be rejected, which includes a probability assessment in statistical applications.

Standard deviation is a measure of how far the data is spread from the mean, and can be used to assess the accuracy of the sample mean.

Type I errors are improper rejections of the null hypothesis.

Type II errors are failures to reject the null hypothesis hen it should be rejected.

Level of Significance measures the likelihood of committing a Type I error.

Power analysis measures the risk of committing a Type II error.

Regression analysis measures the relationship between two groups, and can be used to compare separate groups or the same group after an intervention. There are several ways to perform regression analysis.