Statistical Inference

Statistical inference is the process of using data analysis to deduce properties of an underlying distribution of probability. It is an assumption made about a population parameter based on a statistic calculated from a sample randomly drawn from that population.

Point Estimates

Point estimates are estimates of population parameters based on sample data. For instance, the sample mean is a point estimate of the population mean. The sample standard deviation is a point estimate of the population standard deviation.

Confidence Intervals

A confidence interval provides an estimated range of values which is likely to include an unknown population parameter. The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter. A wider interval may indicate that more data should be collected before anything very definite can be inferred about the parameter.

Hypothesis Testing

Hypothesis testing is a structured method for making inferences from data. It involves creating a null hypothesis, which is a prediction that there is no significant effect or relationship, and the alternative hypothesis, which contradicts the null hypothesis. The data is then used to reject or fail to reject the null hypothesis.

P-values

The p-value is the probability of obtaining results as extreme as the observed results of a statistical hypothesis test, assuming the null hypothesis is true. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

Types of Errors

In hypothesis testing, there can be two types of errors. Type I error occurs when we reject a true null hypothesis (also known as a "false positive"), and Type II error occurs when we fail to reject a false null hypothesis (also known as a "false negative").

Statistical inference is a key component of data analysis, allowing us to draw conclusions from data and make predictions about future data.