Estimates

00:01 Okay, great.

00:02 Let's continue by introducing the concept of an estimate of a population parameter. It is an approximation, depending solely on sample information. A specific value is called an estimate.

00:17 There are two types of estimates.

00:19 Point estimates and confidence interval estimates.

00:23 A point estimate is a single number, while a confidence interval naturally is an interval.

00:31 The two are closely related.

00:33 In fact, the point estimate is located exactly in the middle of the confidence interval. However, confidence intervals provide much more information and are preferred when making inferences.

00:45 Don't worry, we will have separate lessons dedicated to confidence intervals.

00:49 All right. Have we seen estimates so far? Sure we have.

00:55 The sample mean x bar is a point estimate of the population mean mu.

01:01 Moreover, the sample variance as squared was an estimate of the population variance sigma squared.

01:08 There may be many estimators for the same variable.

01:11 However, they all have two properties, bias and efficiency.

01:16 We will not prove them, as the mathematics associated is really out of the scope of this course. However, you should have an idea about the concepts.

01:25 Estimators are like judges.

01:27 We are always looking for the most efficient, unbiased estimators.

01:32 An unbiased estimator has an expected value equal to the population parameter.

01:38 Let's think of a biased estimate or to explain that point.

01:42 What if somebody told you that you will find the average height of Americans by taking a sample, finding its mean, and then adding one foot to that result? So the formula is x bar plus one foot.

01:57 Well, I hope you will trust them.

02:00 They gave you an estimate later, but biased one.

02:04 It makes much more sense that the average height of Americans is approximated just by the sample mean right.

02:11 We say that the bias of this estimate is one foot.

02:16 Clear. Great.

02:19 Let's move on to efficiency.

02:22 The most efficient estimators are the ones with the least variability of outcomes.

02:28 From the estimates. We know so far we haven't seen estimates with problematic variants, so it is hard to exemplify.

02:36 It is enough to know that most efficient means the unbiased estimates are with the smallest variance.

02:43 A final note worth making is about the difference between estimators and statistics.

02:49 The word statistic is the broader term.

02:53 A point estimate is a statistic.

02:57 All right. This is how we can describe estimators and point estimates.

03:02 In the next lecture, we will explore confidence intervals.

03:06 So stick around.