2006 Geog090 Week06 Lecture01 CentralLimitTheorem

Inferential Statistics
• Descriptive statistics (mainly for samples)
• Our objective is to make a statement with reference to a parameter describing a population
• Inferential statistics does this using a two-part process:
• (1) Estimation (of a population parameter)
• (2) Hypothesis testing

Inferential Statistics
• Estimation (of a population parameter) - The estimation part of the process calculates an estimate of the parameter from our sample (called a statistic), as a kind of “guess” as to what the population parameter value actually is
• Hypothesis testing - This takes the notion of estimation a little further; it tests to see if a sampled statistic is really different from a population parameter to a significant extent, which we can express in terms of the probability of getting that result

Estimation
• Another term for a statistic is a point estimate, which is simply an estimate of a population parameter
• The formula you use to compute a statistic is an estimator, e.g. i=n Point
Estimate

x=

Sx i=1 n

i

Estimator

• In this case, the sample mean is being used to estimate m, the population mean

Estimation
• It is quite unlikely that our statistic will be exactly the same as the population parameter (because we know that sampling error does occur), but ideally it should be pretty close to ‘right’, perhaps within some specified range of the parameter
• We can define this in terms of our statistic falling within some interval of values around the parameter value (as determined by our sampling distribution)
• But how close is close enough?

Estimation and Confidence
• We can ask this question more formally:
• (1) How confident can we be that a statistic falls within a certain distance of a parameter
• (2) What is the probability that the parameter is within a certain range that includes our sample statistic
• This range is known as a confidence interval
• This probability is the confidence level

Confidence Interval & Probability
• A confidence