1 / 11

PEP-PMMA Training Session Statistical inference Lima, Peru Abdelkrim Araar / Jean-Yves Duclos

PEP-PMMA Training Session Statistical inference Lima, Peru Abdelkrim Araar / Jean-Yves Duclos 9-10 June 2007. Why statistical inference?. Distributive estimates obtained from surveys are not exact population values.

wolfe
Download Presentation

PEP-PMMA Training Session Statistical inference Lima, Peru Abdelkrim Araar / Jean-Yves Duclos

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PEP-PMMA Training Session Statistical inference Lima, Peru Abdelkrim Araar / Jean-Yves Duclos 9-10 June 2007

  2. Why statistical inference? • Distributive estimates obtained from surveys are not exact population values. • The estimates normally follow a known asymptotic distribution. The parameters of that distribution can be estimated using sample information (including sampling design). • Statistically, we can then peform hypothesis tests and draw confidence intervals.

  3. Statistical inference Assume that our statistic of interest is simply average income, and its estimator follows a normal distribution:

  4. Statistical inference A centred and normalised distribution can be obtained:

  5. Hypothesis testing There are three types of hypotheses that can be tested: • An index is equal to a given value: • Difference in poverty equals 0 • Inequality equals to 20% • An index is higher than a given value: • Inequality has increased between two periods. • An index is lower than a given value: • Poverty has increased between two periods.

  6. The interest of the statistical inferences • The outcome of an hypothesis test is a statistical decision • The conclusion of the test will either be to reject a null hypothesis, H0 in favour of an alternative, H1, or to fail to reject it. • Most hypothesis tests involving an unknown true population parameter m fall into three special cases: • H0 : μ = μ0 against H1: μ ≠ μ0 • H0 : μ ≤ μ0 against H1: μ > μ0 • H0 : μ ≥ μ0 against H1: μ < μ0

  7. The interest of the statistical inferences The ultimate statistical decision may be correct or incorrect. Two types of error can occur: • Type I error, occurs when we reject H0 when it is in fact true; • Type II error, occurs when we fail to reject H0 when H0 is in fact false. • Power of the test of an hypothesis H0 versus H1 is the probability of rejecting H0 in favour of H1 when H1 is true. • P-value is the smallest significance level for which H0 would be rejected in favour of some H1.

  8. Hypothesis tests Reject H0: μ = μ0 versus H1: μ ≠ μ0if and only if :

  9. Hypothesis tests Reject H0: μ ≤ μ0 versus H1: μ > μ0 if and only if :

  10. Hypothesis tests Reject H0: μ >μ0 versus H1: μ ≤ μ0 if and only if :

  11. Confidence intervals • Loosely speaking, a confidence interval contains all of the values that “cannot be rejected” in a null hypothesis. • Three types of confidence intervals can be drawn:

More Related