1 / 17

Design and Data Analysis in Psychology I

Design and Data Analysis in Psychology I. School of Psychology Dpt. Experimental Psychology. Salvador Chacón Moscoso Susana Sanduvete Chaves. Statistical estimation. Lesson 6. 1. Introduction. Parameters (values in the population) are not usually known.

rboothe
Download Presentation

Design and Data Analysis in Psychology I

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. Design and Data Analysis in Psychology I School of PsychologyDpt. Experimental Psychology Salvador Chacón Moscoso Susana Sanduvete Chaves

  2. Statistical estimation Lesson 6

  3. 1. Introduction • Parameters (values in the population) are not usually known. • Statistics can be calculated from samples. • A statistic obtained in a randomized sample will take a concrete value from all the possible values. • A parameter obtained in a population is only one value; it is a constant. • The value that a statistic takes in a randomized sample is a estimation of the parameter (e.g., the statistic is a estimator of μ; the statistic S2 is a estimator of σ2).

  4. 2. Punctual estimation • It consist in obtaining a concrete value for a parameter when we infer it (e.g., μ=10). • It can be done when the sample is representative of the population: • Randomized selection. • Adequate sample size. • A statistic is a good estimator of its parameter when is: • Unbiased: its expected value is equal to its parameter. • Consistent: its variance is 0 when n tends to ∞. • Efficient: the lowest standard error. • Sufficient: its based on all the information of the sample.

  5. 2. Punctual estimation

  6. 3. Interval estimation • It consists in obtaining a range of values with a high probability of containing the parameter (usually 95%; 99%). • Elements: • Risk level = α Level of confidence = 1-α. • Standard score: Zα/2. • Standard error: • Maximum error: • Confidence limits: • Upper. • Lower.

  7. 3.1. Confidence interval for the mean

  8. 3.1. Confidence interval for the mean Most common values: α = 0.05 1-α = 0.95 Z α/2 = 1.96 α = 0.01 1-α = 0.99 Z α/2 = 2.58 Risk level: α/2 Level of confidence 1-α Risk level: α/2

  9. 3.1. Confidence interval for the mean 0.95 α/2=0.025 α/2=0.025 0.475 0.475 Z=-1.96 Z=+1.96 α =0.05

  10. 3.1. Confidence interval for the mean

  11. 3.1. Confidence interval for the mean 0.99 α/2=0.005 α/2=0.005 0.495 0.495 Z=-2.58 Z=+2.58 α =0.01

  12. 3.1. Confidence interval for the mean

  13. 3.1. Confidence interval for the mean.Example We obtain, randomly, a sample of 101 participants. Their mean in a test is 80 and the standard deviation is 10. Calculate the limits in which the true mean of the population is, considering a level of confidence of 0.99.

  14. 3.1. Confidence interval for the mean.Example The true mean in the test will be between 77.42 and 82.58, with a level of confidence of 0.99

  15. 3.2. Confidence interval for the proportion

  16. 3.2. Confidence interval for the proportion. Example A politician would like to know if a group of workers would accept a new work law. In order to know it, he asked 10 workers and only 3 did not agree. Calculate the limits in which the true proportion of workers that did not agree is, considering a level of confidence of 0.99.

  17. 3.2. Confidence interval for the proportion. Example The true proportion of workers that did not agree is between 0 (because we can not obtain negative values in proportions) and 0.674, with a level of confidence of 0.99

More Related