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Statistical Estimation in Psychology: Understanding Parameters and Estimators

Learn about punctual and interval estimation in psychology, including calculating confidence intervals and interpreting results.

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Statistical Estimation in Psychology: Understanding Parameters and Estimators

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  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

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