Estimation, Population Parameters - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

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Ch. 12. Estimation I. Introduction A. Inferential procedures to estimate population parameters. B. Includes point estimation, confidence interval, and hypothesis testing.

II. Point estimation: use an unbiased statistic in estimating a parameter. Sample mean for population mean. Sample variance for population variance.

III. Confidence Interval (for population mean) A. Situation

1. Instead of estimating a single point about a parameter, we want to build an interval around the sample mean which may include the parameter (μ).
2. The interval will include the parameter (1-α)% of the time if we do the sampling process infinitely many times.
3. Therefore, we may say we have (1-α)% of confidence in that

this interval will include the parameter (μ).

B. (1-α)% confidence interval (CI) for μ

1. CI = M ± zα/2(σ/ n ) for the z-case.
2. CI = M ± tα/2(s/ n ) for one-sample t.
3. CI = M 1 -M 2 ± tα/2(SE) for two-independent t. _
4. CI = MD ± tα/2(SE) for two-dependent t.
5. Notice that the location of CI depends on the mean and that the width of CI depends on α, σ (or s), and n. C. Example

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