Confidence Intervals

SAMPLE INFERENCE

  • Statistic: Describes a sample (e.g., sample mean).

  • Parameter: Describes the entire population (e.g., population mean).

POPULATION

  • Determine average height from the population.

  • Sample Collection:

    • Sample 1: 170cm, 188cm, 166cm,…

    • Mean: 176.9cm

    • Sample 2: 160cm, 190cm, 170cm,…

    • Mean: 180.5cm

    • Sample 3: 173cm, 190cm, 187cm,…

    • Mean: 177.6cm

  • Sampling Error: Sample means may differ, affecting accuracy of population representation.

CONFIDENCE INTERVALS

  • Prefer discussing population parameters as an interval rather than a point.

  • Example: 95% confidence that population mean time spent exercising is between 1 to 3 hours.

  • Height Mean Point: 176.9cm, CI: 167.48cm - 186.32cm.

FACTORS AFFECTING CONFIDENCE INTERVAL WIDTH

  1. Population Variation: Higher variation = wider interval.

  2. Sample Size: Larger sample = smaller interval.

  • Wider CI indicates less precision; narrower CI indicates more precision.

CONFIDENCE LEVELS

  • Common levels: 90%, 95%, 99%.

STANDARD ERROR (SE)

  • Describes variability of the sampling distribution of the mean.

CRITICAL Z-VALUES

  • Z values associated with confidence intervals:

    • 90%: 1.645

    • 95%: 1.96

    • 99%: 2.576

CONFIDENCE INTERVAL CALCULATION

  • Formula: CI = M +/- (Critical z * SE)

  • Example: Given M = 5.28, SE = 0.06, CI = 5.16 to 5.40.

REPORTING IN APA FORMAT

  • Format: Report mean (M), standard deviation (SD), and CI.

  • Example: M = 5.28, SD = 0.89, 95% CI [5.16, 5.40].

SUMMARY

  • Confidence intervals provide a range for population parameters, reflecting uncertainty and influencing research conclusions.