BecomingAcquainted WithStatistical Concepts

BecomingAcquainted WithStatistical Concepts

CHAPTER CHAPTER 12

• Statistics is an objective way of interpreting a collection of observations.

Why We Need Statistics

• Types of statistics- Descriptive techniques- Correlational techniques- Differences among groups

Univariate and multivariate

• Frequently used in offices, labs, and homes forstatistical analysis

How Computers Are Usedin Statistics

• Types of software for statistics- Biomedical Series (BIMED)- Statistical Analysis System (SAS)- Statistical Package for the Social Sciences

(SPSS)

• Central tendency scores

Measures of Central Tendencyand Variability

- Mean: Average- Median: Midpoint- Mode: Most frequent

• Variability scores- Standard deviation- Range of scores

• Parametric

Categories of Statistical Tests

- Normal distribution- Equal variances- Independent observations

• Nonparametric (distribution free)- Distribution is not normal

• Normal curve- Skewness- Kurtosis

Normal Curve

Skewness

Kurtosis

• What statistical techniques tell us

Statistics

- Reliability (significance) of effect- Strength of the relationship (meaningfulness)

• Types of statistical techniques- Relationships among variables- Differences among groups

• Probability

Interpreting Statistical Findings

- Alpha: false positive (type I error)

• Typical: p < .05 or p < .01

- Beta: false negative (type II error)

• Meaningfulness (effect size)

• Power: Probability of rejecting the null hypothesiswhen it is false

Truth Table for the Null Hypothesis

H0 true

Correct decision

Type I error (alpha)

H0 false

Type II error (beta)

Correct decision

Accept

Reject

Alpha & Beta

• Alpha = p-level in statistical tests

• 1 - Beta = the power of the statistical test

Ways to Statistical Power

alpha (often preset to .05 or .01)

beta (often preset to .20)

N

Statistical Power and Effect Size• Effect size is invariant

• Overpower = greater N than needed to statistically detect the effect (detect trivial effects)

• Underpower = not enough N to statistically detect the effect (can’t detect meaningful effects)

• Appropriate statistical power is achieved from an a priori power analysis

Power Analysis

• Effect size = statistical power

• With the info of effect size, alpha, and beta, power analysis can tell us what N we need for the study

• Tables, computer programs, and math equations