Lecture 9-I Data Analysis: Bivariate Analysis and Hypothesis Testing Research Methods and Statistics

Quantitative Data Analysis Descriptive statistics: the use of statistics to summarize, describe or explain the essential characteristics of a data set. - Frequency Distributions - Measures of Central Tendency - Measures of Variability Inferential statistics: the use of statistics to make generalizations or inferences about the characteristics of a population using data from a sample. - Estimation - Hypothesis Testing

Standard Normal Distribution ≈ 99% of values fall within 3 standard deviations ≈95% of values fall within 2 standard deviations ≈68% of values fall within 1 standard deviation Mean Mode Median 1SD 2SD 3SD -3SD -2SD -1SD

Standard Deviation and a Normal Distribution A standard normal distribution - 50% of the values fall above the mean, 50% fall below. - The mean, median and mode are the same value. - A fixed proportion of the observations lie between the mean and any other point. - Most values are near the mean, and the farther from the mean the value is, the fewer the number of individuals who attained that value

Confidence Interval A confidence interval is a range around a measurement that conveys how precise the measurement is. “The latest ABC News-Washington Post poll showed 39 percent would vote for Dole. The ABC News-Washington Post telephone poll of 1,014 adults was conducted March 8-10 and had a margin of error of plus or minus 3.5 percentage points (95 confidence interval).” Interpretation: a 95 percent chance that between 35.5 percent and 42.5 percent of voters would vote for Bob Dole (39 percent plus or minus 3.5 percent).

Confidence Interval and Level The confidence level tells you about how stable the estimate is. A larger standard deviation means a wider confidence interval. As confidence intervals are wider, the estimated value is unstable and vice versa.

Inferential Statistics: Hypothesis Testing Inferential statistics is used to determine the probability that relationships or differences are found in data from a sample are also true in the population. Null hypothesis (H0) - There is no relationship/difference between two or more variables in the population Alternate hypothesis (H1) - There is a relationship/difference between two or more variables in the population

Inferential Statistics: Hypothesis Testing Type I and Type II Errors The real situation in the population H0 is true H1 is true Your decision based on your sample data Accept H0 No Error Type II Error Reject H0 Type I Error Statistical significance testing essentially determines how large the chance is that a researcher is committing a Type I error. This chance is given by the level of significance known as the probability value (or p value).

Probability Values and Effect Sizes Probability values indicate the significance level of a relationship. Probability Values 1) p values range between 0 and 1 2) The standard cut-off points for p values is .05 3) If p<.05 then the finding is statistically significant. 4) Statistical significance does not mean importance. 5) Statistical significance does not indicate the strength of the relationship between variables.

Probability Values and Effect Sizes Effect sizes indicate the strength of a relationship Effect Size 1) Indicates the strength of a relationship between variables 0 = no relationship; 1 = perfect positive relationship 2) General effect size interpretations +/- 0.2 = small; +/- 0.5 = moderate; +/- 0.8 = strong