Experimental Design and Statistics

Scientific Method

Hypothesis building Null hypothesis (H 0 ) presumes _______________ between the D.V. and I.V. – The null hypothesis is always assumed _____________ until data show otherwise. – If the data fail to support the null hypothesis the null hypothesis is _________________. Alternative hypothesis (H 1 ) presumes that the null hypothesis is ______________. –If data fail to support the null hypothesis, the alternative hypothesis has been ____________.

Probability Statistical tests report the probability that the results of the study are due to chance, reported as a ______________. The acceptable probability of results being due to chance is known as .  is often set at ____%, meaning that p = _____ is an acceptable risk of the results being due to chance. Therefore, if p < ________, we will: - (  may also be commonly set at ____%.)

Rejection Errors Type I error – _____________ a null hypothesis that is ___________. –This incorrectly supports the prediction. (False positive) –Occurs when  is too liberal. Type II error – _____________ a null hypothesis that is __________. – This incorrectly rejects the prediction. (False negative) – Occurs when  is too restrictive.

Experimental Method Variable – any characteristic that can change over time or across situations. Independent variable – the variable that is Dependent variable – the variable that is

Experimental design Between-groups design (independent group design) – Each group represents a ___________________ – Only the _________ varies between each group. – Requires __________________ of subjects to each group to assure similarity of groups at the beginning of the experiment. –Used when:

Within-subjects design (dependent group design) – Each subject is exposed to ______________ Subjects serve as _____________. – Requires: – ____________ powerful than independent group design, because: Experimental design

Complex design – Two or more independent variables are studied simultaneously. Experimental design

Normal distribution Normal frequency distribution is shown as: A large sample (30+) usually provides a normal distribution. Skewness and kurtosis (provided by Excel) can be used to check for normality in a small sample. If these scores are within __________, parametric statistical tests may be used.

Statistical tests – Single sample design Single sample z-test – 1 sample group – Experiment meets the following assumptions: Data are interval or ratio Data are normally distributed Population mean is known Population standard deviation is known

Statistical tests – Single sample design Single sample t-test – 1 sample group – Experiment meets the following assumptions: Data are interval or ratio Data are normally distributed Population mean is known

Statistical tests – Independent groups design Independent t-test – 2 groups (different groups; each exposed to a single condition of the I.V.) – Experiment meets the following assumptions: Data are interval or ratio Data are normally distributed Variances are equal between groups (a.k.a. Homogeneity of variance).

Statistical tests – Independent groups design Mann-Whitney U test – 2 groups – Experiment breaks one of the following assumptions: Data are interval or ratio Data are normally distributed Variances are equal between groups (a.k.a. Homogeneity of variance).

Analysis of Variance (ANOVA) test – 3 or more groups – Experiment meets the following assumptions: Data are interval or ratio Data are normally distributed Variances are equal between groups (a.k.a. Homogeneity of variance). Statistical tests – Independent groups design

Kruskal-Wallis test – 3 or more groups – Experiment breaks one of the following assumptions: Data are interval or ratio Data are normally distributed Variances are equal between groups (a.k.a. Homogeneity of variance).

Paired (correlated) t-test – 2 groups (same subjects; each exposed to 2 different conditions of the I.V.) – Experiment meets the following assumptions: Data are interval or ratio Data are normally distributed Statistical tests – Dependent groups design

Wilcoxon test – 2 groups – Experiment breaks one of the following assumptions: Data are interval or ratio Data are normally distributed Statistical tests – Dependent groups design

Parametric vs. Nonparametric tests Parametric tests are most powerful. Require normal distribution and interval or ratio data. Includes: –Independent t-tests –Dependent t-tests –ANOVA Nonparametric tests are less powerful. Used when assumptions are extremely violated or with nominal or ordinal data. Includes: –Mann-Whitney U –Wilcoxon –Kruskal-Wallis

Parametric vs. Nonparametric tests Fundamental rule for choosing tests: Choose the most powerful test possible!