Chapter 6 Hypothesis Testing What is Hypothesis Testing? the use - - PowerPoint PPT Presentation
Chapter 6 Hypothesis Testing What is Hypothesis Testing? the use of statistical procedures to answer research questions Typical research question (generic): For hypothesis testing, research questions are statements: This is
2
– You have generated a hypothesis (E.g. The mean of group A is different than the mean of group B) – You have collected some data (samples in group A, samples in group B) – Now you want to know if this data supports your hypothesis – Formally: – H0 (null hypothesis): there is no difference in the mean values of group A and group B – H1 (experimental hypothesis): there is a difference in the mean of group A and group B
3
– Inferential statistics tell us what is the likelihood that the experimental hypothesis is true à by computing a test statistic. – Typically, if the likelihood of obtaining a value of a test statistic is <0.05, then we can reject the null hypothesis – “…significant effect of …”
– Does not mean that the null hypothesis is true – Interpreted to mean that the results you are getting could be a chance finding
– Means that the null hypothesis is highly unlikely
4
5
normal distribution, t-distribution, etc.
6
– Ratio data, interval data
– Ordinal data, nominal data (although limited use for ratio and interval data)
7
M=Male, F=Female Preference ranking Likert scale responses Task completion time Examples
8
– Data are normally distributed (you checked for this by looking at the histograms, reporting the mean/median/standard deviation, and by running Shapiro-Wilks) – If data come from different groups of people à Independent t-test (assumes scores are independent and variances in the populations are roughly equal … check your table of descriptive statistics) – If data come from same group of people à dependent t-test
example in R
9
10
11
12
13
“Significant” implies that in all likelihood the difference observed is due to the test conditions (Method A vs. Method B). “Not significant” implies that the difference observed is likely due to chance. File: 06-AnovaDemo.xlsx
14
Error bars show ±1 standard deviation Note: SD is the square root of the variance Note: Within-subjects design
1 ANOVA table created by StatView (now marketed as JMP, a product of SAS; www.sas.com)
Probability of obtaining the observed data if the null hypothesis is true
Thresholds for “p”
– Uppercase for F – Lowercase for p – Italics for F and p – Space both sides of equal sign – Space after comma – Space on both sides of less-than sign – Degrees of freedom are subscript, plain, smaller font – Three significant figures for F statistic – No zero before the decimal point in the p statistic (except in Europe)
Error bars show ±1 standard deviation
Probability of obtaining the observed data if the null hypothesis is true Note: For non-significant effects, use “ns” if F < 1.0,
19
20
– If n is the number of test conditions and m is the number of participants, the degrees of freedom are… – Effect à (n – 1) – Residual à (n – 1)(m – 1) – Note: single-factor, within-subjects design
21
– Fisher PLSD, Bonferroni/Dunn, Dunnett, Tukey/Kramer, Games/ Howell, Student-Newman-Keuls, orthogonal contrasts, Scheffé
22