T-test

● Are the scores from two groups really different?

T-test

● Are the scores from two groups really different?

1) Who uses a broader range of intonational pitch? men or women?

2) Are stressed vowels longer in Argentine or Mexican Spanish?

3) Do French-English bilinguals recognize French words that have English cognates faster than French monolinguals?

T-test

● Do surfers front the /u/ in dude more than non-surfers?

– You record surfers and non-surfers– F2 is measure of tongue frontness– F2 for non-surfers is 1702– F2 for surfers is 1811

Histogram

T-tests and histograms

1811 1702

Results of t-test

Are the scores from two groups really different?

t 14.924

df 191

p .0005

Mean difference 109.109

Results of t-test

Are the scores from two groups really different?

t 14.924

df 191

p .0005

Mean difference 109.109

Small effect = +/- .2

Medium effect = +/- .5

Large effect = +/- .8

Reporting the results of a t-test

We observed that surfers had an F2 that was on average 109 Hz higher than non-surfers. A t-test revealed that this difference was statistically significant (t (191) 14.924, p < .0005). Additionally, the effect size was quite large (Cohen's d = 2.159), therefore, it appears that surfers have a much more fronted /u/ in dude than non-surfers.

ANOVA (analysis of variance)

T-test compare means of two groups

ANOVA (analysis of variance)

● T-test compare means of two groups● ANOVA compares the means of two or more groups

1 Do voice onset times differ significantly after /p, t, k/?

2 Three teaching methods are applied in three different ESL classrooms. Which one results in higher reading comprehension scores?

3 Non-native speakers are judged according to how fluent they are perceived to be by native listeners. How does the listeners' level of education (high school graduate, college graduate, advance degree) affect their judgments?

Example ANOVA

Who learns English better?● Speakers of Germanic languages● Speakers of Asian languages● Speakers of other European languages

Example ANOVA

Who learns English better?● Speakers of Germanic languages 285● Speakers of Asian languages 297● Speakers of other European languages 258

Example ANOVA

● Significance of Native Language (smaller is better)● F-value (bigger is better)● Degrees of freedom (measure of number of measurements taken)● R-square (how much of the variance is accounted for)● Partial eta-square (measure of effect size)

Example ANOVA

All the .012 says is that there is some difference between the 3 groups. It doesn't say which differ from each other

Example ANOVA

Post hoc tests compare each group to each other

Example ANOVA

How to report the results:The main effect of L1 type and effect size in terms of partial eta square could be

summarized and reported as: F (2, 27) = 5.271, p < .012, η2 =.281. The results of the post hoc analysis always needs to be reported when using an ANOVA. In this case you could state that the only significant difference is that Asians scored significantly higher than other Europeans as shown by a Tukey post hoc test at a significance level of p = .010.