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One‐Way T‐Tests in R
The one-sample t- test is not used as frequently as the independent-samples or paired- samples t- test in second language research, but as it could from time to time be useful I will outline briefly here how it can be performed.
When to Use a One‐Sample T‐Test
To determine whether some obtained value is statistically different from a neutral value, from a previously published population mean, from zero, or from some other externally dictated mean score, a one-sample t- test can be used. The one-sample t- test asks whether the mean score from the sample you have tested is statistically different from the externally determined mean score you are using to compare it to. I use Torres’s (2004) study as an example of how the one-sample t- test works (although it is likely that polytomous IRT methods, which are beyond the scope of this book, would be a better way to analyze this data).
Torres gave a 34-item five-point Likert scale questionnaire to 102 adult ESL learners to determine whether the students preferred native or non-native teachers. Torres wanted to know whether the learners would prefer one type of teacher over the other both in general and in specific skill areas such as pronunciation and grammar. In the scale a 5 indicated a preference for native-speaking English teachers (NEST), a 1 indicated a preference for non-native English speaking teachers (non-NEST), and a 3 indicated no particular preference. In order to test whether the mean scores that were recorded were substantially different from a mean of 3, a one-sample t- test was conducted for each of the areas of
investigation.
Calling for a One‐Sample T‐Test
We will examine the question of whether ESL learners preferred NESTs or non-NESTs in the areas of culture and speaking in this example. I use the Torres.sav file, imported as torres. For the one-sample t -test, in R Commander choose S TATISTICS > M EANS > SINGLE - SAMPLE T- TEST (see Figure 1). For the “Alternative Hypothesis” area, you want to put the value to test against in the “Null hypothesis: mu” box. For Torres’s questionnaire, the number “3” was neither agree nor disagree, so what we want to test is whether values depart from neutral, so I have entered “3” here. However, other numbers are possible for your data. For example, if you wanted to test whether your own students’ scores on an internal test were different from the mean of previous administrations of the test, whose mean score was 456, you could put 456 in the “Test Value” box.
Figure 1 Opening a one-sample t- test dialogue box in R Commander.
is not substantially larger than 3, so although there does seem to be a real preference, it seems like a fairly mild preference.
The R code for this test is: t.test(torres$culture, alternative='two.sided', mu=3, conf.level=.95) t.test (x,.. .) Gives the command for all t- tests, not just the one-sample test torres$culture This is the Culture variable in the torres dataset alternative="two.sided" This default calls for a two-sided hypothesis test; other alternatives: "less", "greater" mu=3 Tells R that you want a one-sample test; it compares your measured mean score to an externally measured mean conf.level=.95 Sets the confidence level for the mean difference
Performing a One-sample T-Test 1 On the R Commander drop-down menu, choose STATISTICS > M EANS > SINGLE - SAMPLE T- TEST. Choose one variable, and then put the value you want to test your data against in the “Alternative Hypothesis” area in the “Null 2 hypothesis: mu” box.Basic R code for this command is (N.B. items in red should be replaced with your own data): t.test(torres$culture, mu=3)
Performing a Robust One‐Sample T‐Test
In this section I will use Wilcox’s WRS package to perform robust paired-sample t- tests. I am assuming that you have read through Section 8.4.4 of the book and have installed all of the packages that are necessary and have loaded the WRS package.
To perform a 20% trimmed mean percentile bootstrap for a one-sample t- test, use Wilcox’s command trimpb( ) (this is very similar to the robust command for independent samples t- tests, which was trimpb2( )). Basically, the only difference in syntax between the two tests is that we add an argument specifying the neutral value: null.value = 3. Thus, this test contains means trimming (default is 20%) and uses a non-parametric percentile bootstrap. The syntax to test the Grammar variable is:
trimpb(torres$grammar, tr=.2, alpha=.05, nboot=2000, null.value=3)
Here is the output from this call:
The output shows that the 20% trimmed mean percentile-bootstrap 95% confidence interval for the population mean of the Grammar variable is [2.97, 3.48]. Since the CI contains the neutral value of 3, we cannot reject the null hypothesis that the true population mean might be equal to 3.
trimming and bootstrapping). Do you find any differences? What are the effect sizes? 3 Dewaele and Pavlenko Bilingual Emotions Questionnaire (2001–2003) data. Use the BEQ.sav dataset, imported as beq. Test the hypothesis that the people who took the online Bilingualism and Emotions Questionnaire will rate themselves as fully fluent in speaking, comprehension, reading, and writing in their first language (ratings on the variable range from 1, least proficient, to 5, fully fluent). Use the variables L1SPEAK, L1COMP, L1READ, and L1WRITE. Calculate effect sizes and comment on their size.
Bibliography
Chernick, M. (2007). Bootstrap methods: A guide for practitioners and researchers. New York: John Wiley & Sons. Crawley, M. J. (2007). The R book. New York: Wiley. Kirby, K. N., & Gerlanc,D. (2013). BootES: An R Package for Bootstrap Confidence Intervals on Effect Sizes. Behavior Research Methods , 45(4), 905–927. Torres, J. (2004). Speaking up! Adult ESL students’ perceptions of native and non-native English speaking teachers. Unpublished MA, University of North Texas, Denton.
