1. Using statistics in small-scale language education research Jean Turner © Taylor & Francis 2014

2.  Calculate and report descriptive statistics.  Create and review a histogram.*  Calculate and interpret the Shapiro–Wilk statistic. *a.k.a. frequency distribution © Taylor & Francis 2014

3. Student #ScoreStudent #Score 1st412th13 2nd513th13 3rd714th13 4th815th14 5th816th14 6th917th14 7th918th15 8th1019th15 9th1020th15 10th1021st15 11th13 © Taylor & Francis 2014

4.  Mean = 11.14286  Median = 13  Mode = 13 and 15  Range = 11 points  Standard deviation = 3.42927 © Taylor & Francis 2014

6.  The descriptive statistics give a sense of... ◦ central tendency ◦ dispersion  The histogram gives a sense of... ◦ the general shape of the distribution ◦ the possibility of outlier scores © Taylor & Francis 2014

7.  In Parametric Statistics Land... ◦ Researchers believe their data will match the normal distribution model.  The hypothesis that one of these researchers would propose is: ◦ Null hypothesis: The data are (probably) normally distributed. © Taylor & Francis 2014

8. How likely is it that the scores are normally distributed? The Shapiro–Wilk statistic Tests that hypothesis! © Taylor & Francis 2014

9.  Enter the data. >mydata = c(4, 5, 7, 8, 8, 9, 9, 10, 10, 10, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15) © Taylor & Francis 2014

10.  Calculate descriptive statistics. (Remember how?) >summary >subset (table (mydata), table(mydata)==max (table(mydata))) >sd > maximum score – minimum score © Taylor & Francis 2014

11.  Make a histogram. >hist (mydata, col = “orange”, breaks = 10) © Taylor & Francis 2014

12.  Calculate the Shapiro–Wilk statistic. >shapiro.test (mydata) Shapiro–Wilk normality test data: mydata W = 0.9002, p-value = 0.03527 © Taylor & Francis 2014

13.  The observed value of the Shapiro–Wilk statistic is: W = 0.9002  The exact probability of the outcome, W = 0.9002, is: p-value = 0.03527 © Taylor & Francis 2014

14. What does this mean?—are the data probably normally distributed or not? © Taylor & Francis 2014

15.  For the Shapiro–Wilk statistic: ◦ If p is more than.05, we can be 95% certain that the data are normally distributed. (In other words, the null hypothesis is probably true.) ◦ If p is less than.05, we can be 95% certain that the data are not normally distributed. (In other words, the null hypothesis is probably false.) © Taylor & Francis 2014

16.  Oh, p = 0.03527 is less than.05. ◦ The null hypothesis is probably not true. ◦ I can be 95% certain that it isn’t true! ◦ The data are probably not normally distributed. © Taylor & Francis 2014

17.  Check homework practice problem #19 from Chapter Two. The null hypothesis: The data are (probably) normally distributed.  Enter the data. >spanish.vocab = c(41, 33, 32, 29, 27, 27, 26, 24, 19, 19, 18, 17, 14) © Taylor & Francis 2014

18.  shapiro.test (spanish.vocab) Shapiro–Wilk normality test data: spanish.vocab W = 0.958, p-value = 0.7225 © Taylor & Francis 2014

19.  The observed value of the Shapiro–Wilk statistic is: W = 0.958  The exact probability of the observed value, W = 0.958, is: p-value = 0.7225 © Taylor & Francis 2014

20. I’m reminding myself…  For the Shapiro–Wilk statistic: ◦ If p is more than.05, we can be 95% certain that the data are normally distributed. (In other words, the null hypothesis is probably true.) ◦ If p is less than.05, we can be 95% certain that the data are not normally distributed. (That is, the null hypothesis is probably false.) © Taylor & Francis 2014

21.  For the Spanish data, p =.7725, which is greater than.05. ◦ The null hypothesis is probably true. ◦ I can be 95% certain the hypothesis is true. ◦ The data probably are normally distributed. © Taylor & Francis 2014