Conducting and Analyzing Statistical Tests

Conducting and Analyzing Statistical Tests

Argosy University

Beth Boardley

A study wants to examine the relationship between student anxiety for an exam and the number of hours studied. The data is as follows:

Student Anxiety Scores (X)Study Hours (Y)

51

106

52

118

125

41

34

26

65

12

51 -0.9 -3 0.81 9 2.70

1. Why is a correlation the most appropriate statistic?
   • Correlation is appropriate because it allows us to see a possible association between variables. “Correlations strictly determine whether a relationship exists between the two variables under investigation” (Argosy University Online, 2014). It is also easy to calculate as well as easy to interpret. Since the study wants to find out if there is a relationship between student anxiety for an exam and the number of hours studied, correlations are the best choice.
2. What is the null and alternate hypothesis?
   • Ho (Null Hypothesis): There is no relationship between student anxiety for an exam and the number of hours studied.
   • Ha (Alternative Hypothesis): There is a relationship between student anxiety for an exam and the number of hours studied.
3. What is the correlation between student anxiety scores and number of study hours? Select alpha and interpret your findings. Make sure to note whether it is significant or not and what the effect size is.
   • XYxyx^2 y^2 xy

   106 4.1 216.81 4 8.20

   52 -0.9-20.81 4 1.80

   118 5.1 426.01 16 20.40

   125 6.1 137.21 1 6.10

   41 -1.9-33.61 9 5.70

   34 -2.9 08.41 0 0

   26 -3.9 215.21 4 -7.80

   65 0.1 10.01 1 0.10

   12 -4.9-224.01 4 9.80

   Sums = 59 40 0 0132.9 52 47

   n = 10

   Mean of x= 5.9

   Mean of y= 4 =

   SourceSS (df) MSFp-value

   1. The correlation between student anxiety for an exam and the number of hours studied is +0.5654.
      • (df)= 8 (N-2), with an alpha of 0.05, the required r value is 0.632 (Siegle, 2009).
   2. 0.5654 < 0.632, the correlation is not significant.
      • We can use coefficient of determination) to measure effect size. . Therefore only about 31.97% of the variation in the hours studied is due to the variation in anxiety scores.
      • How would you interpret this?
   3. I would conclude that study hours and anxiety scores are not significantly correlated since only about 32% of the observed variation in the study scores accounted for by the anxiety scores.
      • What is the probability of a type I error? What does this mean?
      • Probability of a Type I error: a= .05. Therefore, 5% of the time, rejecting Ho will be wrong or the 5% of the time we will see a correlation between anxiety scores and study scores when there really is not one.
      • How would you use this same information but set it up in a way that allows you to conduct a t-test? An ANOVA?
      • To conduct t test, we would use the t- statistic with the (df), N-2.
      • Hypotheses:
      • Ho (Null Hypothesis): There is no significant correlation, that is = 0
      1. t (Two-tailed), α = 0.05
      2. (df)=10 – 2 = 8
      1. Lower Critical t- score = -2.306
      2. Upper Critical t- score = 2.306
      • Reject Ho if |t| > 2.306
      • Test Statistic:
      • SE =√(1-r^2 )/(df) = √(1 -)/8) = 0.2916
      • t = r/SE = 0.5654/0.2916 = 1.939
      • p- value = 0.0885
      • Decision (in relation to the hypotheses): Since 1.939 < 2.306 we fail to reject Ho
      • Conclusion (in relation to the problem): There is no sufficient evidence that the variables are correlated.
      • For the ANOVA there is only one predictor variable, therefore an ANOVA will report an F value equal to but the same p- value.
      • ANOVA table

      Regression 16.6215 1 16.6215 3.76.0885

      Residual 35.3785 8 4.4223

      Total 52.0000 9

      References

      1. The p- value is the same as for t- test, 0.0885. The effect size = SSR/SST = 16.6215/52 = 0.3197 (31.97%) same as before

      Argosy University Online. (2014). Course Home- Module 1- Module 5. Psychological Statistics. Retrieved September 20, 2014, from http://myeclassonline.com/re/DotNextLaunch.asp?courseid=10168746&userid=22842622&sessionid=826156845d&tabid=DGxvR/TqGVriTTm5PYnB8UvXUzLgYbQNKXJixcxsTOPr4sSwI69YdHtMJZV+cHiaPL+dI56EE2pz6s/N5vimUA==&sessionFirstAuthStore=true&macid=qWI4bMshOpJeHO9zqnlym9ciy

      Heiman, G. W. (2012). Behavioral sciences STAT (Student ed.). Belmont, CA: Wadsworth Cengage Learning. Retrieved from https://digitalbookshelf.argosy.edu/#/books/9781285404691/pages/56698900?return=/books/9781285404691/outline/1

      MathBits.com. (2014). Statistics 2 – Correlation Coefficient and Coefficient of Determination. Statistics 2 – Correlation Coefficient and Coefficient of Determination. Retrieved September 20, 2014, from http://mathbits.com/MathBits/TISection/Statistics2/correlation.htm

      Siegle, D. (2009, October 14). Critical Values of the Correlation Coefficient. Critical Values of the Correlation Coefficient. Retrieved September 20, 2014, from http://www.gifted.uconn.edu/siegle/research/correlation/corrchrt.htm