Question

A teacher wanted to see if social anxiety affects performance on an oral assignment. To examine this, students completed social anxiety scales and were classified into “low,” “average,” and “high” levels of social anxiety. The data presented in the table below are the oral presentation grades (in percentages) earned by the 45 students separated by their social anxiety classification. Conduct the most appropriate statistical analysis to determine whether grades on the oral assignment differed based on level of social anxiety. (Hint: see week 1 presentations)

Oral presentation grade (%)
Low social anxiety	Average social anxiety	High social anxiety
72	80	77
68	85	71
73	73	73
75	81	69
97	73	90
73	91	74
95	73	76
88	73	67
89	71	81
97	75	75
88	78	68
89	90	79
93	89	58
89	88	83
79	75	81

State the independent variable in the scenario, its scale of measurement, and its number of levels.

Calculate and interpret the effect size

Answer 1

The independent variable here in this case level of social anxiety. It's scale of measurement is Ordinal because it is rank type( LOW,AVERAGE AND HIGH)

It has three 3 levels: LOW,AVERAGE AND HIGH

Null hypothesis H0:

μ(L) = μ(A) = μ(Η)

ALTERNATIVE HYPOTHESIS Ha: Not all means are same

where $\mu (L)$ is Population mean for Low social anxiety

$\mu (A)$is Population mean for AVERAGE social anxiety

$\mu (H)$ is Population mean for HIGH social anxiety

By using EXCEL WE HAVE

Anova: Single Factor Count Sum Sum SUMMARY Groups Low social anxiety Average social anxiety High social anxiety 15 1265 1195 1122 Average 84.33333333 79.66666667 74.8 Variance 99.52380952 51.52380952 60.02857143 SS MS Fcrit ANOVA Source of Variation Between Groups Within Groups P-value 0.012788075 2 4.844696115 3.219942293 681.7333333 2955.066667 340.8666667 70.35873016 Total 3636.8

Test statistic F= MS (BETWEEN)/MS( Within)

F= 340.87/70.36

F= 4.84

P value=0.012788

Since P value smaller than level of significance 0.05 therefore SIGNIFICANT

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to conclude that grades on the oral assignment differed based on level of social anxiety at 0.05 level of significance.

Effect size= h² = SSbetween / SS_total

=681.73/3638.8

=0.1874

0.1874 is the proportion of the total variance that is attributed to an effect ( level of social anxiety)