Question

School psychologists hypothesize that more negative externalizing behaviors are related to less anxiety (e.g., causing fights). The table below contains the response from a sample of middle school students. What can the psychologist conclude with α = 0.01?

anxiety	neg. behavior
17 22 27 34 15 20 29 20 31 24 26 21	9 7 7 3 11 6 2 7 6 9 5 10

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected in a):  

b) Input the appropriate value(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;    ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

There is a significant positive relationship between negative externalizing behaviors and anxiety.

There is a significant negative relationship between negative externalizing behaviors and anxiety.     

There is no significant relationship between negative externalizing behaviors and anxiety.

Answer 1

a) correlation

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	286.00	82.00	361.67	79.67	-131.33
mean	23.83	6.83	SSxx	SSyy	SSxy

correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.77372
t-test statistic = r*√(n-2)/√(1-r²) =        -3.8620

b)

DF=n-2 =   10  
p-value =    0.0031  
Decison:   p value < α , So, Reject Ho  

c)

effect size= r² = 0.5986 (medium)

d) There is a significant negative relationship between negative externalizing behaviors and anxiety.