Question

Your task is this: conduct one of the two possible tests on the data in slide 14 (regression or correlation). Refer to the previous slides in doing the exercise. Be sure to provide a write up (narrative), which explains both the statistical significance (slide 8) and the practical significance (slide 11). A sentence for each kind of significance is sufficient.

• Perform the appropriate test and provide a narrative write up for the Depression and Anxiety analysis.
• Remember, state the statistical and practical significances.

Depress Anxiety

79 80

87 97

95 85

93 85

86 94

96 94

95 94

98 76

84 61

97 97

97 97

97 88

100 97

98 94

94 88

98 97

98 94

94 73

89 94

93 82

83 79

90 97

88 100

84 91

93 94

86 94

84 88

88 94

92 94

95 89

95 79

83 76

Answer 1

Let us calculate the corerlation coefficient and test it:

Let us denote x as depression and y as anxiety.

The correlation is calculated by

where

  

We need the square of x and y and the cross products.

	x	y	x^2	y^2	x*y
	79	80	6241	6400	6320
	87	97	7569	9409	8439
	95	85	9025	7225	8075
	93	85	8649	7225	7905
	86	94	7396	8836	8084
	96	94	9216	8836	9024
	95	94	9025	8836	8930
	98	76	9604	5776	7448
	84	61	7056	3721	5124
	97	97	9409	9409	9409
	97	97	9409	9409	9409
	97	88	9409	7744	8536
	100	97	10000	9409	9700
	98	94	9604	8836	9212
	94	88	8836	7744	8272
	98	97	9604	9409	9506
	98	94	9604	8836	9212
	94	73	8836	5329	6862
	89	94	7921	8836	8366
	93	82	8649	6724	7626
	83	79	6889	6241	6557
	90	97	8100	9409	8730
	88	100	7744	10000	8800
	84	91	7056	8281	7644
	93	94	8649	8836	8742
	86	94	7396	8836	8084
	84	88	7056	7744	7392
	88	94	7744	8836	8272
	92	94	8464	8836	8648
	95	89	9025	7921	8455
	95	79	9025	6241	7505
Total	2846	2766	262210	249130	254288

We shall test the correlation coefficient for significance:

The null hypothesis: There is no correlation between X and Y.

Alternate Hypothesis: There is a correlation between X and Y

ie

Level of significance :

Test statistc : follows a t with 31-2=29 df.

.

The critical value of t=2.0452. Since the calculated value of t <teh critical value, we fail to reject the null hypothesis. Hence, we conclude that there is not enough evidence to claim that there is a correlatio n between Depression and anxiety.