RESEARCH STUDY 8.2: Dr. Moynihan conducts a study examining the relationship between the number of panic attacks a person experienced in the past month, the number of nightmares experienced in the past month, and people’s levels of neuroticism (a personality trait characterized by instability, anxiety, and worry). She collects a convenience sample of 50 community college students (25 males, 25 females). Below are her findings. A (number of panic attacks in the past month and neuroticism): r = - .03, not sig. B (number of panic attacks in the past month and number of nightmares in the past month): r = - .14 (p = .05). C (number of nightmares in the past month and neuroticism): r = .48 (p = .003). Explain the three associations from Dr. Moynihan’s study in terms of direction of each association (a), statistical significance (b), and effect size (c), using Cohen’s benchmarks.

A. Negative association, not statistically significant and very weak effect size

B. Negative association, statistically significant and very weak size.

C. Positive association, statistically significant and strong effect size.

Step-by-step explanation:

Cohen's d is an effect size used to indicate the standardised difference between two means. It can be used, for example, to accompany reporting of t-test and ANOVA results. It is also widely used in meta-analysis. Cohen's d is the difference between two group means divided by the pooled standard deviation for the two groups.

A statistically significant result is a result that is always not attributed to chance attributed to chance. The probability value shows the probability of observing the difference if no difference exists.

In statistics , two variables is said to have negative association when the values of one variable seem to decrease as the values of the other variable increase. In statistics, a perfect negative association is represented by the value -1.00, while a 0.00 indicates no association.

A (number of panic attacks in the past month and neuroticism): r = - .03, not sig.

Negative association, not statistically significant and very weak effect size.

B (number of panic attacks in the past month and number of nightmares in the past month): r = - .14 (p = .05).

Negative association, statistically significant and very weak size.

C (number of nightmares in the past month and neuroticism): r = .48 (p = .003).

Positive association, statistically significant and strong effect size.

It is important to note that:

There is covariance because there is presence of significant correlation. You cannot say for a fact about temporal precedence because it is not clear if neuroticism or nightmares came first. You also can't rule out the possibility this relationship is due to a third variable, hence Dr. Moynihan cannot say that neuroticism causes nightmares.

NUMBER 1

(i) negative direction

(ii) statistically insignificant

(iii) very small effect size

NUMBER 2

(i) negative direction

(ii) the relationship between (A) and (B) is statistically significant

(iii) small effect size

NUMBER 3

(i) positive direction

(ii) the relationship between (B) and (C) is statistically significant

(iii) large effect size

Step-by-step explanation:

Let (A) = the number of panic attacks a person experienced in the past month

(B) = the number of nightmares a person experienced in the past month

(C) = Neuroticism level

1. Association between (A) and (C)

r = -0.03, p = not significant

2. Association between (A) and (B)

r = -0.14, p = 0.05

3. Association between (B) and (C)

r = 0.48, p = 0.003

Let's now see what Cohen's Benchmark is all about.

Cohen's Benchmarks are specified for various Effect Sizes. Effect size is the quantitative measure of the magnitude (how great or small) of a certain phenomenon of scientific or psychological interest.

The terms 'small', 'medium' and 'large' are relative to another and to the particular content and research design or method. For this reason, Jacob Cohen gave conventional scales or benchmarks for effect sizes.

He set small effect size at d=0.2

This corresponds to an r of 0.1

He set medium effect size at d=0.5

This corresponds to an r of 0.3

He set large effect size at d=0.8

This corresponds to an r of 0.5

Based on this, we can now answer the questions.

1. Association between (A) and (C)

(i) Direction of the association is negative. This implies that as one variable increases, the other decreases. If plotted, the curve or graph would be downward sloping from left to right. If (A) comes first - if (A) is on the vertical axis - and (B) is on the horizontal axis, then as (A) increase, (B) will decrease.

(ii) The association is not significant, as already stated in the question. But then this means that the p-value is very high or is higher than 0.05 (same as 5%). This implies that the relationship between both variables is largely caused by chance.

* p-value is the probability that a relationship between or among variables is caused or is explainable by chance.

(iii) * r is the correlation coefficient and it shows the effect size.

According to Cohen's benchmarks,

The ES here is very small.

r = 0.03 is much smaller than r = 0.1

2. Association between (A) and (B)

(i) The direction of the association is negative. As one variable increases, the other decreases and vice versa.

(ii) Statistical significance exists. The results from the data collected (on variables (A) and (B)) are largely explained by statistics, as p=0.05

* A p-value of 0.05 (5%) or below is usually considered to describe the relationship among variables as statistically significant.

(iii) According to Cohen's benchmarks,

The ES here is small.

r = 0.14 is close to r = 0.1

3. Association between (B) and (C)

(i) The direction of the association is positive. There is no negative sign before the r value of 0.48. In this case, both variables increase simultaneously. If a graph were to be plotted, the shape of the curve would be upward sloping from left to right.

(ii) The relationship is statistically significant. The p-value of 0.003 is very small and is less than the p-value benchmark of 0.05. Hence there is very minute probability that chance explains the research results.

(iii) The ES is large, when placed on a Cohen scale. r of 0.48 is approximately r = 0.5 (to 1 decimal place) and this is the r value for which an effect size is considered to be large.

KUDOS!

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

step-by-step explanation:

(x) - (y) = (1 + 4i)