Downs and Abwender (2002) found neurological deficits in soccer players who are routinely hit on the head with soccer balls compared to swimmers, who are also athletes but who are not regularly hit in the head. Is this an example of an experimental or a non-experimental study?
18) For the following scores, find the value of each expression:
a. _X
b. _X2
c. (_X)2
d. _(X _ 1)
X
4
2
1
5
Well, this study seems like a non-experimental study to me. They're comparing soccer players who regularly get hit on the head with soccer balls to swimmers who don't have to worry about that. It's like comparing someone who eats cake every day to someone who eats kale smoothies - not exactly a controlled experiment, is it?
As for the scores, let me put on my math hat:
a. The value of _X is the average of the scores, so in this case, (4 + 2 + 1 + 5) / 4 = 3
b. The value of _X^2 is the average of the squared scores. So we square each score first, then find the average. It would be ((4^2) + (2^2) + (1^2) + (5^2)) / 4 = (16 + 4 + 1 + 25) / 4 = 46 / 4 = 11.5
c. (_X)^2 is just the square of the average score. In this case, it would be (3)^2 = 9
d. _(X - 1) just means subtracting 1 from each score, then finding the average. So, ((4-1) + (2-1) + (1-1) + (5-1)) / 4 = (3 + 1 + 0 + 4) / 4 = 8 / 4 = 2
Hope that helps! If not, I'll be here all week... just kidding, I'm here all the time!
To determine if the study described is experimental or non-experimental, we need to understand the key characteristics of each type of study.
In an experimental study, the researchers manipulate or control at least one variable to determine its effect on other variables. They randomly assign participants into different groups to compare the effects of different conditions or interventions. The goal is to establish cause-and-effect relationships.
In a non-experimental study, the researchers do not manipulate variables or randomly assign participants. They observe and measure variables as they naturally occur, typically in existing groups or populations. Non-experimental studies are useful for describing associations or relationships between variables but cannot establish causality.
In the case of Downs and Abwender (2002) comparing neurological deficits in soccer players who are hit on the head with soccer balls versus swimmers who are not, it is a non-experimental study. The researchers did not manipulate any variables or randomly assign participants to groups. They simply observed the differences between the two groups of athletes.
Now, let's move on to solving the second part of your question.
To find the value of each expression for the given scores, we need to understand what each expression represents.
a. _X represents the mean or average of the scores. To find this, sum up all the scores and divide by the total number of scores.
(_X) = (4 + 2 + 1 + 5) / 4 = 12 / 4 = 3
b. _X^2 represents the sum of the squared scores. Square each individual score and sum them up.
(_X^2) = (4^2 + 2^2 + 1^2 + 5^2) = (16 + 4 + 1 + 25) = 46
c. (_X)^2 represents the square of the mean or average score.
(_X)^2 = (3)^2 = 9
d. _(X - 1) represents the sum of the scores minus 1.
_(X - 1) = 4 - 1 + 2 - 1 + 1 - 1 + 5 - 1 = 10
So, the values of each expression are:
a. _X = 3
b. _X^2 = 46
c. (_X)^2 = 9
d. _(X - 1) = 10