For problems 12 to 14, do the following: (a) Make a scatter diagram of the
scores; (b) describe in words the general pattern of correlation, if any; (c) figure
the correlation coefficient; (d) figure whether the correlation is statistically significant
(use the .05 significance level, two-tailed); (e) explain the logic of what
you have done, writing as if you are speaking to someone who has never heard
of correlation (but who does understand the mean, deviation scores, and hypothesis
testing); and (f) give three logically possible directions of causality, indicating
for each direction whether it is a reasonable explanation for the correlation
in light of the variables involved (and why).
12. Four research participants take a test of manual dexterity (high scores mean better dexterity)
and an anxiety test (high scores mean more anxiety). The scores are as follows.
(c)
(e)
(d)
(f)
Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 -2
13. Four
To complete the given instructions for problems 12 to 14, follow these steps:
(a) Make a scatter diagram of the scores:
To create a scatter diagram, plot each participant's dexterity score on the x-axis and their anxiety score on the y-axis. Mark each point on the graph according to the participant's scores.
(b) Describe in words the general pattern of correlation, if any:
Analyze the scatter diagram and describe the relationship between the dexterity and anxiety scores. Look for any noticeable trends or patterns, such as a general increase or decrease in anxiety as dexterity increases, or vice versa.
(c) Figure the correlation coefficient:
Calculate the correlation coefficient to quantify the strength and direction of the relationship between dexterity and anxiety. You can use a statistical software or a calculator that has a correlation function.
(e) Explain the logic of what you have done, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, deviation scores, and hypothesis testing):
Correlation measures the degree of association between two variables. In this case, we are examining the relationship between manual dexterity and anxiety scores. By plotting the scores on a scatter diagram, we can visualize any potential relationship. The correlation coefficient then provides a numerical value that indicates the strength and direction of this relationship. We can interpret this coefficient to determine whether there is a significant correlation between the two variables.
(d) Figure whether the correlation is statistically significant (use the .05 significance level, two-tailed):
To determine if the correlation is statistically significant, we need to compare the correlation coefficient to a critical value. We use a significance level of .05 (which means a 5% chance of the correlation occurring by random chance alone). If the calculated correlation coefficient falls within the critical region (below the lower critical value or above the higher critical value), we can conclude that the correlation is statistically significant.
(f) Give three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and why):
1. Dexterity causing anxiety: It is reasonable to assume that individuals with lower manual dexterity might experience more anxiety during tasks, as they may feel frustrated or overwhelmed. However, the direction of causality should be supported by a theoretical rationale or existing research.
2. Anxiety causing a decrease in dexterity: It is possible that anxiety could negatively affect manual dexterity, as increased stress and tension could impair fine motor skills. This direction of causality is also plausible, but additional evidence would be required to establish causation.
3. Common underlying factors: It is crucial to consider that both dexterity and anxiety may be influenced by other variables. For instance, factors like stress, coordination, or neurological conditions might affect both dexterity and anxiety independently, creating a correlation without a direct causal relationship between the two variables. Further research would be needed to explore potential common factors.
To analyze the data for problems 12 to 14, we will follow these steps:
(a) Make a scatter diagram of the scores
(b) Describe in words the general pattern of correlation, if any
(c) Calculate the correlation coefficient
(d) Determine if the correlation is statistically significant
(e) Explain the logic of what we have done using mean, deviation scores, and hypothesis testing
(f) Provide three logically possible directions of causality and evaluate their plausibility
Let's start with problem 12:
12. Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows:
Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 -2
(a) Scatter diagram:
To create a scatter diagram, we plot the dexterity scores on the x-axis and the anxiety scores on the y-axis.
(b) General pattern of correlation:
By observing the scatter diagram, we can determine whether there is a general pattern of correlation between the two variables.
(c) Correlation coefficient:
To calculate the correlation coefficient, we can use a statistical formula such as Pearson's correlation coefficient.
(d) Statistical significance:
To determine if the correlation is statistically significant, we can perform a hypothesis test using a significance level of 0.05 and apply appropriate statistical tests.
(e) Explanation of logic:
Correlation measures the relationship between two variables. By calculating the correlation coefficient, we obtain a numerical value that indicates the strength and direction of this relationship. To determine the statistical significance, we perform hypothesis testing to evaluate if the observed correlation is due to chance or if it reflects a true association between the variables.
(f) Possible directions of causality:
1. Dexterity causing anxiety: It is possible that better manual dexterity leads to reduced anxiety because individuals may feel more confident and in control of their actions.
2. Anxiety causing dexterity: It is also possible that increased anxiety negatively affects manual dexterity. Anxiety can lead to increased muscle tension and decreased concentration, which could impair fine motor skills.
3. Common underlying factor: Both dexterity and anxiety could be influenced by a common factor, such as overall cognitive ability or neurological processes. In this case, the observed correlation would be a result of this shared factor rather than a direct causal relationship.
Please note that the specific steps for parts (a) to (d) will depend on the statistical software or methods used to analyze the data.