Exposure Therapy
Introduction
A team of researchers wanted to test the effectivity for exposure therapy for college age students who have a fear of spiders. The researchers took 25 Counseling and Human Services students who wanted to overcome their fear of spiders. Before the few sessions of exposure therapy began, the students were exposed to a tarantula enclosed in a glass closed box. During this, the researchers took the heartrate of each of the 25 students. This allowed them to be able to analysis the data and ultimately determine the effectivity of the exposure therapy sessions for these 25 students. See Figure 1 in Appendix to see the findings from this research study.
Relevance to Major
How could math possibly relate to the counseling and human services field is a question that people may ask themselves. However, it is clear to researchers in the …show more content…
Counseling and Human Services field, that math, especially, measures of central tendency and dispersion, is an important tool in the field. From research that explores the accurately of certain techniques in therapy to the statistics of how services at an agency are being utilized by different populations, the measures of central tendency and measures of variation are useful for researchers and other professionals in the field.
Measures of Central Tendency
Measures of Central Tendency are descriptive statistics. This means that they summarize the data in understandable and measurable ways (Measures of Central Tendency). There are three times of central tendencies: the mean, the mode, and the median. The three of them “provides you with a different type of information about the distribution of scores” (Salkind, p. 21).
Mean
The mean of a data set is the average of all the data points. It is calculated by the sum of all the values in a data set divided by the number of values in the data set. In a math equation, it looks like this: = / n
For the data in this particular research study, the stigma of x, which is the sum of all the data sets, is 2,098. Now, researchers took 2,098 and divided by 25, which was the “n” or the number of values in our data set. The X bar, which is the mean, is 83.92, which rounded is 84 heartbeats per minute (bpm). Since the mean tells researchers the average, researchers can say that the heartrate of the clients in this therapy session was around 84 beats per minute. Luckily for this study, the researchers did not have any outliners. Outliners are extreme scores. These extreme scores affect the mean and do not accurately show the disruption of the data (Salkind, 2014). If the researchers were to have an outliner or multiple, it would be more accurate use the median.
Median
Now, the median is the midpoint of the data set.
This works for instances with outliners because it removes the off-balance of the values within the data set (Salkind, 2014). To find the median, researchers had to use the following formula:
Median = (n+1/2) th term
The researchers found the middle term to be the 13th one. Researchers found this by taking the total number of clients and adding 1 to that for a total of 26 and then dividing it by 2 to get the answer of 13. Then taking the 13th term from the data set, the researchers found that the median was 84. This is significant because the team knows that 50% of the heartrates from the clients were below 84 beats per minute and 50% of the heartrates from clients were above 84 bpm. Mode
The last measure of central tendency is mode. Mode is the most frequent occurring value in a data set. To find the mode in this data set, the researchers looked for the value that occurred the most. In this data set, the researchers found that the value 76 bpm was the mode since it occurred 5 times in the data set, more than any other value in the data set.
Measures of
Variation
The next vital tool for statistics are measures of variability. The measures of variability look at “how scores differ from one another” (Salkind, p.41). Two of these measures were used by the researcher team. These were standard deviation and z-score.
Standard Deviation
Standard deviation, SD, “represents the average amount of variability in a set of scores” (Salkind, p.44). In other words, the stranded deviation is how much a value in the data set deviates from the mean. The research team complied their data in a table (see Figure 2). The following is the formula for stranded deviation:
∂ =
The researchers took the last column in the table, )^2, and added them together, to get a total of 1,906. Then, the researchers took 1,906 and divided it by n -1 (25-1) to get 79.42. The last step to get the standard deviation, the researchers found the square root of 79.42, which was 8.91. The team rounded it to the next whole number, 9. This tells the researchers that how a value compares to the average of the data set. Researchers were able to create a visual of the data set with a bell curve graph (see Figure 3). For the completion of the bell curve, you also need the other measure of variability, z score.
Z- Scores
A z-score is a “measure of how many standard deviations below or above the population mean a raw score is” (“Z-Score”). This tells the researcher how much a client’s heartrate is above, if positive, the average, or how much lower than the average, if negative. The researchers found the z score by using the formula below:
Z = (x-µ) / ∂
X represents the raw score of the value, mu is the mean, and ∂ symbolizes standard deviation. The researchers took each raw score, X, and subtracted the mean, 84, from it then it was divided by the standard deviation, 9. Figure 4 in the appendix displays the calculations made by the research team for each raw score.
Conclusion
In conclusion, both the measures of central tendencies and measures variability help researcher analysis their data. These analyses allow the research to be explained in more descriptive and understandable terms. The researcher team because of both type of statistics was able to conclude on how efficient the exposure therapy session was on the 25 Counseling and Human Services student who were afraid of spiders.
A team of researchers wanted to test the effectivity for exposure therapy for college age students who have a fear of spiders. The researchers took 25 Counseling and Human Services students who wanted to overcome their fear of spiders. Before the few sessions of exposure therapy began, the students were exposed to a tarantula enclosed in a glass closed box. During this, the researchers took the heartrate of each of the 25 students. This allowed them to be able to analysis the data and ultimately determine the effectivity of the exposure therapy sessions for these 25 students. See Figure 1 in Appendix to see the findings from this research study.
Relevance to Major
How could math possibly relate to the counseling and human services field is a question that people may ask themselves. However, it is clear to researchers in the …show more content…
Counseling and Human Services field, that math, especially, measures of central tendency and dispersion, is an important tool in the field. From research that explores the accurately of certain techniques in therapy to the statistics of how services at an agency are being utilized by different populations, the measures of central tendency and measures of variation are useful for researchers and other professionals in the field.
Measures of Central Tendency
Measures of Central Tendency are descriptive statistics. This means that they summarize the data in understandable and measurable ways (Measures of Central Tendency). There are three times of central tendencies: the mean, the mode, and the median. The three of them “provides you with a different type of information about the distribution of scores” (Salkind, p. 21).
Mean
The mean of a data set is the average of all the data points. It is calculated by the sum of all the values in a data set divided by the number of values in the data set. In a math equation, it looks like this: = / n
For the data in this particular research study, the stigma of x, which is the sum of all the data sets, is 2,098. Now, researchers took 2,098 and divided by 25, which was the “n” or the number of values in our data set. The X bar, which is the mean, is 83.92, which rounded is 84 heartbeats per minute (bpm). Since the mean tells researchers the average, researchers can say that the heartrate of the clients in this therapy session was around 84 beats per minute. Luckily for this study, the researchers did not have any outliners. Outliners are extreme scores. These extreme scores affect the mean and do not accurately show the disruption of the data (Salkind, 2014). If the researchers were to have an outliner or multiple, it would be more accurate use the median.
Median
Now, the median is the midpoint of the data set.
This works for instances with outliners because it removes the off-balance of the values within the data set (Salkind, 2014). To find the median, researchers had to use the following formula:
Median = (n+1/2) th term
The researchers found the middle term to be the 13th one. Researchers found this by taking the total number of clients and adding 1 to that for a total of 26 and then dividing it by 2 to get the answer of 13. Then taking the 13th term from the data set, the researchers found that the median was 84. This is significant because the team knows that 50% of the heartrates from the clients were below 84 beats per minute and 50% of the heartrates from clients were above 84 bpm. Mode
The last measure of central tendency is mode. Mode is the most frequent occurring value in a data set. To find the mode in this data set, the researchers looked for the value that occurred the most. In this data set, the researchers found that the value 76 bpm was the mode since it occurred 5 times in the data set, more than any other value in the data set.
Measures of
Variation
The next vital tool for statistics are measures of variability. The measures of variability look at “how scores differ from one another” (Salkind, p.41). Two of these measures were used by the researcher team. These were standard deviation and z-score.
Standard Deviation
Standard deviation, SD, “represents the average amount of variability in a set of scores” (Salkind, p.44). In other words, the stranded deviation is how much a value in the data set deviates from the mean. The research team complied their data in a table (see Figure 2). The following is the formula for stranded deviation:
∂ =
The researchers took the last column in the table, )^2, and added them together, to get a total of 1,906. Then, the researchers took 1,906 and divided it by n -1 (25-1) to get 79.42. The last step to get the standard deviation, the researchers found the square root of 79.42, which was 8.91. The team rounded it to the next whole number, 9. This tells the researchers that how a value compares to the average of the data set. Researchers were able to create a visual of the data set with a bell curve graph (see Figure 3). For the completion of the bell curve, you also need the other measure of variability, z score.
Z- Scores
A z-score is a “measure of how many standard deviations below or above the population mean a raw score is” (“Z-Score”). This tells the researcher how much a client’s heartrate is above, if positive, the average, or how much lower than the average, if negative. The researchers found the z score by using the formula below:
Z = (x-µ) / ∂
X represents the raw score of the value, mu is the mean, and ∂ symbolizes standard deviation. The researchers took each raw score, X, and subtracted the mean, 84, from it then it was divided by the standard deviation, 9. Figure 4 in the appendix displays the calculations made by the research team for each raw score.
Conclusion
In conclusion, both the measures of central tendencies and measures variability help researcher analysis their data. These analyses allow the research to be explained in more descriptive and understandable terms. The researcher team because of both type of statistics was able to conclude on how efficient the exposure therapy session was on the 25 Counseling and Human Services student who were afraid of spiders.