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Statistics for the Behavioral & Social Sciences Assignments | Online Homework Help

06245 Topic: PSY 325 Statistics for the Behavioral & Social Sciences

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Number of Pages: 3 (Double Spaced)

Number of sources: 1

Writing Style: APA

Type of document: Article Critique

Academic Level: Undergraduate

Category: Physics

Language Style: English (U.S.)

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GARDINER

 

MY POST IS THE ONE ON TOP: PLEASE ANSWER EACH PERSON NAMES BELOW WITH COMMENTS AND GIVE EXAMPLE AS QUESTION CRITIQUE. HOWEVER UNDER EACH PERSON NAMES AS SHOWING. Guided Response:  Review your classmates’ posts.  Respond substantively to at least three peers.  What did you find useful about their explanations and examples?  What suggestions would you make for improvement?  Ask a question for further clarification as to the meaning and use of the z-scores.

 

 

Standard Normal Distribution

My Name

PSY 325 Statistics for the Behavioral & Social Science

 

When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?

 

In the statistical analysis, one may be interested in comparing the performance of individual of the different distributions. However, the kind of comparison is not possible because of the variances in their parameters. In order to ensure that we are able to directly do a comparison of different distributions, the standard normal distribution used where all distribution are all converted to and a common measurement value is used that ensures that comparison is made.  In the process of the standardization, all the distributions are standardized such that their mean is equal to zero and their standard deviation is equated to 1 (Tanner, 2016). For example, one may wish to make a comparison of the computerized teaching method and non-computerized teaching method. A claim may be made that there is no significant difference between computerized teaching method and non-computerized and in order to measure the effectiveness of each method, performance is used for the students using computerized method and another sample for the students using non-computerized teaching method.

In this case, samples were different and their parameters are different.  Therefore, in order to do this analysis and determine which method is efficient than the other, each of the distribution has to be standardized so that a common measurement value can be obtained upon which comparison can be carried out.

  • What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution?

 

In order to establish the extent of how raw scores are below or above mean value and the range within which it falls in the standard deviation, Z-score is used.  They are very important in the transformation of the data because analysis raw scores cannot be used until they are converted to a standard normal distribution using the z-scores and these z-scores are then are on the standard distribution table. For example, given the population mean weight as 50, the population standard deviation of 25 and then one is required to evaluate the probability of the weight of the 40kg.  In order to do this analysis, z-score will be required to convert the raw data to standardized form which can be read on the standard probability distribution table. In this scenario, Z-score= (40-50)/5=-2. Reading the z-score, the probability of the weight of 40kg is equal to 0.4772.

  • What is the relationship between z-scores and percentages? 

Given the Z-scores, one may be in a position to determine the percentage within the scores. Additionally, one may also determine the percentage on one end which could be on the upper end or lower end of the calculated z-scores. Using the percentage, one may be in a position to explain better the observed difference in the Z-scores. For example, when one is given the following data of the sales; 6, 7, 9, 10, 12.  With this data, we may be interested in finding the percentage of sales between 6 and 12. In this data, the sample mean is 8.8 and the standard deviation is 2.4. First get the z-score when x=6, (6-8.8)/2.4=-1.16 and when x=12, (12-8.8)/2.4=1.33. With these two z-scores, reading on the z-stable, z-score -1.16= 0.377 or 37.7% and z-score 1.33=0.4082 or 40.82%. Therefore, summing the two we have 78.52%. This shows that the percentage of the sales between 6 and 12 is 78.52% which shows it is not 100% and this means that may have some sales either below 6 or above 12 of 29.48% which is within the population.

In your opinion, does one do a better job of representing the proportion of the area under the standard curve?  Give an example that illustrates your answer.

 

In my opinion, believe one does a good job by representing the proportion of the area under the standard curve. This helps in giving a clear simple view of the proportion of the data that is within the particular phenomenon that is calculated.  Considering the example in regard to question 3, the standard curve of the proportion of the percentage of the sale between 6 and 12 may be shown as follows:

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-1.16z             z 78.52%              +1.33z

 

Additionally, we above representation of the proportion in the standard curve, it becomes easier to carry another test such as hypothesis testing (Statistics Learning Centre, 2011).

References

Tanner, D. (2016). Statistics for the Behavioral and Social Sciences (2nd ed.) San Diego, CA: Bridgepoint Education, Inc.

Statistics Learning Centre. (2011, December 5). Hypothesis tests-value-statistics help. Retrieved https://www.youtube.com/watch?v=0zZYBALbZgg

 

Sandrene McFarlane

Hi Angela,

Your description of standard normal distribution was very accurate. You detailed the benefits of transforming data from other distributions into this one because as you stated, “it ensures that we are able to make a comparison of different distributions directly”. Learning this information was interesting because it changes how I view scholarly articles that utilize different methods of distribution. Now I know what they are doing, and I know how they were tested for their results by sampling the population, determining the mean, and from there the distribution. So, though it was confusing to understand, it is quite useful. I also appreciated the examples that you gave for the relationship between the z-score and the percentage because I have always had difficulties when it comes interpreting some of those mathematical processes, but you made it easier for me to understand. It seems as though the information was effortless for you to follow. Furthermore, it seems as though you have a great understanding of the material, and you can articulate in a way that helps others. Which of the options did you believe that a better job of representing the proportions overall? Thanks for sharing this information. It was effective.

I am looking forward to seeing what else you provide.

– Sandrene

 

 

Monique Offutt

When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?

Homes that are for sale usually report the median price of homes because the median is more related to populations. Aptitude results, intelligence, and other population data tend to be normally distributed. Standard normal distribution allows measurements of different distributions to be able to be compared. Standard normal distribution always has a fixed mean of 0 and the standard deviation is always 1. The benefit of transforming data to the standard distribution because it allows the data to be viewed and compared to other sets of data (Tanner, 2016). For example when I move I like to look at the school ratings before I make the final decision and having a standard distribution of test scores, ratings, reviews, ratios of students per teacher, etc. All of the school ratings are distributed to the standard normal measurement system in order to be able to compare all of the different sets of data to be able to compare multiple sets of data to make a collaborative decision in life.

What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution?

The role z-scores plays in the transformation of data is the individual scores of standard normal distribution. The Z score allows the individual to be able to find out the distribution from the mean, the raw score, and the standard deviation. The z transformation does not affect the distribution but it will indicate how far from the mean score is in standard deviations (Tanner, 2016).

What is the relationship between z-scores and percentages?

The relationship between z-scores and percentages are often used when trying to figure out probability. For example trying to compare scores for test using the z scores can be viewed as decimals that can easily be converted into percentages. Using a percentage value to view population sets of data or scores can allow the table or graph of data to indicate probability. The z score can be converted into the percentage to be able to be recorded on a table (Tanner, 2016).

In your opinion, does one do a better job of representing the proportion of the area under the standard curve?  Give an example that illustrates your answer.

In my opinion the z scores using the standard distribution data will be the best representation under the standard curve. I think the standardized scores using the z scores allow the data to be represented visually to represent the results that fall above and below the mean and standard deviation. For example, comparing scores of students in the district, using the z scores in order to compare separate parts to the test. This converts the scores into standardized scores which can be compared to other variables (Tanner, 2016).

Reference:

Tanner, D. (2016). Statistics for the Behavioral & Social Sciences (2nd ed.). San Diego, CA: Bridgepoint Education, Inc.

 

 

Corie Langland

  • When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?

When reading through the text about data and the different distributions the common error is an interpretation of the data. To solve the problem “is to convert the scores from different distributions into a common metric, or measurement system. If researchers alter scores from different distributions so that they both fit the same distribution, they can compare scores directly.” (Tanner 2011)

  • What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution?

Transforming z-scores into standard normal distribution is used to create a sample group that is drawn and normally distributed they can call that normal, as it is rare that a large groups scores would fall within normal range.

  • What is the relationship between z-scores and percentages?

Based on the z score that is fitted for the test researchers and can look up where their score falls on a chart or graph to see what percentile the subject falls within. “Researchers can use the table values associated with z scores to determine the percentage of the distribution occurring below a point, it is not difficult to take one more step and turn that percentage into a percentile score.” (Tanner 2011)

  • In your opinion, does one do a better job of representing the proportion of the area under the standard curve?  Give an example that illustrates your answer.

Understanding the z scores and comparing it with percentages I completely understand, but really grasping their purpose and the work behind them have me a little confused. I can do the math and what not all day but interpreting it is still new to me.

 

Kayla Pressley-Brummer

 

When comparing data from different distributions what is the benefit of transforming data from these distributions to conform to the standard distributions?

Not all data sets mean the same as other data forms, therefore, the distributions are different. Tanner (2016) explains that if researchers take the scores from the different distributions so that they all fit the same distribution they can compare the scores directly. The standard normal distribution helps the purpose of comparisons.

What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution?

The z-score is the results when scores from any of the distributions are made to conform to the characteristics of the standard normal. It locates the distribution and creates the percentages allowing us to compare data.

What is the relationship between z-scores and percentages?

The z-scores can be turned into percentages allowing researchers to compare the data presented.

In your opinion does one do a better job of representing the proportion of the area under the standard curve?

Personally, I barely understand any of it. I understand the formulas but the real meaning behind it all confuses me.

Tanner, D. (2016). Statistics for the Behavioral Social Sciences, 2nd edition. Bridgepoint Education

 

 

 

 

Brian Perry

 

  • When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution? 

When comparing the different distributions, the benefit of transforming the data to a z-score helps compare.  If the distributions has different values, it is harder to compare unless the values are changed in a way that can be related.  Transforming the data becomes very important because it the numbers are but in a metric that makes sense.

  • What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution? 

The z-score is called the standard score that helps us figure out the probability of a score from a normal distribution.  It is also helpful to compare between different normal distribution by standardizing scores.  When it comes to multiple distributions, the raw scores need to be changed into either percentages or proportions.

What is the relationship between z-scores and percentages? 

The z-scores shows how many standard deviations it is from the mean.  Percentages will provide a different number by giving a percent of the piece of data.  The Z-score is based on the mean. Percentages can also be easier to convert to percentiles than z-scores which Is usually out of 100.

  • In your opinion, does one do a better job of representing the proportion of the area under the standard curve?  Give an example that illustrates your answer.   

When it comes to a standard curve, I can see how both z-scores and percentages can be useful when describing information.  I feel that a percentage will be the best to represent a standard curve.  It is more common to look at data with percentages from the whole amount.  For example, a mean score may reveal an average number and to communicate the probability of how often it occurs is most common with a percentage.  The Z-score is like a percentage but just between the standard deviation.  A percentage can however talk about the entire standard curve and make the break down of the information a bit more relatable.

 

 

 

Rickey Gray

Hello class,

It is great to be here after a recent scare over the weekend which left me in the hospital.

When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?
After reading the text, the way I understood the benefit was because different distribution are difficult to analyze and by transforming the data it made it easies to understand.

What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution?
According to the text z scores to determine the percentage of the distribution occurring below a point, it is not difficult to take one more step and turn that percentage into a percentile score. Tanner, D. (2016).

What is the relationship between z-scores and percentages?
The way I understood the text is that z-scores can be changed into percentages.

In your opinion, does one do a better job of representing the proportion of the area under the standard curve? Give an example that illustrates your answer.
I would say that percentages do a better job of representing the proportion of the area. I say that because z scores are difficult to read for me. For an example is Jet Engine parameters. In our technical manuals for work we have both charts for Engine Fan and Turbine speed. The percentage table is much easier to understand.

 

References:
Tanner, D. (2016). Statistics for the Behavioral and Social Sciences (2nd ed.) San Diego, CA: Bridgepoint Education, Inc.
Yolanda Bias

 

 

Sandrene McFarlane

The standard normal distribution formula is utilized to convert the scores from the various distributions method into a universal and widely accepted one for solving problems (Tanner, 2016). One of the benefits that I discovered is that it allows everyone who is searching for distributions a common way to calculate their answers and to gauge probability. Another benefit of transforming data to this distributions method is that some of the values never change; it is standardized. The mean is always zero, and the standard deviation is always 1.0 (Tanner, 2016). Many other distributions methods have a variety of values that they use to compute mean and standard deviations (Tanner, 2016). So, using the standard normal streamlines and simplifies the process, expediting the results and making it faster to find how the data is dispersed. According to Tanner (2006), standard normal deviation also helps us to calculates the proportions that happened in different areas, especially when we are applying it to the population as a whole to find how it affects people. So, other formulas for distributions follow the guidelines that the standard normal one provides.

The standard normal distribution is also referred to as the Z distribution since it calculates for Z-scores, or distance from the mean (Tanner, 2016). It plays a role in this transformation of data from multiple distributions to the standard normal one because it automatically converts the results to fit its system. This calculation is used to determine if that score is within normal distribution, using the standard deviation where X equals zero, meaning that it aligns with the mean/average (Tanner, 2016). Positive numbers are plotted above the mean and negative below, and the numbers correlate the position to the standard deviation and mean (Tanner, 2016). The equation utilizes the mean (M) which is subtracted from the original distribution (X) and then divided by the standard deviation (S) scores from the original distribution to get the Z-score. Furthermore, according to Tanner (2016), this type of X transformation is also utilized when they believe that a normal distribution has occurred which is very rare at that point using this formula will help to display the findings. Therefore, using the standard normal distribution allows us to transform the results from any distribution to identify and predict different outcomes, such as percentages.

The relationship between the Z-score and percentage is that it helps us to know what is occurring between the Z-score and its absolute value; keeping in mind its distance from the mean (Tanner, 2016). Also, it seems as though by calculating for Z, one can easily convert that score to a percentage by multiplying it by a hundred. Then one can use that converted percentage in combination with another to determine how it relates to a population or situation by subtracting or adding those values — allowing us to compare the results for different distributions (Tanner,2016). This information can then be displayed on the standard curve.

Based on the information that I have gathered I do believe that the Z-score or decimal does a better job of representing the proportions of the area under the standard curve than percentages, though it seems both could be used simultaneously. I know that the curve is usually used to convert those Z-scores into a percentage, but as a relates to the bottom of the curve, I think the score is necessary. Another reason I selected the Z-score is that I learned that the normal distributions are considered symmetrical (Tanner, 2016). With X equaling 0 and if it does change from a negative to a positive, it will reflect symmetry on the other end of the spectrum aiding proportional (Tanner, 2016). Plus, according to Tanner (2016), the tail ends of the curve will never touch the graph instead it continues outward because there is always a possibility that there is a different answer; hundred percent accuracies are not feasible, so using percentages under the curve would not do the best job.

Reference

Tanner, D. (2016). Statistics for the Behavioral and Social Sciences (2nded.) [Electronic version]. Retrieved from https://content.ashford.edu/books/AUPSY325.16.1

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