# Statistics: The Behavioral Sciences Essay

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## Question:

Discuss about the Statistics for the behavioral sciences.

### Introduction

Tv shows and DVD are widely used and they are favoured by everyone. Preference of Tv shows depend on the endings of the shows. Amount of money spent on purchasing DVD also depend on the preference of the movies (Albatineh et al. 2015). In this assignment, a business research topic is provided and it is based on amount spent on purchasing of DVD of the favourite movies and the preference of the TV shows depending on the ending of the TV shows.
In this assignment, the data set of 100000 samples is given. Out of the 100000 samples, 100 would be chosen for the analysis and summary of the result (Bickel and Lehmann 2012. These 100 samples would be used to understand the concept of data representation, data manipulation and its summarisation based on certain criteria. Various primary statistical analyses would be performed and inference would be drawn from the analysis. These basic inferences would interpret the results of the tests and would give an idea about the choice of the viewers about the Tv shows and the amount spent to purchase DVD of their favourite movies. Graphs and charts would be presented in this assignment to give a better idea of the inference.
Description of the data set
100000 respondents were surveyed for this research topic. 100 out of the 100000 respondents were chosen for this business assignment. The chosen respondents belonged to three categories in respect to Tv shows. The first category consist of the respondents whose favourite television show was the “TV show with ending 1” (Sheehan et al. 2013). The second category was of respondents who preferred “TV shows with ending 2” and the third category was the respondents who liked “TV show with ending 3”. The purchase of the DVD of movies depends on the likings of the movies. Amount spent to purchase the DVD is also influenced by the favouritism of the movies by the buyer.
In this assignment, there are two kinds of variables were used; one is categorical variable and another is numerical variable. Numerical variable represents the “amount of money spent to purchase DVD of their favourite movies” and categorical variable represents the “preference of the television shows” based on “endings of the shows” (Bickel and Lehmann 2012.
Criticising the given questions
In this assignment, two questions are given. The first one states “Do they like the movie?” This question gives an idea about the likings of the movies and this liking depends on the end of the movies. From the data set, it was seen that 57 respondents liked the movies while 43 of them did not like the movies. This data set comprised of 100 samples that were chosen for the analysis. Out of the preferred movies, it was seen that 13 viewers liked movie of “ending 1” and 21 of them liked movie with “ending 2”. 23 of them liked movie with “ending 3” (Albatineh et al. 2015). Remaining respondents did not like any of the movies. It was also seen that 34 of them watched the movie with “ending 1” was watched by 32 viewers and movie with “ending 2”. 34 viewers watched movie with “ending 1”.
Another question that was asked in this survey was “How much would they pay for the DVD?” The survey revealed that 4.01 units were spent for DVD of movie with “ending 1”, 7.05units was spent for “DVD of movie with ending 2” and 6.50units were spent for DVD of movie with “ending 3”.
Summary of the data set
On analysing the given data, it was seen that “phat1” was 0.382352941. This denotes the sample proportion who favoured movies with “ending 1”. The value of “phat2” was 0.65625 and it depicts the proportion of respondents who favoured movies with “ending 2”. The value of “phat3” was found to be 0.676470588 and this tells the proportion of samples who liked movies with “ending 3” (Bickel and Lehmann 2012).
The analysis also gave the values of “phat1 – phat2”, and “phat2 – pha3”. “phat1 – phat2” had a value of -0.273897059 and it gives an idea that 0.273897059 proportion of viewers favoured movie with “ending 2” more than movie with “ending 1” (Weiss and Weiss 2012). This also gives an idea about the difference in the proportion of preference between the movies with “ending 1” and movies with “ending 2”.
The value of “phat2 – phat3” was found to be -0.020220588, which gives an idea that the proportion of viewers who preferred movies with “ending 3” was 0.02022058 more than the proportion of people who preferred movies with “ending 2” (Tian and Li 2015). This number denotes the difference between the proportion of preferences between movies with “ending 2” and movies with “ending 3”.
The preferential proportions of the different types of movies as per the endings of the movies are given below in the column chart.
Chart 1: preferential proportions of three different television shows with different endings

(Source: created by author)

Xbar1 had the value 4.008823529 units, xbar2 had the value 7.05 units and xbar3 had the value of 6.5 units. This gives an idea that the “average expenditure” to purchase DVD of movies with “ending1” is 4.008823529 units, the average expenditure to buy DVD with “ending 2” is 7.05 units and the average expenses to buy DVD with “ending 3” is 6.5 units (Gravetter and Wallnau 2016).

“xbar1-xbar2” was found to have a value of -4.216 and “xbar2-xbar3” was found to have a value of -3.041176471. This can be interpreted that the average expenses to buy “DVD of movie with ending 2” was 3.041176471units more than the average amount of expenditure to buy movies of “ending 1” (Albatineh et al. 2015). The value of “xbar2-xbar3” depicts that the average expenses to buy movies with “ending 2” was 0.55 units more than the average expenses to buy “DVD of movies with ending 3”. Thus, it can be seen that the maximum average amount of money spent to buy the “DVD was for movies with ending 3”.
The “histogram” below shows the amount of money required to buy DVD of movies with “ending 1”:

Chart 2: “Histogram” for the expenses to purchase DVD of movie with “ending 1”

(Source: created by author)

The “histogram” below shows the amount of money required to buy DVD of movies with “ending 2”:

Chart 3: “Histogram” for the expenses to purchase “DVD of movie with ending 2”

(Source: created by author)

The “histogram” below shows the amount of money required to buy DVD of movies with “ending 3”:

Chart 4: “Histogram” for the expenses to purchase “DVD of movie with ending 3”

(Source: created by author)

The analysis showed that the mean amount of money spent on movie with “ending 1” was 4.00882 units and its standard deviation is 4.7184 units (Albatineh et al. 2015). The minimum amount of money spent was found to be 0 units and the maximum amount of money spent was found to be 13 units. The value of Q1 was 0.4 while the value of Q3 was 8.75. The median of this data set was 0.75 units.

The analysis for the amount spent on movies with “ending 2” depicted that the mean value spent of the DVD of movie with “ending 2” was 7.05 units and the standard deviation was 5.060282 units (Gravetter and Wallnau 2016). The minimum amount spent to purchase these DVD was 0 units and the maximum amount spent was 13 units. The Q1 had a value of 0.8 and Q3 had a value of 11.25. The median of this data set was 9.

The “average expenditure” to buy movie with “ending 3” was 6.5 units and the “standard deviation” had a value of 4.542393 units (Weiss and Weiss 2012). The minimum amount spend was 0 units and the maximum amount spent was 12 units. The value of Q1 was of the value 0.65 and the value of Q3 was 10. The median was found to have a value of 10 units.

Discuss the results of section 3

“Do they like the tv show” compares the different movies based on their endings. This comparison gave a result that 0.382952941 proportion of viewers liked to watch movie with “ending1” and proportion of 0.65625 viewers liked to watch movie with “ending 2”. Proportion of 0.676470588 liked to watch movie that had “ending 3” (Tian and Li 2015).

The analysis of variable “how much would they pay” gave three different histograms for the expenditures to purchase them. It can be seen the movie with “ending 1” was positively skewed and non-symmetric. It is a moderate right tailed distribution. The expenditure for the DVD of movie with “ending 2” was negatively skewed distribution and it had moderate density of left tail (Bickel and Lehmann 2012). For the distribution of the amount spent on purchasing DVD of movie with “ending 3” shows that it is a left tailed distribution and it is negatively skewed.

The problems of getting survey data in the real world

Many problems are faced while “collecting data” for the survey. Sometimes, the respondents give wrong information about the questions asked to them. This is because either they might think the survey as unimportant or they might be busy while giving the interview. They also provide bias answers to the researchers, which influence the outcome of the test. Some respondents behave in this manner because they do not want to provide the correct answer to the questions. The respondents sometimes did not give response to the questions and the researchers are bound to put arbitrary data in their research data (Sheehan et al. 2013). The researchers are sometimes bound to put arbitrary data because the respondents do not answer their questions and they need the data for their research. This gives incorrect information about the survey and they influence the result. In order to overcome these problems, the people who are interested in movies and regularly watches movies should be interviewed. They would give few wrong information about this business research topic.

Hypothesis tests

The claim that the “ending type” is independent of the variable of preference of Tv shows is false. This is because the “ending type” influences the “preference of the TV shows” by the views. Thus, “ending type” is dependent on the “preference of TV shows” (Harlow et al. 2013).

From the standard deviation it can be seen that the standard deviation of “ending 1” is more than the standard deviation of “ending 2”. This depicts that there is a difference for money spent by people on movies with “ending 1” and “ending 2”.

The claim that the ending of movies of “ending 2” and “ending 3” do not influence the preference of the TV shows is wrong. This is because it was seen earlier that the viewers prefer the TV shows as per their endings. Thus, Endings influence the preference of TV shows and it is dependent of preference of TV shows (Efron 2012).

The standard deviations of both the variables are nearly equal (Koch 2013). This suggests that both the variables have nearly same value. Thus, the claim that the people would pay different, for “ending 2” and “ending 3” is false.

A discussion about the concept of “sampling distribution”

“Sampling distribution” refers to the “probability distribution of the random variables” from the chosen population. This gives an idea about the population and its characteristics, which is tough to predict, otherwise (Hsu 2014). In this assignment the two variables “Do they like the movie?” and “How much would they pay for the DVD?” gave a brief idea about the population they were selected. This idea was given from through the methods of descriptive statistics and other distribution methods. Graphs and charts drawn against these variables also briefed about the samples and the population they belong.

## Conclusion

Quantitative methods were used in this assignment to analyse the two variables, “Do they like the movie?” and “How much would they pay for the DVD?” The analysis lead to the inference that the preference of the TV shows varied with the ending of the movies. It was also seen that the amount spent to purchase DVD depend on the likings of the movies by the viewers. The concept of “sampling distribution” was also briefed in this assignment and this was done in the context of the business topic. Graphs and charts were also used to give an idea about the samples and its populations.

## References

Albatineh, A.N., Boubakari, I. and Kibria, B.G., 2015. New Confidence Interval Estimator of the Signal-to-Noise Ratio Based on Asymptotic Sampling Distribution. Communications in Statistics-Theory and Methods, (just-accepted).

Bickel, P.J. and Lehmann, E.L., 2012. Descriptive statistics for nonparametric models IV. Spread. In Selected Works of EL Lehmann (pp. 519-526). Springer US.

Efron, B., 2012. Large-scale simultaneous hypothesis testing. Journal of the American Statistical Association.

Gravetter, F. and Wallnau, L., 2016. Statistics for the behavioral sciences. Cengage Learning.

Harlow, L.L., Mulaik, S.A. and Steiger, J.H., 2013. What if there were no significance tests?. Psychology Press.

Hsu, D., 2014. Weighted sampling of outer products. arXiv preprint arXiv:1410.4429.

Koch, K.R., 2013. Parameter estimation and hypothesis testing in linear models. Springer Science & Business Media

Sheehan, S., Harris, K. and Song, Y.S., 2013. Estimating variable effective population sizes from multiple genomes: a sequentially Markov conditional sampling distribution approach. Genetics, 194(3), pp.647-662

Tian, G.L. and Li, H.Q., 2015. A new framework of statistical inferences based on the valid joint sampling distribution of the observed counts in an incomplete contingency table. Statistical methods in medical research, p.0962280215586591.

Weiss, N.A. and Weiss, C.A., 2012. Introductory statistics. USA: Pearson Education.