Working with Inferential Statistics

/in /by

Working with Inferential Statistics

Introduction

Inferential statistics is the method used to draw inferences regarding a population after analyzing a randomly selected sample. According to (Simonsohn & Nelson, 2015) inferential statistic allows one to use a small portion of the population to make assumptions about the whole at large. Independent t-test is used to test if the means of two unrelated groups are statistically differ from each other whereas the ANOVA helps to determine if there are any differences between the means of more than one independent groups. The data provided can be analyzed to investigate whether injures caused by children differed based on type of movie, length or years of creating the movie, and even the violence time in a movie.

ORDER A PLAGIARISM – FREE PAPER NOW

Determining Statistics using a One-Tailed t-test (Question 1) Working with Inferential Statistics

To investigate whether the children who were exposed to movies that were created before 1980 actually caused more injuries than those children who were exposed to movies after 1980, we perform an independent t-test. Injuries variable is considered to be the dependent variable whereas the year of movie release is the independent variable. The independent variable in this case will have two groups: “children exposed to movies created before 1980”, labelled as 1 and “children exposed to movies created after 1980”, labelled as 2. The SPSS (Ho, 2006) output for comparing the means is as shown below:

Table 1: Group Statistics

Group Statistics
  Movie_Created N Mean Std. Deviation Std. Error Mean
Injuries children exposed to movies created before 1980 23 .74 1.010 .211
  children exposed to movies created after 1980 51 2.12 2.016 .282
Table 2

Independent Samples Test Results
 
  Levene’s Test for Equality of Variances t-test for Equality of Means
  F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
                Lower Upper
Injuries Equal variances assumed 9.439 .003 -3.100 72 .003 -1.379 .445 -2.265 -.492
  Equal variances not assumed     -3.914 71.10 .000 -1.379 .352 -2.081 -.676

The study determined that the hypothesis that those children who were exposed to movies created before the year 1980 caused more injuries than those children who were exposed to movies after 1980 was false since they caused statistically significantly lower injuries compared to those children who were exposed to movies after 1980, t (72) = -3.1, p=0.003Working with Inferential Statistics.

ANOVA (Question 2)

To investigate the group that actually caused a lot of injuries we analyzed injuries as the dependent variable and year as the independent variable with the following groups:

“1” = children exposed to movies created between 1937-1960

“2” = children exposed to movies created between 1961-1989

“3” = children exposed to movies created between 1990-1999

Table 3: Descriptive Statistics

Descriptive
Injuries                
  N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum
          Lower Bound Upper Bound    
1937-1960 13 1.00 1.000 .277 .40 1.60 0 3
1961-1989 21 1.62 2.037 .444 .69 2.55 0 6
1990-1999 40 1.95 1.974 .312 1.32 2.58 0 9
Total 74 1.69 1.872 .218 1.26 2.12 0 9

As required

Table 4: ANOVA

ANOVA
Injuries          
  Sum of Squares df Mean Square F Sig.
Between Groups 8.999 2 4.499 1.294 .281
Within Groups 246.852 71 3.477    
Total 255.851 73      

Based on the results, it can be deduced that there is a statistically significance difference between the three groups as shown by one-way ANOVA (F (2,71) = 1.294, p =0.281). The group that has caused more injuries is that group with children who were exposed to movies that were created between 1990-1999 with a mean of 1.95, followed by that group of children who were exposed to movies that were created between 1961-1989 with 1.62 mean and children exposed to movies created between the years 1937-1960 cause the least injuries characterized by a mean of 1 as shown in the Table 2 of descriptive statistics.

Conclusion

The assumptions for the Analysis of Variance (ANOVA) and the one tailed t- test were met prior to conducting the analysis by ensuring that the dependent variable “injuries” was a continuous approximately normally distributed variable while the independent variable “year” consisted of two independent groups: movie that were created before 1980 and those movies that created after 1980 (Moore et al., 2015).. There was also homogeneity of variances as demonstrated by the Levene’s test (Lowry, 2014). Additionally, there were no significant outlies in the variables analyzed. In conclusion, the discussed statistical analysis can be very instrumental in deducing assumptions of a population by simple analyzing a sample. How different variable relate can also be determined. Working with Inferential Statistics

References

Ho, R. (2006). Handbook of univariate and multivariate data analysis and interpretation with SPSS. Chapman and Hall/CRC.

Lowry, R. (2014). Concepts and applications of inferential statistics.

Simonsohn, U., Simmons, J. P., & Nelson, L. D. (2015). Specification curve: Descriptive and inferential statistics on all reasonable specifications.

Moore, D. S., Notz, W. I., Flinger, M. A. (2015). Basic Practice of Statistics 6th Edition. Working with Inferential Statistics