Inferential Statistics

Working with Inferential Statistics
Discussion
In seeking to determine whether children exposed to movies created prior to the year 1980 caused more injuries than children who were exposed to movies after the year 1980, we formulate our null and alternative hypothesis as below:
H0:µ before 1980=µ after 1980
H1:µ before 1980 ? µ after 180
µ is the mean of injuries
The level of significance ?=0.05
From the result derived from the SPSS software at 95% confidence interval, we reject the null hypothesis and come to the conclusion that there is no significant difference between mean in the injuries for the movies created before 1980(M=0.74 s=1.010) and the injuries reported for the movies created after 1980(M=2.12 s=2.016) t(72), p=0.0015 ?=0.05. In the words of Hinton, Brownlow, and McMurray (2004), “if the Levene’s test is not significant (p>0.05), this indicates the variances are approximately equal” (180). In essence, it is evident from the Levine test that the t test assumption has been since the p value =0.03.
It would also be prudent to highlight the group that has caused more injuries: children exposed to movies created between 1937-1960, children exposed to movies created between 1961-1989, or children exposed to movies created between 1990-1999. From the Anova table, at 95% confidence interval, the p value happens to be < ?. We conclude that there is a significance difference between groups f(2,71) = 1.294, p = 0.281. In an attempt to bring out detailed comparison, the post hoc test would come in handy by way of assisting with the comparison table. It would also be important to point out that the test of homogeneity is conducted using SPSS so as to assist in the verification of the test’s assumption.
It is also evident that the dependent variable, i.e. injuries, is continuous and the independent variable is categorical, i.e. 1937-1960, 1961-1989 and 1990-1999. The data contained herein clearly demonstrates that no significant outliers exist. This is more so the case given that the total mean is 1.69 – with the rest of the mean lying between 1 and 1.95.
References
Field, A. (2009). Discovering Statistics Using SPSS (3rd ed.). Washington, DC: SAGE Publications.
Hinton, P.R., Brownlow, C. & McMurray, I. (2004). SPSS Explained. New York, NY: Psychology Press
Appendices
Group Statistics
year of the movie before and after 1980
N
Mean
Std. Deviation
Std. Error Mean
injuries
before 1980
23
.74
1.010
.211
after 1980
51
2.12
2.016
.282
Independent Samples Test
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
71.100
.000
-1.379
.352
-2.081
-.676
The p value for the one tailed t-test is given by 0.003/2=0.0015
Since we have a p value that happens to be < ?(0.05), we would therefore reject the null hypothesis and come to come to the conclusion that there no significant difference exists between mean in the injuries for the movies created before 1980 (M=0.74 s=1.010) and the injuries reported for the movies created after 1980 (M=2.12 s=2.016) t(72), p=0.0015 ?=0.05
Oneway
The descriptive statistics are shown in the table below:
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
Test of Homogeneity of Variances
.injuries
Levene Statistic
df1
df2
Sig.

3.781
2
71
.028
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
Robust Tests of Equality of Means
Injuries


Statistica
df1
df2
Sig.
Welch
2.627
2
38.899
.085
Brown-Forsythe
1.611
2
53.773
.209
a. Asymptotically F distributed.
Since the p value happens to be < ? we ought to come to the conclusion that there exists significant difference between groups f(2,71)=1.294,p=0.281
From the descriptive statistics, the years that had more injuries reportedwere 1990-1999
The assumptions made using one way Anova and the t-test are:
Dependent variable ought to be measured in either interval or ratio scale
Independent variable ought to be categorical
The observations ought to be independent
Dependent variable ought to be normally distributed
The variance ought to be homogeneous