The design of the study is a fixed study, specifically an experimental design since a cause-effect relationship is to be established between the two groups using scientific methods (Bunt, 2012). The researcher can only control the independent variable, and how it impacts the dependent variables of the study. In the experimental design, the independent variable is the gender of the participants, whether they are male or female, and the Group they are in, either they are socially anxious or they are they are nonanxious, based on the clinical diagnosis. The dependent variable is the single mean Reaction Time score (MeanRT) of the children, measured in milliseconds.
Presence of outliers
Bunt (2012) describes outliers as quantitative data with extreme values which do not follow the pattern of the other data points. They can be too low or too high, and can be determined using a scatterplot. In our case, we can use the scatterplot to determine if there are outliers in the MeanRT dataset. Below is the output.
Based on the scatterplot above, there is one outlier visible, which corresponds to the 31st participant with a MeanRT score of 2662.94 milliseconds.
Determining the distribution of the data
A test of normality is used to determine whether a sample data is drawn from a normally distributed population. One of the test used to checked normality of numerical data is the Shapiro-Wilk test. It is appropriate for datasets with a size of 50 and below. The dataset will be split by the Group to determine the normality of each group. The Shapiro-Wilk uses the null hypothesis that the data is normally distributed. The output table is displayed below
Tests of Normality
Group
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
MeanRT
socially_anxious
.181
25
.033
.933
25
.103
nonanxious
.226
25
.002
.763
25
.000
a. Lilliefors Significance Correction
Based on the Shapiro-Wilk test, only the Nonanxious group is normally distributed with a p-value of 0.000 whereas the socially-anxious group is not since its p-value of 0.103 is greater than the level of significance. Therefore, we reject the null hypothesis for the socially_anxious group and fail to reject for the nonanxious group.
The same information can be presented graphically using the normal QQ plots.
The Normal QQ plot of the nonanxious group shows a normally distributed data since the points approximately follow the diagonal line whereas those of socially anxious group do not display this pattern.
Descriptive statistics
The dataset has an equal number of participants in the nonanxious group and the socially-anxious group, each one containing 25 participants. By gender, 60% (n = 30) are female and 40% (n = 20) are male.
The descriptive statistics of the MeanRT has a mean of 982.1528 milliseconds with a standard deviation of 336.67. the minimum and maximum value are 557.15 and 2662.94 milliseconds respectively. The Kurtosis of MeanRT is 11.718 ± 0.662 and the skewness is 2.657 ± 0.337.
Inferential statistics
Analysis of Variance
Since the dependent variable is quantitative and the independent variables are all categorical, the analysis of variance are used to determine whether there is a statistical difference between the two groups, the nonanxious and the social-anxious groups.
The null hypothesis tested is that the mean between the two groups are equal whereas the alternative hypothesis stated that there were the two groups are different. A 95% level of significance is used in the analysis.
The SPSS output of both the descriptive and the ANOVA are displayed below
Descriptives
MeanRT
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Min
Max
Lower Bound
Upper Bound
socially_anxious
25
789.9171
99.45179
19.89036
748.8654
830.9688
557.15
989.07
nonanxious
25
1174.3885
379.99212
75.99842
1017.5355
1331.2416
614.48
2662.94
Total
50
982.1528
336.56611
47.59764
886.5018
1077.8038
557.15
2662.94
The mean of the socially_anxious group is 99.45 ± 19.89 whereas the mean of the nonanxious group is 1174.3885 ± 379.99.
ANOVA
MeanRT
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
1847728.680
1
1847728.680
23.952
.000
Within Groups
3702832.025
48
77142.334
Total
5550560.704
49
Based on the ANOVA output, it is evident that there was a statistically significant difference between the two groups as determined by the ANOVA, with a F (1, 48) = 23.953, p = 0.000, and therefore, we reject the null hypothesis and conclude that the socially_anxious group has a shorter MeanRT of 99.45 ± 19.89 than the nonanxious group which had a MeanRT of 1174.3885 ± 379.99.
Findings summary
The findings of the analysis show that there is a significant difference between the socially anxious and the anxious group. Based on the results calculated above, the findings are in line with the hypothesis of the researcher, which stated that the reaction time of the socially anxious children was shorter whcn compared to the reaction time of the nonanxious children.
Part B
The researchers were interested in determining the use of specific words to influence the estimation of people. In the study, two words were used, Move and sprint, to categorize the participants. There were two set of questions, differing with the use of word sprint and move. The researcher hypothesis was that those who heard the word sprint would predict a shorter period of time than those who heard the word move.
The descriptive statistics of the data collected shows that there were 40 participants, 20 in each group. The mean duration of the groups was 29.16 with a standard deviation of 7.365. However, the ‘move’ group registered a mean of 31.64 with a standard deviation of 8.060 and the ‘sprint’ group had a mean of 23.97 and a standard deviation of 5.784.
According to Kushwaha (2016), The one-way ANOVA is a statistical test used to check whether there a significant difference between the two groups. In our case, a 95% level of significance will be used. The null hypothesis tested was that there was no difference between the two groups.
ANOVA
Event duration estimate
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
245.832
1
245.832
4.996
.031
Within Groups
1869.851
38
49.207
Total
2115.683
39
Based on the ANOVA table, a statistically significant difference existed between the group which heard move and those which heard sprint with an F statistics, F (1, 38) = 4.996 and a p-value of 0.031. The null hypothesis is therefore rejected and conclude that the group which heard sprint predicted a lower duration, with a mean of 26.68 ± 5.784 than the group which heard move which had a predicted mean duration of 31.64 ± 8.060.
The results of the analysis are therefore similar which the hypothesis of the researcher that the specific word influence the prediction.
References
Kushwaha, K. S. (2016). Inferential statistics. New Delhi: New India Publishing Agency
Bunt, G. G. (2012). Descriptive and inferential statistics in the social sciences. London: Pearson Education.
