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# An Analysis of Variance of Socially Anxious and Nonanxious Children

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.

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