Effect of Reaction Time on Gender: One-Way ANOVA and T-Test Analysis

This study analyzes the effect of reaction time on gender using one-way ANOVA and t-test analysis. The study examines the difference between the reaction time of congruent, neutral, and incongruent on gender. The data is collected for 113 females and 17 males for each type of reaction time. The study finds significant differences between the mean reaction time of congruent and neutral, congruent and incongruent, and neutral and incongruent.

Title
The researcher wants to know the effect of reaction time on the gender. To find the evidence about the
difference between the reaction time of congruent, neutral and incongruent on gender the one way
analysis of variance will be used.
To know about the whether there is a significant difference between the mean reaction time of
congruent, neutral and incongruent on gender, the independent sample t-test will be used for each type
of reaction time.
To know about the whether there is a significant difference between the mean reaction time of
congruent and neutral, congruent and incongruent, and neutral and incongruent, the pair sample t-test
will be used.
Abstract
The purpose of the study is to know about the effects of the reaction time on gender. The question for
the study is whether there is significance effect of reaction time on the gender and whether there is a
significant difference between the mean reaction time of congruent and neutral, congruent and
incongruent, and neutral and incongruent. The data is collected for the 113 female and 17 males for
each type of reaction time, the variable gender was measured into two categories 0 as male and 1 as
female, so it is belongs to the nominal level, and the variables age, reaction time (Congruent, neutral
and incongruent) contains integer values, so it can be consider as a quantitative variable. The main
findings of statistical analysis is shown below:
Statistics
Gender Age RT_Congruent RT_Neutral RT_Incongruent
Female N Valid 113 113 113 113
Missing 0 0 0 0
Male N Valid 17 17 17 17
Missing 0 0 0 0

The descriptive statistics for each type of reaction time is shown below:
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
Age 130 18 25 19.08 1.335
RT_Congruent 130 348 998 685.38 190.722
RT_Neutral 130 350 992 672.62 187.270
RT_Incongruent 130 351 997 798.78 132.100
Valid N (listwise) 130
The mean age of respondents is 19 years, the mean reaction time for the congruent is 685.38, for
neutral is 672.62 and for incongruent is 798.78.
Method
Design:
It is required to know about the effect of reaction time of congruent, neutral and incongruent on
gender, so it is a pure research. It is an experimental design where it is required to test the hypothesis
for the relationship between the independent variables (Age, congruent, neutral and incongruent) and
the dependent variable gender. The data can be divided into two categories as qualitative or
quantitative. The qualitative data contains the qualitative values in different levels as binary, nominal
and ordinal and the quantitative data contains the numeric values (Tesch, 2013). The variable gender
has two categories 0 as male and 1 as female, so it is belongs to the nominal level, and the variables
age, reaction time (Congruent, neutral and incongruent) contains integer values, so it can be consider
as a quantitative variable. The variable age is a quantitative variable, It indicates the age of gender.
Participants:
The 100 participants took part in the research. There were total 113 female and 17 males in total of
130 participants. The minimum age of participants for female category was 18 years and maximum
age was 25 years, the mean age of 113 females was 19 years. The minimum age of participants for
male category was 18 years and maximum age was 22 years, the mean age of 17 male was about 19.5

years. The mean reaction time for 113 female for the congruent is 679.96, for neutral is 680.66 and for
incongruent is 795.19 . The mean reaction time for 113 male for the congruent is 721.97, for neutral is
619.18 and for incongruent is 822.71.
Materials:
Statistical methods is a process of gathering, brief, examination and the explanation of the analysis.
The features of the study contained, a detailed plan, arrangement to get relative results from the
respondents. The statistical tests applies on the basis of research design, type of variable and the
distribution of data. If the data is distributed normally, then the parametric tests used for analysis, and
if the data is not normally distributed then the non-parametric tests use for the analysis.
Procedure:
To find the evidence about the difference between the reaction time of congruent, neutral and
incongruent on gender the one way analysis of variance will be used. The one-way analysis of
variance (ANOVA) used to know about significant differences between the means of two or more
independent (unrelated) groups. Here, independent variables are Age, congruent, neutral and
incongruent and the dependent variable gender.
The assumptions are given below:
1. Dependent variable must contain continuous scale.
2. Independent variable must be contain two categorical groups, "related groups" or "matched pairs".
3. The major outliers should not exists.
5. There is no relationship between the each group observations and between groups.
5. Dependent variable should follow a normal distribution.
6. Variances should be homogenous for combination of groups.
To check the assumptions of normality and outliers, follow the below process:
i. Write the provided data into SPSS data editor.

ii. Click on “Analyze > Descriptive statistics > Explore”, a new dialog box will appear, select the
dependent variables.
iii. Now, click on the “Plots” option and select the “Normality plots with tests”.
iv. Click on the “Continue” option and then press “OK” to get the results.
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Age .253 130 .000 .786 130 .000
RT_Congruent .064 130 .200* .959 130 .001
RT_Neutral .100 130 .003 .944 130 .000
RT_Incongruent .086 130 .019 .946 130 .000
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
The Shapiro-Wilk test provide more appropriate results for the sample size 50 to 2000, thus in this
case the data is 130 which indicates Shapiro-Wilk will be appropriate to test the normality. The p-
value for the Shapiro-Wilk test for all samples is less than 0.05 level of significance, which indicates
that data is non-normal. The data is not normally distrusted.
The analysis procedure is given as below:
1. Click on Analyze > Comparison means > One-way ANOVA, a new dialog box will appear, select
the dependent variable as “Age, congruent, neutral and incongruent” and the fixed factors as “Gender”
2. Click of the “Options” tab and Select the options “Descriptive and Homogeneity of variances”.
3. Press “Continue” then press “OK” option to get output. The results are:
Test of Homogeneity of Variances
Levene Statistic df1 df2 Sig.
Age 1.522 1 128 .220
RT_Congruent 1.228 1 128 .270
RT_Neutral .020 1 128 .889
RT_Incongruent .062 1 128 .804
The p-value for age, reaction time of congruent, neutral and incongruent is greater than 5%
significance level. Hence, homogeneity of variance assumption being met.

ANOVA
Sum of Squares df Mean Square F Sig.
Age
Between Groups 2.093 1 2.093 1.175 .280
Within Groups 227.976 128 1.781
Total 230.069 129
RT_Congruent
Between Groups 25467.755 1 25467.755 .699 .405
Within Groups 4666913.014 128 36460.258
Total 4692380.769 129
RT_Neutral
Between Groups 55866.839 1 55866.839 1.600 .208
Within Groups 4468189.692 128 34907.732
Total 4524056.531 129
RT_Incongruent
Between Groups 11191.342 1 11191.342 .640 .425
Within Groups 2239896.627 128 17499.192
Total 2251087.969 129
The t-test applied to test whether the mean of a sample is a characteristic of the population or not. The
t-test applied on the samples which contains quantitative values and variables measured in the interval
or ratio level (Davis, 2013). The samples are related to each other because, the sample is tested twice
for the reaction time of congruent, natural, and congruent, incongruent, and natural, incongruent for
gender. Hence, to test that there is a significance difference between reaction time, the dependent
sample t-test will be used for each relation.
Paired-samples t-test assumptions:
1. Dependent variable must contain continuous scale.
2. Independent variable must be contain two categorical groups, "related groups" or "matched pairs".
3. The major outliers should not exists between the differences of two group values.
4. The distribution between the differences of two group values should be approximately normal.
According to the results obtained for the ANOVA assumptions, the data is not normally distributed.
The pair sample t-test procedure:

1. Click on the Analyze > Compare means > Paired sample t- test. Select the paire1 as “Congruent and
natural”, pair 2 as “Congruent and incongruent”, and pair 3 as “Natural and incongruent”. Press ok.
The results are:
Paired Samples Test
Paired Differences t df Sig. (2-
tailed)Mean Std.
Deviation
Std.
Error
Mean
95% Confidence
Interval of the
Difference
Lower Upper
Pair
1
RT_Congruent -
RT_Neutral 12.762 278.758 24.449 -35.611 61.134 .522 129 .603
Pair
2
RT_Congruent -
RT_Incongruent
-
113.400 231.073 20.266 -153.498 -73.302 -
5.595 129 .000
Pair
3
RT_Neutral -
RT_Incongruent
-
126.162 235.367 20.643 -167.004 -85.319 -
6.112 129 .000
The P-value is larger than the level of significance 0.05, which indicates that the null hypothesis does
not gets rejected for difference between the mean reaction time of congruent and neutral.
The P-value is smaller than the level of significance 0.05 for difference between the mean reaction
time of congruent and incongruent, and neutral and incongruent.
Results
The data were split for the categorical variable gender to know about the number of valid and invalid
responses in each variable of reaction time and age, according to the results all the values are valid and
there is no missing value in the dataset. The analysis of the data without splitting indicates a positive
Skewness (1.370) in the age of 130 participants, negative Skewness (-0.061) reaction time of
congruent, negative Skewness (-0.128) reaction time of neutral and negative Skewness (-0.550)
reaction time of incongruent participants. So, it can say that trials are somehow biased and also it can
conclude that some of the trials are incorrect.
The parametric tests makes assumptions for the parameters of the population from which the sample
data is drown. The parametric tests applied on the ratio or interval types of data in which data is

normally distributed. (Lorena, 2012). The nonparametric tests makes less assumptions about the
parameters of the population distribution from which the sample data is drown. The nonparametric
tests applied on the binary (Two category), nominal (More than two categories) and ordinal (The
orders of categories) types of data in which data is non-normally distributed. (Mark, 2011). Thus the
data for the reaction time quantitative which have a parametric value (mean), so data was considered
as parametric. The analysis of the data without splitting indicates a positive Skewness (1.370) in the
age of 130 participants, negative Skewness (-0.061) reaction time of congruent, negative Skewness (-
0.128) reaction time of neutral and negative Skewness (-0.550) reaction time of incongruent
participants. The analysis of the data without splitting indicates a positive kurtosis (2.068) in the age of
130 participants, negative kurtosis (-1.061) reaction time of congruent, negative kurtosis (-1.257)
reaction time of neutral and negative kurtosis (-0.253) reaction time of incongruent participants.
The table for the mean and standard deviation table for each group of reaction tine and age is shown
below:
Descriptive Statistics
N Minimu
m
Maximu
m
Mean Std.
Deviatio
n
Skewness Kurtosis
Statistic Statistic Statistic Statisti
c
Statistic Statisti
c
Std.
Error
Statisti
c
Std.
Error
Age 130 18 25 19.08 1.335 1.370 .212 2.068 .422
RT_Congruent 130 348 998 685.38 190.722 -.061 .212 -1.061 .422
RT_Neutral 130 350 992 672.62 187.270 -.128 .212 -1.257 .422
RT_Incongruen
t 130 351 997 798.78 132.100 -.550 .212 .253 .422
Valid N
(listwise) 130
The mean for reaction time of incongruent (798.78) is highest and the mean for the reaction time of
neutral (672.62) is lowest. The standard deviation for reaction time of incongruent (132.100) is lowest
and the standard deviation for reaction time of congruent (190.722) is highest.

The p-value for the one-way ANOVA for Age is 0.280, for congruent is 0.405, for neutral is 0.208 and
for incongruent is 0.425 which are is greater than 5% significance level. Thus, the null hypothesis of
the test does not get rejected and the test is significant. Hence, there is not a significance difference
between the mean age for female and male, there is not a significance difference between the mean
reaction time of congruent for for female and male, there is not a significance difference between the
mean reaction time of neutral for female and male and there is not a significance difference between
the mean reaction time of incongruent for for female and male.
The calculated value of pair sample t-test for mean difference between reaction time of congruent
and neutral is 0.522 and the degree of freedom is 129. The obtained P-value corresponding to the test
statistic value is 0.603. So, the P-value is larger than the level of significance 0.05, which indicates
that the null hypothesis does not gets rejected. Thus it can be concluded that there is no significance
difference between the mean reaction time of congruent and neutral.
The calculated value of pair sample test-statistic for mean difference between reaction time of
congruent and incongruent is -5.595 and the degree of freedom is 129. The obtained P-value
corresponding to the test statistic value is 0.000. So, the P-value is smaller than the level of
significance 0.05, which indicates that the null hypothesis gets rejected. Thus it can be concluded that
there is significance difference between the mean reaction time of congruent and incongruent.
The calculated value of pair sample test-statistic for mean difference between reaction time of neutral
and incongruent is -6.112 and the degree of freedom is 129. The obtained P-value corresponding to the
test statistic value is 0.000. So, the P-value is smaller than the level of significance 0.05, which
indicates that the null hypothesis gets rejected. Thus it can be concluded that there is significance
difference between the mean reaction time of neutral and incongruent.
Discussion
The Skewness results indicates that data is not normally distributed. So, it can say that trials are
somehow biased and also it can conclude that some of the trials are incorrect.

The ANOVA results indicates that, there is not a significance difference between the mean age for
female and male, there is not a significance difference between the mean reaction time of congruent
for for female and male, there is not a significance difference between the mean reaction time of
neutral for female and male and there is not a significance difference between the mean reaction time
of incongruent for for female and male.
The pair sample t-test results indicates that there is no significance difference between the mean
reaction time of congruent and neutral. There is significance difference between the mean reaction
time of congruent and incongruent. There is significance difference between the mean reaction time of
neutral and incongruent.
The data is not approximately normally distributed, so, it can say that there was some biasedness the
data collection procedure and due to this the analysis may mislead the results.
References
Davis, C. (2013). SPSS for Applied Sciences: Basic Statistical Testing. Csiro Publishing.
Tesch, R., (2013). Qualitative Research: Analysis Types and Software. Routledge: Education.
Mark, H., (2011). Nonparametric Testing in Excel-The Excel Statistical Master.
Lorena, M., (2012). Statistics for anthropology. Cambridge university press: Science.

Supplementary materials
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
Age 130 100.0% 0 0.0% 130 100.0%
RT_Congruent 130 100.0% 0 0.0% 130 100.0%
RT_Neutral 130 100.0% 0 0.0% 130 100.0%
RT_Incongruent 130 100.0% 0 0.0% 130 100.0%
Statistics
Age RT_Congruent RT_Neutral RT_Incongruent
N
Valid 130 130 130 130
Missing 0 0 0 0
Mean 19.08 685.38 672.62 798.78
Std. Deviation 1.335 190.722 187.270 132.100
Variance 1.783 36375.045 35070.206 17450.294
Skewness 1.370 -.061 -.128 -.550
Std. Error of Skewness .212 .212 .212 .212
Kurtosis 2.068 -1.061 -1.257 .253
Std. Error of Kurtosis .422 .422 .422 .422
Minimum 18 348 350 351
Maximum 25 998 992 997
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error
Age 130 18 25 19.08 1.335 1.370 .212 2.068 .422
RT_Congruent 130 348 998 685.38 190.722 -.061 .212 -1.061 .422
RT_Neutral 130 350 992 672.62 187.270 -.128 .212 -1.257 .422
RT_Incongruent 130 351 997 798.78 132.100 -.550 .212 .253 .422
Valid N (listwise) 130
Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Age .253 130 .000 .786 130 .000
RT_Congruent .064 130 .200* .959 130 .001
RT_Neutral .100 130 .003 .944 130 .000
RT_Incongruent .086 130 .019 .946 130 .000
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction

Descriptives
N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum
Lower Bound Upper Bound
Age
Female 113 19.04 1.316 .124 18.79 19.28 18 25
Male 17 19.41 1.460 .354 18.66 20.16 18 22
Total 130 19.08 1.335 .117 18.85 19.32 18 25
RT_Congruent
Female 113 679.96 193.463 18.199 643.90 716.02 348 998
Male 17 721.47 172.300 41.789 632.88 810.06 420 978
Total 130 685.38 190.722 16.727 652.29 718.48 348 998
RT_Neutral
Female 113 680.66 187.203 17.611 645.77 715.56 350 992
Male 17 619.18 184.248 44.687 524.44 713.91 376 911
Total 130 672.62 187.270 16.425 640.13 705.12 350 992
RT_Incongruent
Female 113 795.19 128.055 12.046 771.32 819.05 361 997
Male 17 822.71 158.767 38.507 741.08 904.34 351 982
Total 130 798.78 132.100 11.586 775.86 821.71 351 997
Test of Homogeneity of Variances
Levene Statistic df1 df2 Sig.
Age 1.522 1 128 .220
RT_Congruent 1.228 1 128 .270
RT_Neutral .020 1 128 .889

RT_Incongruent .062 1 128 .804
ANOVA
Sum of Squares df Mean Square F Sig.
Age
Between Groups 2.093 1 2.093 1.175 .280
Within Groups 227.976 128 1.781
Total 230.069 129
RT_Congruent
Between Groups 25467.755 1 25467.755 .699 .405
Within Groups 4666913.014 128 36460.258
Total 4692380.769 129
RT_Neutral
Between Groups 55866.839 1 55866.839 1.600 .208
Within Groups 4468189.692 128 34907.732
Total 4524056.531 129
RT_Incongruent
Between Groups 11191.342 1 11191.342 .640 .425
Within Groups 2239896.627 128 17499.192
Total 2251087.969 129
Mean plots:

Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1
RT_Congruent 685.38 130 190.722 16.727
RT_Neutral 672.62 130 187.270 16.425
Pair 2
RT_Congruent 685.38 130 190.722 16.727
RT_Incongruent 798.78 130 132.100 11.586
Pair 3
RT_Neutral 672.62 130 187.270 16.425
RT_Incongruent 798.78 130 132.100 11.586
Paired Samples Correlations
N Correlation Sig.
Pair 1 RT_Congruent & RT_Neutral 130 -.088 .321
Pair 2 RT_Congruent & RT_Incongruent 130 .009 .923
Pair 3 RT_Neutral & RT_Incongruent 130 -.058 .511
Paired Samples Test
Paired Differences t df Sig.

(2-
tailed)
Mean Std. Deviation Std. Error Mean 95% Confidence
Interval of the
Difference
Lower Upper
Pair
1
RT_Congruent - RT_Neutral 12.762 278.758 24.449 -35.611 61.134 .522 129 .603
Pair
2
RT_Congruent - RT_Incongruent -113.400 231.073 20.266 -153.498 -73.302 -5.595 129 .000
Pair
3
RT_Neutral - RT_Incongruent -126.162 235.367 20.643 -167.004 -85.319 -6.112 129 .000