Intro to Psychology Research – Statistics Paper
Introduction
In this paper we have to analyze students’ performance in completing two kinds of mathematical problems: addiction problems and subtraction problems. 100 math problems were given for 36 students, and their performance was tested in two different ways. The first way was to complete math tasks in an organized fashion to minimize task switching (Task A). The second way was in a disorganized fashion (Task B) – it requires a task switch for every problem attempted.
- Would you finish the test faster if you completed all of the addition problems first and all of the subtraction problems second?
- Is it more efficient to complete all of the addition problems first?
- If you switch back and forth between addition and subtraction, will the mental effort of ‘task-switching’ actually slow you down?
- Or is simple math so easy that there will be no difference?
When using the test two cases can be distinguished. In the first case it is used to test the hypothesis of equality of the general average of two independent, unrelated samples (the so-called two-sample t-test). In this case, there is experimental and the control group (experimental) group, the number of subjects in the groups may be different. In the second case, when the same group of objects generates a numerical material to test hypotheses about the medium, a so-called paired t-test. Sample is then called the dependent-related.
We are given with the following data set of 36 observations from task A and task B
We have to check if there is a significant difference between the completion time of Task A and Task B. The first step is to formulate null and alternative hypotheses:
Null hypothesis: there is no significant difference in completion time between Task A and Task B
H0: μ1=μ2
Alternative hypothesis: there is a significant difference in completion time between Task A and Task B.
Ha: μ1≠μ2
Set the level of significance alpha, as given:
α=0.05
For task A:
For task B:
nA=nB=36
Perform statistical calculations:
XA=511036=141.944XB=562636=156.278
SSA=921546-5110236=196209.889
SSB=1192414-5626236=313195.222s2=SSAn-1=196209.88935=5606sA=5606=74.87s2=SSBn-1=313195.22235=8948.43sB=8948.43=94.6
df=36+36-2=70Sp2=196209.889+313195.22270=7277.22sXA-XB=7277.22236+7277.22236=1715.26t=141.944-156.278-01715.26=-0.008
This test was two-tailed. The critical t-value is t(70,0.05)=1.995.
Since the absolute value of t-observed is lesser than t-critical we failed to reject the null hypothesis. There is no significant difference in completion time between Task A and Task B at 5% level of significance.
However, this doesn’t mean that the both tasks are equally difficult. The number of mistakes on each task may be different.
Correlation analysis
In this section we would like to investigate the relationships between the given variables. We will check two pairs of variables to answer the following questions:
- Does being older make people faster or slower in completing the task
- Is there a relationship between age and the number of errors?
The answer on these questions may be obtained by using correlation analysis. The correlation coefficient is one of the most demand of mathematical statistics in psychological and educational research. Formally simple, this method allows you to get a lot of information and make the same errors. In this article we will look at the nature of the correlation coefficient, its properties and types. The correlation coefficient is a measure of the relationship of the measured phenomena. The correlation coefficient (denoted «r») is calculated by a specific formula and changes from -1 to +1. Figures close to 1 indicate that an increase in the value of one variable increases the value of another variable. Figures close to -1 indicate the inversed relationship, i.e. by increasing the value of one variable, the other values are reduced.
We use MS Excel to test the relationships between the pairs.
According to the analysis we see that the coefficient of correlation is almost 0 in both cases. This means that there is no real association between age and completing time of the tasks. Some older people are faster than younger and vice versa – there is no concrete relationship.
Now about number of errors and age:
We can say that there is a weak positive association between Age and number of errors. Sometimes older people do more mistakes than younger.
References
Schervish, Mark J. (1995). Theory of statistics (Corr. 2nd print. ed.). New York: Springer. ISBN 0387945466.
Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression. Boston: Addison-Wesley.
"Karl Pearson (1857–1936)". Department of Statistical Science – University College London.
Lund Research Ltd. "Descriptive and Inferential Statistics". statistics.laerd.com. Retrieved 2014-03-23.
Hand, D. J. (2004). Measurement theory and practice: The world through quantification. London, UK: Arnold.
