Assignment | What Are Psychological Statistics?

Running head: PSYCH STAT 3200 1
PSYCH STAT 3200
Student’s Name
Institutional Affiliation

PSYCH STAT 3200 2
1. A student is interested in determining how well people can predict the flip of a coin, specifically if they
predict the outcome at a significantly greater rate than 50%. She has 15 volunteers flip a coin 50 times
predicting the outcome of each flip. The student records the percentage of the time the volunteers
correctly predicted their coin flip.
a. State the null and alternative hypothesis.
Null Hypothesis (Ho): The percentage of the time the volunteers correctly predicted their coin
flip is equal to 50%
Alternative Hypothesis (H1): The percentage of the time the volunteers correctly predicted their
coin flip is greater than 50%
In terms of symbols, it can be expressed as;
The hypothesis is Ho: μ =50, H1: μ >50
b. State a research question for the data.
Is the predicted outcome of flipping a coin significantly greater rate than 50%?
c. Did the volunteers predict their flips at a rate different from 50%?
No. Because the p-value of .085 it implies that there was no statistically significant difference at
alpha=.05.
d. What is the effect size and how would you categorize that effect?
According to Rosenthal (2014), the Cohen's dz can be calculated directly from checking the t-
value and the number of respondents in the experiment.
Cohen's dz = t/√n
Therefore from the resultant table t=-1.852 and n=15.
Thus Cohen's dz= 1.852/SQRT(15) =0.4781
According to (Cohen, 2013) one can interpret the value of effect size d as follows;
Value of d=0.8 implies a large effect with a mean difference of 0.8 standard deviation
Value of d=0.5 implies a medium effect with a mean difference of 0.5 standard deviation
Value of d=0.2implies a small effect with a mean difference of 0.2 standard deviation
The effect size is d=0.4781.This case is approximately 0.5 (1 decimal place)
This suggests a medium effect size
e. Write the results of the study using APA format as appropriate.

PSYCH STAT 3200 3
The flipping coin experiment resulted in (M =48.07, SD = 4.04) with a t(14) = -1.852,p=.085.
The probability value .085>.05 which is the selected alpha level hence we do not the null
hypothesis.
This, therefore, implies that there exists sufficient evidence to conclude that the predicted outcome
of flipping a coin is equal to 50%?
Table 1: One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
predictablecorrectyble 15 48.0667 4.04381 1.04411
Table 2: One-Sample Test
Test Value = 50
t df Sig. (2-tailed)
Mean
Difference
95% Confidence Interval of
the Difference
Lower Upper
predictablecorrectyble -1.852 14 .085 -1.93333 -4.1727 .3061
2. Researchers are interested in comparing different treatment modalities and their effect on depression. A
group of participants was divided into three treatment conditions. One group received psychotropic anti-
depressant medication, the second group received eight weeks of psychotherapy for depression, the third
group acted as a control group and received no treatment whatsoever. Participants were asked to rate
their depression levels weekly throughout the treatment. The participants average depression level was
then recorded for each condition for comparison.
a. State the null and alternative hypothesis.
Null Hypothesis (Ho): The treatment modalities (psychotropic anti-depressant medication, the
psychotherapy for depression) have no significant influence on the depression level.
Alternative Hypothesis (H1): The treatment modalities (psychotropic anti-depressant medication,
the psychotherapy for depression) have a significant influence on the depression level.
b. State a research question for the data.
Do the various treatment modalities (psychotropic anti-depressant medication, the psychotherapy
for depression) have a significant influence on the depression levels?
c. Test the assumption of equal variances. Do the data suggest unequal variance between the
groups?
The equality of variance assumption is tested using the Levene test