Paired Samples Statistics

The provided assignment content discusses the analysis of paired samples statistics, correlations, and tests for sweetness perception after THC treatment. It also explores the influence of cannabinoids on human sweetness perception using a paired-samples t-test. Additionally, it examines the difference in means between Fixed (FW.pick) and decreasing (DW.pick) using a paired t-test and concludes that there is no significant difference. Furthermore, it discusses the descriptive statistics for Fixed (FW.pick) and decreasing (DW.pick), including skewness and kurtosis, which indicates that the data is skewed and non-parametric tests should be used instead of parametric ones.

Question 1:
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 No THC 67.9800 50 8.73999 1.23602
Post THC 72.0400 50 10.40400 1.47135
Paired Samples Correlations
N Correlation Sig.
Pair 1 No THC & Post THC 50 .104 .474
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
No THC -
Post THC -4.06000 12.87524 1.82083 -7.71910 -.40090 -
2.230 49 .030
From the data we found that comparing treatments, Mean Sweetness perception scores
were (higher) to a degree for the Post-THC condition (M = 72.0400, SD = 10.40400) in
comparison to the Baseline condition (M = 67.9800, SD = 8.73999) group.

Question 2:
Correlations
No THC Post THC
No THC
Pearson Correlation 1 .104
Sig. (2-tailed) .474
N 50 50
Post THC
Pearson Correlation .104 1
Sig. (2-tailed) .474
N 50 50
I want to study the dependency of No THC and Post THC. There is no significant linear
relationship between No THC and Post THC with p-value > 0.05 and low value of correlation
coefficient. Since I am applying paired t test I am keen to know about the linear relationship
between No THC and Post THC.
Question 3:
To examine the influence of cannabinoids on human sweetness perception, a paired-
samples t-test was performed, t(-2.230, df=49 p = .015, r=.104), suggesting that post-THC
sweetness perception (did) appear enhanced compared to the no-THC condition.

Question 4:
Consider the null hypothesis, ho: there is no significant difference in the mean between
Fixed (FW.pick) and decreasing (DW.pick). This is tested against alternative hypothesis, h1: the
mean for Fixed (FW.pick) is more than that of decreasing (DW.pick).
The histogram for FW.pick and DW.pick are given below.
The mean for Fixed (FW.pick) and decreasing (DW.pick) are observed to lie between 0 –
50 and 40 – 60. Hence I expect that there is not much significant difference in the mean between
Fixed (FW.pick) and decreasing (DW.pick).
Since data is dependent I apply paired t test. the output is given below.
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 values.FWnpick 54.44 50 53.339 7.543
values.DWnpick 61.76 50 32.707 4.626
Paired Samples Correlations
N Correlation Sig.
Pair 1 values.FWnpick &
values.DWnpick 50 .451 .001
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
values.FWnpick -
values.DWnpick
-
7.320 48.372 6.841 -21.067 6.427 -
1.070 49 .290
With (t = -1.070, df=49) and p-value > 0.05, I fail to reject the null hypothesis and
conclude that there is no significant difference in the mean between Fixed (FW.pick) and
decreasing (DW.pick).

Question 5
The descriptive statistics for Fixed (FW.pick) and decreasing (DW.pick) is given below.
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
values.FWnpick 50 100.0% 0 0.0% 50 100.0%
values.DWnpick 50 100.0% 0 0.0% 50 100.0%
Descriptives
Statistic Std. Error
values.FWnpick
Mean 54.44 7.543
95% Confidence Interval for
Mean
Lower Bound 39.28
Upper Bound 69.60
5% Trimmed Mean 50.91
Median 31.00
Variance 2845.068
Std. Deviation 53.339
Minimum -33
Maximum 194
Range 227
Interquartile Range 71
Skewness 1.054 .337
Kurtosis .383 .662
values.DWnpick Mean 61.76 4.626
95% Confidence Interval for
Mean
Lower Bound 52.46
Upper Bound 71.06
5% Trimmed Mean 60.89
Median 56.00
Variance 1069.778
Std. Deviation 32.707
Minimum 0
Maximum 143
Range 143

Interquartile Range 45
Skewness .400 .337
Kurtosis .005 .662
From the value of skewness I can say that data is skewed. This indicates that I can’t apply
parametric test. Wilcoxon rank sum test for paired samples is counterpart of the paired samples t-
test.
Consider the null hypothesis, ho: there is no significant difference in the median between
Fixed (FW.pick) and decreasing (DW.pick). This is tested against alternative hypothesis, h1: the
median for Fixed (FW.pick) is more than that of decreasing (DW.pick).
With p-value < 0.05, I reject the null hypothesis and conclude that the median for Fixed
(FW.pick) is more than that of decreasing (DW.pick).

Question 6
Consider the null hypothesis, ho: performance and drug MDMA are independent
variables. This is tested against alternative hypothesis, ho: performance and drug MDMA are not
independent variables.
Here both variables performance and drug MDMA are measured on nominal scale of
measurement as they are categorical. Hence I use chi square test of independence to test my
hypothesis. Its test statistic is given by sum (Oi-Ei)^2/Ei. Where Oi is the observed frequencies
and Ei are the expected frequencies.
If p-value is less than alpha (0.05) I reject null hypothesis at 5% level of significance and
conclude that performance and drug MDMA are not independent variables. else if p-value is
greater than alpha (0.05), I fail to reject null hypothesis at 5% level of significance and conclude
that performance and drug MDMA are independent variables.