Question

In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a non-browser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. The data collected are contained in the file Browsing.xlsx. Use a significance level α=0.05α=0.05 to test for differences among mean comfort levels for the three types of browsers. Hint: Refer to Sections 13.2 and 13.3 to help answer this question. (1) State the hypotheses. (2) Use XLSTAT to compute the F test statistic and the p-value. Hint: Select Modeling data > ANOVA. Select cells B1:B25 for “Y / Dependent variables: Quantitative” and select cells A1:A25 for “X / Explanatory variables: Qualitative.” The F test statistic and the p-value are in the last two columns of the Analysis of variance table in the XLSTAT output. (2) What is your hypothesis test decision? Hint: There are two possible decisions: reject H0 in favour of Ha or fail to reject H0. (2) What is your conclusion in the context of the application? Hint: The conclusion should relate back to the question. (4) If the conclusion in part (d) is that the population means are not all equal, use Fisher’s Least Significant Difference (LSD) Procedure to determine which pairs of browser types differ in terms of comfort. Hint: Calculate the sample means for each browser type and the absolute pairwise differences between the means. Then, calculate Fisher’s LSD critical value using the formula LSD=tα/2MSE(1ni+1nj)−−−−−−−−−−−−−√LSD=tα/2MSE(1ni+1nj) , where tα/2tα/2 is a critical value from a t-distribution with nT−k=24−3=21nT−k=24−3=21 degrees of freedom, MSE can be found in the Analysis of variance table in the XLSTAT output, and ni=nj=8ni=nj=8 . Then, see if any of the absolute pairwise differences between the means exceeds the calculated value of LSD. (4) Suppose we are not willing to assume that the populations have a normal distribution with the same standard deviations. Then, we should not use a parametric analysis of variance F-test, but we can instead use a nonparametric Kruskal-Wallis test for differences among median comfort levels for the three types of browsers. Use XLSTAT to compute the H test statistic and the p-value. Is the p-value similar to the corresponding value you obtained in part (b)? Hint: Select Nonparametric tests > Comparison of k samples (Kruskal-Wallis, Friedman, …). Make sure “One column per variable” is checked, select cells B1:B25 for Data, select cells A1:A25 for Sample identifiers, and select “Kruskal-Wallis test.” Under “Options” make sure “Asymptotic p-value” is selected. The H test statistic is labelled “K (Observed value)” in the XLSTAT output.

          In a study conducted to investigate browsing activity by
shoppers, each shopper was initially classified as a non-browser,
light browser, or heavy browser. For each shopper, the study
obtained a measure to determine how comfortable the shopper was in
a store. Higher scores indicated greater comfort. The data
collected are contained in the file Browsing.xlsx. Use a
significance level α=0.05α=0.05 to test for
differences among mean comfort levels for the three types of
browsers.
Hint: Refer to Sections 13.2 and 13.3 to help answer this
question.
(1) State the hypotheses.
(2) Use XLSTAT to compute the F test statistic and the
p-value.
Hint: Select Modeling data > ANOVA. Select cells B1:B25
for “Y / Dependent variables: Quantitative” and select cells A1:A25
for “X / Explanatory variables: Qualitative.” The F test statistic
and the p-value are in the last two columns of the Analysis of
variance table in the XLSTAT output.
(2) What is your hypothesis test decision?
Hint: There are two possible decisions: reject H0
in favour of Ha or fail to reject
H0.
(2) What is your conclusion in the context of the
application?
Hint: The conclusion should relate back to the
question.
(4) If the conclusion in part (d) is that the population means
are not all equal, use Fisher’s Least Significant Difference (LSD)
Procedure to determine which pairs of browser types differ in terms
of comfort.
Hint: Calculate the sample means for each browser type and
the absolute pairwise differences between the means. Then,
calculate Fisher’s LSD critical value using the formula
LSD=tα/2MSE(1ni+1nj)−−−−−−−−−−−−−√LSD=tα/2MSE(1ni+1nj)
, where tα/2tα/2 is a critical value from a
t-distribution with
nT−k=24−3=21nT−k=24−3=21 degrees of
freedom, MSE can be found in the Analysis of variance table in the
XLSTAT output, and
ni=nj=8ni=nj=8 . Then, see if
any of the absolute pairwise differences between the means exceeds
the calculated value of LSD.
(4) Suppose we are not willing to assume that the populations
have a normal distribution with the same standard deviations. Then,
we should not use a parametric analysis of variance F-test, but we
can instead use a nonparametric Kruskal-Wallis test for differences
among median comfort levels for the three types of browsers. Use
XLSTAT to compute the H test statistic and the p-value. Is
the p-value similar to the corresponding value you obtained in part
(b)?
Hint: Select Nonparametric tests > Comparison of k
samples (Kruskal-Wallis, Friedman, …). Make sure “One column per
variable” is checked, select cells B1:B25 for Data, select cells
A1:A25 for Sample identifiers, and select “Kruskal-Wallis test.”
Under “Options” make sure “Asymptotic p-value” is selected. The H
test statistic is labelled “K (Observed value)” in the XLSTAT
output.

Added by James H.

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