The Skew Statistic Biostatistics Questions

1. The tables and charts below summarize daily sugar intake (g) among the adults in the
NHANES 2001 dataset. Use this information to answer the following questions. (8 points)
a. How many subjects are included in this analysis?
b. What level of sugar intake separates the top and bottom half of the sample?
c. What is the range of sugar intake associated with the middle 50% of this sample?
d. Using the Descriptives table, comment on the symmetry of the distribution:
1) based on the appearance of the histogram
2) based on the relationship between the mean and median
3) based on the skew statistic
4) based on the relationship between the mean and the standard deviation
5) Using 1-4, come to a final conclusion as to whether the dist’n is skewed.
Descriptives
Statistic Std. Error
Total sugars (gm) Mean
128.1562 3.60412
95% Confidence Interval Lower Bound 121.0759
for Mean
Upper Bound 135.2365
5% Trimmed Mean
121.1260
Median
112.1200
Variance
6819.567
Std. Deviation
82.58067
Minimum
2.95
Maximum
589.53
Range
586.58
Interquartile Range
93.78
Skewness
1.628
.107
Kurtosis
4.482
.213
2. Suppose the mean bone height following a new grafting procedure was 10.0 mm and
that the SD was 3.0 mm (5 points).
a. What are the approximate 95% confidence limits defining the range of raw values?
b. Suppose a minimum of 7 mm is needed for a successful dental implant placement. What
proportion of bones treated with this procedure are estimated to provide adequate height?
c. The bone in one subject was measured as 5 mm. What is the approximate rate of occurrence
of a bone at least this tall?
d. The bone from another subject is described as being in the top 16%; at a minimum, how tall
(in mm) was that bone?
e. What distributional assumption would these data need to satisfy for the estimates in (2a-d) to
be accurate?
3. The table below summarizes household size reported by the adults in the NHANES
2001 dataset. Use this information to answer the following questions.
a. How many households had exactly 4 members?
b. What proportion of households had 4 or fewer members?
c. What is the difference between ‘Percent’ and ‘Valid Percent’ in SPSS output?
d. Estimate the median number of people per household.
4. a. In addition to type 1 and 2 error rates, what (2) other quantities are needed to do a power
analysis?
b. Other things equal, what is the effect on power of decreasing alpha (say from .05 to .01)?
c. Other things equal, what is the effect on power of using a 1-tail, rather than, 2-tail, test?
5. (6 points) The mean blood sugar level in a sample of type 2 diabetics in one sample
was reported to be 8 mg/dL and the US population µ (σ) are known to be 10 (2).
a. Set up the 4 steps in a traditional test of the hypothesis that the sample is less than
the population at a .05 significance level.
i.
ii.
iii.
iv.
The significance test then showed that the test result had a 10% probability of
occurrence in the sampling distribution.
Select the correct item: We tested whether the blood sugar levels of type 2 diabetics in this
sample were similar to that reported in the population. We (rejected, failed to reject) the null
hypothesis, implying that the sample value was (less than, different from, similar to) the national
mean of 10.
6. Dr. D. has grown colonies of P gingivalis (Pg) exposed to several compounds thought
to be anti-Pg (A, B and C), as well as a negative (NC) and positive (PC-CHX) controls. She
wants to know which compounds, if any, are anti-microbial. Using the SPSS output
below, answer the following.
a. Which groups are compared?
b. Do these data satisfy the assumption of homogeneous variances (Y or N)?
c. What is the correct p-level for the comparison of these means with a t-test?
d. If alpha was set at .05, these data lead one to (reject, fail to reject) the hypothesis that
these two means are equal.
7. Using the bar graph below and α= .05,
a. (reject, do not reject) Ho: mean NC = mean C?
b. (reject, do not reject) Ho: mean NC = mean B?
8. A paper reports the 95% CL in a normal sampling distribution of 25 individuals to be
(90,110). What is the SD in the raw score distribution (you may approximate z to the
nearest integer)?
9. (2 pts). Dr. N never uses any correction when doing post-hoc tests. Dr. B
always uses a Bonferroni correction and Dr. T always uses the Tukey HSD. Order
the 3 good doctors (careful, there might be ties),
a. first, with regard to the increasing risk of a type 2 error, and
b: second, wrt increasing risk of making a type 1 error.
10. It is hypothesized that alcohol and beta blocker (BB) use may have interacting
effects on HDL (high density lipoprotein) levels in the blood. To investigate this, a
2 way ANOVA was performed with HDL level as the dependent variable, and
alcohol and blocker use (both binary) as independent variables. What aspect of the
figure provides visual evidence that BB use interacts with EtOH use?
NO,
EtOH
Yes,
EtO
H
11. Fix at least 5 errors in content or interpretation based on the table below. Dr.
D. grew colonies of P. Gingivalis (Pg) and exposed them to several compounds thought
to be anti-Pg (A, B and C), as well as a negative (NC) and positive (PC-CHX) controls.
Inspection of the distributions in each treatment group (n= 6) showed some asymmetry
and potentially heterogeneous variances (below). Given the sample size, one can be
confident that the skewness seen in the raw data was not carried over to the sampling
distributions. The means for compound C, NC and PC were ordered as hypothesized.
One-way ANOVA showed at least one pair of means was different from each other
F(4,25)= 13.2, P= .000). Post-hoc Tukey tests then showed that compound C had an
effect that was intermediate to and statistically different from both the NC or the PC
(below). These data suggest that compounds A and B are anti-microbial.
ANOVA
P gingivalis colonies (per mg; log10)
Sum of
Squares
Mean
df
Square
Between Groups
43.501
4
10.875
Within Groups
20.615
25
.825
Total
64.115
29
F
13.189
Sig.
.000
Complete any four (4) of the following:
12. Name the specific measurement scale implied by the valid arithmetic shown in each
of the following:
a. (3 – 2) = (2 – 1)
b. 1 ≠2 ≠ 3
c. 2 + 2 ≈ 4
13. Dr. B measures temperature under control and experimental treatment conditions.
What statistical test would you use to determine the significance of mean effects, if:
a. 5 different samples were used for each treatment
b. the same 5 samples were tested under both conditions
14. Why is the null hypothesis always stated to indicate no effect?
15. Under circumstances where the raw data are skewed, what statistical principle can
you invoke to justify using a t-test to compare mean differences between samples each
composed of 30 or more individuals?
16. After computing descriptive statistics for a set of 40 scores, you discover a typing
error and the highest score was actually a bit smaller, but still highest. How would
correcting this error affect each of the following (ie, less, equal, or greater)?
a. median
b. SD
17. You read a study that reports a a statistical test result based on 1000 people with a p
between .01 and .05, ie, .01 < p < .05. Given what you know about power analysis, what concern should you have about the importance of these results?