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Basic Statistics
Tim Horn
AIDSmeds.com/ATAC
[email protected]
Overview
Statistics defined
Mean, Median & Mode
Ranges
Standard Deviation
Standard Error
Confidence Intervals
Hypotheses and P-values
Risk Ratios
Statistics Defined
 The mathematics of the collection,
organization, and interpretation of numerical
data, especially the analysis of population
characteristics by inference from samples
Population: a complete set of people to be studied.
e.g. All people living with HIV
Sample: a smaller part of that population
 Using research involving a sample, statistics
can draw conclusions or make predictions
about what may happen in the larger
population
Mean, Median & Mode
Mean, Median & Mode
Three kinds of “averages” in statistics:
Mean
Median
Mode
All numbers in a set of data fall within a
range
Mean Example
J Acquir Immune Defic Syndr. 2010 Apr 1;53(4):456-63.
Long-term efficacy and safety of the HIV integrase inhibitor raltegravir in patients with limited
treatment options in a Phase II study.
Gatell JM, Katlama C, Grinsztejn B, Eron JJ, Lazzarin A, Vittecoq D, Gonzalez CJ, Danovich RM, Wan
H, Zhao J, Meibohm AR, Strohmaier KM, Harvey CM, Isaacs RD, Nguyen BY; Protocol 005 Team.
Abstract
BACKGROUND: Raltegravir in combination therapy has demonstrated potent suppression of HIV-1
with a favorable safety profile. This report provides 96-week efficacy and safety data from Protocol
005, a Phase II study. METHODS: HIV-infected patients with very limited treatment options and
failing antiretroviral therapy were randomized to raltegravir 200, 400, or 600 mg or placebo b.i.d.,
plus optimized background therapy for >or=24 weeks; all patients were then offered open-label
raltegravir 400 mg b.i.d. Efficacy measurements included changes in viral load and CD4 count
from baseline and percent of patients with HIV-1 RNA <400 and <50 copies/mL. RESULTS: One
hundred and thirty-three patients received raltegravir and 45 received placebo. No dosedependent differentiation in the safety or antiviral activity of raltegravir was observed during the
double-blind phase. For the combined raltegravir groups, mean change in viral load from baseline
was -1.60 log10 copies/mL at week 48 and -1.38 log10 copies/mL at week 96 (observed failure
approach). At week 48, HIV-1 RNA levels were <400 copies/mL in 68% of raltegravir recipients
and <50 copies/mL in 55%; these levels were maintained in 55% and 48% of raltegravir
recipients, respectively, at week 96 (noncompleter = failure). There were few discontinuations of
raltegravir (4%) due to adverse events. CONCLUSIONS: In patients with limited treatment
options, raltegravir with OBT had a potent and sustained antiretroviral effect and was generally
well tolerated through 96 weeks.
Mean
The mean is the average you're used to,
where you add up all the numbers and
then divide by the number of numbers
11 injection drug users (IDUs) who tested
positive for HIV at the following ages:
19, 24, 32, 32, 27, 29, 21, 32, 36, 39, 31
(19, 24, 32, 32, 27, 29, 21, 32, 36, 39, 31)
÷ 11 = 29
Median Example
AIDS Patient Care STDS. 2010 Apr 8. [Epub ahead of print]
Hepatitis B Virus Drug Resistance in HIV-1-Infected Patients Taking Lamivudine-Containing
Antiretroviral Therapy.
Wongprasit P, Manosuthi W, Kiertiburanakul S, Sungkanuparph S.
1 Department of Medicine, Faculty of Medicine, Ramathibodi Hospital, Mahidol University , Bangkok, Thailand
.
A cross-sectional study was conducted in HIV-1-infected patients receiving lamivudine-containing
antiretroviral therapy (ART) to determine the prevalence and risk factors of hepatitis B virus drug
resistance (HBV-DR). HBV DNA and HBV genotypic resistance test were performed. Patients were
categorized into two groups: with and without HBV-DR. There were 84 patients with a mean age
(standard deviation [SD]) of 42.2 (10.2) years and 77% were males. Median (range) duration of ART and
lamivudine use was 46 (3-177) and 40 (3-140) months, respectively. Median (range) CD4 cell count was
352 (49-790) cells/mm(3). Of all, 19 (23%) had HBV-DR with a median (range) HBV DNA of 2.56 x 10(7)
(2.54 x 10(3)-11 x 10(7)) IU/mL. In univariate analysis, there were no differences in age, gender, ART
regimen, liver function test, anti-HBc antibody, anti-HCV antibody between the two groups. Patients with
HBV-DR had a higher proportion of positive HBeAg (68.4% versus 3.8%, p < 0.001). In multivariate
analysis, positive HBeAg (odds ratio [OR) 16.64; 95% confidence interval [CI], 3.31-83.60] and duration
of lamivudine use [per 6-month increment, OR 1.24; 95% CI, 1.06-1.36] were significant risk factors for
HBV-DR. All 19 patients with HBV-DR had lamivudine resistance with the mutations as follows: M204V/I
(95%), L180M/A181T (95%), L80V/I (47%), V173L (32%), and N236T (21%). Of these, 95%, 84%, 84%,
and 0% of patients had HBV-DR to telbivudine, entecavir, adefovir, and tenofovir, respectively. HBV-DR is
common in HBV/HIV-1 coinfected patients receiving lamivudine-containing ART without tenofovir.
Positive HBeAg and longer duration of lamivudine use are risk factors for HBV-DR. In addition to
lamivudine resistance, cross-resistance to other anti-HBV drugs is also frequently observed.
Median
The median is the middle value (age), so
they need to be listed in chronological
order
19, 21, 24, 27, 29, 31, 32, 32, 32, 36, 39
There are 11 numbers in the list, so the
middle one will be the 5th number:
19, 21, 24, 27, 29, 31, 32, 32, 32, 36, 39
The median is 31
Mode
The number (age) that occurs most often
in the group
19, 21, 24, 27, 29, 31, 32, 32, 32, 36, 39
32 is the mode
Rarely used in HIV epidemiology or
treatment research
Ranges and Centiles
Ranges
Median provides no information about
range of values or how values are grouped
around the median
The range
Difference between highest and lowest number
The Interquartile range
Data divided into quarters:
• First quartile (25th centile)
• Second quartile (50th centile)
• Third quartile (75th centile)
Ranges
19, 21, 24, 27, 29, 31, 32, 32, 32, 36, 39
The largest value in the list is 39, and the
smallest is 19, so the range is 39 – 19 = 20
Interquartile Range
19, 21, 24, 27, 29, 31, 32, 32, 32, 36, 39
First quartile is 24
Second quartile is 31 (median)
Third Quartile is 32
IQR: 32-24=8
IQR Example
Infection. 2010 Mar 29. [Epub ahead of print]
Safety and Efficacy of a Saquinavir-Containing Antiretroviral Regimen in Previously ART-Naïve or Pretreated but
Protease Inhibitor-Naïve HIV-Positive Patients.
Knechten H, Stephan C, Mosthaf FA, Jaeger H, Lutz T, Cargnico A, Stoehr A, Koeppe S, Mayr C, Schewe K, Wolf E, Wellmann
E, Tappe A.
Practice Center Blondelstrasse (PZB), Blondelstr. 9, 52062, Aachen, Germany, [email protected].
Abstract
BACKGROUND: The RAINBOW survey is a multinational observational study assessing the tolerability and efficacy of ritonavirboosted saquinavir (SQV/r), using the 500-mg film-coated SQV formulation, in routine clinical practice. This analysis
presents data from the German subgroup of antiretroviral therapy (ART)-naïve and pretreated but protease inhibitor (PI)naïve patients. METHODS: This was a multicenter, prospective, open-label, 48-week observational cohort study. Tolerability
assessments included changes in liver enzymes and lipid levels from baseline to week 48. Efficacy assessments included
changes in the proportion of patients with HIV-1 RNA <50 and <400 copies/ml, and changes in CD4 cell count from baseline
to week 48. RESULTS: The analysis included 275 ART-naïve and 179 pretreated but PI-naïve patients. The proportion of
ART-naïve patients achieving <50 copies/ml by 48 weeks was 53.1% by intent-to-treat (ITT) analysis and 67.3% using last
observation carried forward (LOCF) analysis. In pretreated but PI-naïve patients, the proportions achieving <50 copies/ml by
48 weeks were 53.1% (ITT) and 70.4% (LOCF). The median increase in CD4 count at week 48 was +174 cells/mm(3)
(interquartile range [IQR] 86, 265) in the ART-naïve group and +100 cells/mm(3) (IQR 0, 209) in the pretreated but PI-naïve
group (p < 0.01 for both; LOCF). Drug-related adverse events were reported in 7.6% of ART-naïve and 2.8% of pretreated
but PI-naïve patients. Treatment with SQV/r was stopped in 21.5% of ART-naïve and 17.9% of pretreated but PI-naïve
patients (due to side effects in 3.3% and 2.8%, respectively). There were no clinically relevant changes in liver enzyme
levels. Overall, the total cholesterol, triglyceride, low-density lipoprotein, and high-density lipoprotein levels increased to
week 48, although the levels remained within normal ranges in the majority of patients. CONCLUSIONS: The results of this
observational cohort study of treatment with the 500-mg tablet formulation of SQV are consistent with high efficacy and
tolerability results seen in controlled studies of SQV/r. This analysis confirms that SQV/r is effective and well tolerated in
ART-naïve and pretreated but PI-naïve patients in 'real-world' clinical settings.
Standard Deviation
Standard Deviation (SD)
IQR indicates the variation of data where
the median average is used
Standard deviation (SD) is used when the
mean average is used
Indicates the difference between a group of
values and their mean
The larger the SD, the more spread out the
values
Standard Deviation (SD)
 Represented as number of SDs away from mean
 Approximately 68% of the scores will fall between one SD
above the mean and one SD below the mean; 95% of all
scores will fall between 2 SDs above and below the
mean; 99.7% of scores will fall between 3 SDs above and
below the mean
Standard Deviation (SD)
 Example: The average height for adult men in the U.S.
is about 70 inches, with a SD of around 3 in.
 This means that most men (68%) have a height within
3 in of the mean – one standard deviation, whereas
almost all men (about 95%) have a height within 6 in
of the mean (64–76 in) – 2 standard deviations.
 If the standard deviation were zero, then all men would
be exactly 70 in (178 cm) high.
 If the standard deviation were 20 in, then men would
have much more variable heights, with a typical range
of about 50 to 90 in.
 Three standard deviations account for 99.7% of the
sample population being studied.
Standard Deviation (SD) Example
AIDS Patient Care STDS. 2010 Apr 8. [Epub ahead of print]
Hepatitis B Virus Drug Resistance in HIV-1-Infected Patients Taking Lamivudine-Containing
Antiretroviral Therapy.
Wongprasit P, Manosuthi W, Kiertiburanakul S, Sungkanuparph S.
1 Department of Medicine, Faculty of Medicine, Ramathibodi Hospital, Mahidol University , Bangkok, Thailand
.
Abstract
A cross-sectional study was conducted in HIV-1-infected patients receiving lamivudine-containing
antiretroviral therapy (ART) to determine the prevalence and risk factors of hepatitis B virus drug
resistance (HBV-DR). HBV DNA and HBV genotypic resistance test were performed. Patients were
categorized into two groups: with and without HBV-DR. There were 84 patients with a mean age
(standard deviation [SD]) of 42.2 (10.2) years and 77% were males. Median (range) duration of ART and
lamivudine use was 46 (3-177) and 40 (3-140) months, respectively. Median (range) CD4 cell count was
352 (49-790) cells/mm(3). Of all, 19 (23%) had HBV-DR with a median (range) HBV DNA of 2.56 x 10(7)
(2.54 x 10(3)-11 x 10(7)) IU/mL. In univariate analysis, there were no differences in age, gender, ART
regimen, liver function test, anti-HBc antibody, anti-HCV antibody between the two groups. Patients with
HBV-DR had a higher proportion of positive HBeAg (68.4% versus 3.8%, p < 0.001). In multivariate
analysis, positive HBeAg (odds ratio [OR) 16.64; 95% confidence interval [CI], 3.31-83.60] and duration
of lamivudine use [per 6-month increment, OR 1.24; 95% CI, 1.06-1.36] were significant risk factors for
HBV-DR. All 19 patients with HBV-DR had lamivudine resistance with the mutations as follows: M204V/I
(95%), L180M/A181T (95%), L80V/I (47%), V173L (32%), and N236T (21%). Of these, 95%, 84%, 84%,
and 0% of patients had HBV-DR to telbivudine, entecavir, adefovir, and tenofovir, respectively. HBV-DR is
common in HBV/HIV-1 coinfected patients receiving lamivudine-containing ART without tenofovir.
Positive HBeAg and longer duration of lamivudine use are risk factors for HBV-DR. In addition to
lamivudine resistance, cross-resistance to other anti-HBV drugs is also frequently observed.
Standard Error
Standard Error (SE)
 The standard error (SE) is important in
describing how well the sample mean
represents the true population mean
Every random sample will give a slightly different
estimation of the whole population
SE gives you a measure of how precise your sample
mean is compared to the true population mean
Calculated by the standard deviation divided by the
square root of the mean
Depends on the sample size. As the sample size gets
larger, then variability gets smaller, yielding more
precise measurement of the truth
Standard Error Example
CROI Paper 972
Life Expectancy of Persons at the Time of Initiating cART in High-income Countries
Robert Hogg and Antiretroviral Cohort Collaboration
BC Ctr for Excellence in HIV/AIDS and Simon Fraser Univ, Vancouver, Canada
Background: To characterize changes in mortality and life expectancy among HIV + persons initiating combination ART
(cART).
Methods: The Antiretroviral Cohort Collaboration (ART-CC) is a multinational cohort study of ART-naive patients
initiating cART in Europe and North America. Patients were included in this analysis if they were on cART for at
least a year. The primary endpoint was all-cause mortality. Abridged life tables were constructed to estimate life
expectancies among ART-naive persons at the time of initiating cART in 3 periods 1996-1999, 2000-2002, and
2003-2005. These tables were stratified by gender, baseline CD4 cell count, and history of injection drug use. For
this exercise, the expectation of life at age 20 years was reported and refers to the average number of years
remaining to be lived by those initiating cART at that age. Potential years of life lost from 20 to 65 years and crude
death rates were also calculated for this exercise.
Results: A total of 14,993, 9895, and 3614 patients initiated and were on cART for at least 1 year in 1996-1999, 20002002, and 2003-2005, respectively. A total of 1531 (5.4%) deaths were observed in this population during the study
period with crude death rates decreasing from 45.1 deaths per 1000 person years in 1996-1999 to 27.8 deaths per
1000 person-years in 2003-2005. Potential years of life lost per 1000 person-years also decreased over the same
time interval from 1796.7 to 1296.2. Life expectancy at exact age 20 years increased from 24.3 years (standard
error, SE, 0.8) to 33.2 (SE 0.8) during this time span. Life expectancy levels were comparable for men and women
at 33.5 years (SE 1.2) and 33.0 years (SE 1.3), respectively in 2003-2005. Patients with a history of injection drug
use had significantly lower life expectancies than those from other transmission groups (28.2 years, SE
1.0, vs 34.7 years, SE 0.9, in 2003-2005). During 2003-2005, life expectancy decreased at lower baseline CD4
counts, ranging from 38.3 years (SE 0.8) for those with baseline CD4 counts of ≥350 cells/mm 3 to 30.9 (SE 1.3)
for those with baseline CD4 counts of <200 cells/mm 3.
Conclusions: The average number of years remaining to be lived by those initiating cART at age 20 years were
approximately half those observed among the general population in these countries. In the United States, life
expectancy at age 20 years was 58.3 years in 2003.
Confidence Intervals
Confidence Intervals (CIs)
 CIs used to estimate how far away the
population mean is likely to be from the
sample mean, with a degree of certainty
 A CI is an estimate of the spread between the
lowest likely result (lower confidence limit)
and the highest likely result (upper
confidence limit) of a study
The true result of the study probably lies somewhere
within this CI
The smaller the spread of the confidence interval, the
more precise the result is likely to be
Confidence Intervals (CIs)
Most research studies display results
using 95% CI
i.e., there is a 95% chance that the true study
result lies between these two confidence limits
Uses standard error
The mean plus or minus two times the standard
error
Confidence Intervals (CIs)
In a hypothetical example, it may be
reported that "The estimated number of
people living with HIV among a group of
IDUs was 18.6% with a 95% CI of 12.924.0.”
This means that the study investigators are
95% sure that the true prevalence lies
somewhere between the two confidence limits
of 12.9% and 24.0%
Confidence Intervals (CIs) Example
N Engl J Med. 2009 Dec 3;361(23):2209-20. Epub 2009 Oct 20.
Vaccination with ALVAC and AIDSVAX to prevent HIV-1 infection in Thailand.
Rerks-Ngarm S, Pitisuttithum P, Nitayaphan S, Kaewkungwal J, Chiu J, Paris R, Premsri N, Namwat C, de Souza
M, Adams E, Benenson M, Gurunathan S, Tartaglia J, McNeil JG, Francis DP, Stablein D, Birx DL, Chunsuttiwat
S, Khamboonruang C, Thongcharoen P, Robb ML, Michael NL, Kunasol P, Kim JH; MOPH-TAVEG Investigators.
Abstract
BACKGROUND: The development of a safe and effective vaccine against the human immunodeficiency virus type 1
(HIV-1) is critical to pandemic control. METHODS: In a community-based, randomized, multicenter, double-blind,
placebo-controlled efficacy trial, we evaluated four priming injections of a recombinant canarypox vector vaccine
(ALVAC-HIV [vCP1521]) plus two booster injections of a recombinant glycoprotein 120 subunit vaccine (AIDSVAX
B/E). The vaccine and placebo injections were administered to 16,402 healthy men and women between the ages
of 18 and 30 years in Rayong and Chon Buri provinces in Thailand. The volunteers, primarily at heterosexual risk
for HIV infection, were monitored for the coprimary end points: HIV-1 infection and early HIV-1 viremia, at the end
of the 6-month vaccination series and every 6 months thereafter for 3 years. RESULTS: In the intention-to-treat
analysis involving 16,402 subjects, there was a trend toward the prevention of HIV-1 infection among the vaccine
recipients, with a vaccine efficacy of 26.4% (95% confidence interval [CI], -4.0 to 47.9; P=0.08). In the per-protocol
analysis involving 12,542 subjects, the vaccine efficacy was 26.2% (95% CI, -13.3 to 51.9; P=0.16). In the
modified intention-to-treat analysis involving 16,395 subjects (with the exclusion of 7 subjects who were found to
have had HIV-1 infection at baseline), the vaccine efficacy was 31.2% (95% CI, 1.1 to 52.1; P=0.04). Vaccination
did not affect the degree of viremia or the CD4+ T-cell count in subjects in whom HIV-1 infection was subsequently
diagnosed. CONCLUSIONS: This ALVAC-HIV and AIDSVAX B/E vaccine regimen may reduce the risk of HIV
infection in a community-based population with largely heterosexual risk. Vaccination did not affect the viral load or
CD4+ count in subjects with HIV infection. Although the results show only a modest benefit, they offer insight for
future research. (ClinicalTrials.gov number, NCT00223080.) 2009 Massachusetts Medical Society
Putting it All Together
CD4 Cell Counts in Random Sample of 50 PLWHIV
Putting it All Together
CD4 Cell Counts in Random Sample of 50 PLWHIV
Putting it All Together
CD4 Cell Counts in Random Sample of 50 PLWHIV
Hypotheses and P-Values
Hypotheses and P-values
A study begins with a null hypothesis and
an alternative hypothesis
Null: Isentress plus OBT is no more effective
than OBT alone in keeping VL <50 copies for 48
wks
Alternative Isentress plus OBT more effective
than OBT alone in keeping VL <50 copies for 48
wks
Researchers always hope to reject the null
hypothesis and prove the alternative
hypothesis
Hypotheses and P-values
 After data are collected, statistician calculates
p-value
Determines whether the study supports the null or
alternative hypotheses
P-value is the probability that these results would
occur if there was truly no difference between the
groups -- that is, how likely the results would have
been observed purely by chance
P-values are between 0 and 1; the closer to zero the
less likely the null hypothesis is true
Closely tied to the confidence interval
Hypothesis and P-values
 65% of pts. receiving Isentress/OBT have VLs <50
after 48 weeks, vs. 35% receiving OBT w/out
Isentress
 P-value is 0.01 (P=0.01)
Represents 1 in 100 probability that the null hypothesis
is true – a very small, highly significant (statistical)
difference.
 A statistical significance level below 5% is
considered to be “good enough.” However, if the
findings are likely to have very important
consequences for medical interventions or public
policy, a lower p-value is demanded (e.g.,
p < 0.01).
Hypothesis and P-values
P-values and CIs often reported together
The p-value is a single number that guides
whether or not to reject the null hypothesis
The 95% CI provides a range of plausible
values for describing the underlying population
If CIs do not overlap, differences are statistically
significant
If CIs do overlap, differences may not be statistically
significant
Risk Ratios
Relative Risk (RR)
Risk of an event (or of developing a
disease) relative to exposure. Relative risk
is a ratio of the probability of the event
occurring in the exposed group versus a
non-exposed group
Generally used in randomized controlled
trials and cohort studies
Not the same as absolute risk!
Relative Risk (RR)
 A relative risk of 1 indicates a lack of
difference between the two groups in terms of
risk (e.g., RR=1.0)
 A relative risk less than 1 indicates the trait
has a lesser likelihood of being expressed in
the experimental group than in the control
group (e.g., RR=0.7)
 A relative risk greater than 1 indicates the
trait has a greater likelihood of being
expressed in the experimental group than in
the control group (e.g., RR=1.16)
Relative Risk – D:A:D Example
The RR of chronic kidney disease (CKD)
increases by 16% per year among those
taking regimens containing tenofovir (e.g.,
Atripla)
Compared to the same person’s underlying risk
of CKD (and never exposed to tenofovir)
Relative Risk – D:A:D Example
 If a person has an underlying absolute risk of
0.50 percent for developing CKD within the
next 12 months one year of tenofovir
exposure would lead to a 16% relative
increase in the absolute risk of CKD – i.e. an
absolute risk of 0.58 percent (0.5x1.16)
 If a person has an underlying absolute risk of
20% for developing CKD in the next 12
months, one year of tenofovir exposure would
lead to an increase in this absolute of CKD to
23.2%
Hazard Ratio
Broadly equivalent to relative risk (RR);
useful when the risk is not constant with
respect to time. It uses information
collected at different times.
The term is typically used in the context of
survival over time.
If the HR is 0.5 then the relative risk of
dying in one group is half the risk of dying
in the other group
Odds Ratio (OR)
Like RR and HR, the OR compares the
likelihood of an event or treatment effect
between two groups
Often used in case-controlled and
retrospective studies
When events are rare the OR is analagous
to the relative risk (RR), but as event rates
increase the OR and RR diverge
Risk Ratios: Putting it All Together
In a randomized trial of 100 patients given
a study drug to prevent PCP (50 given
placebo and 50 given study drug)
PCP
No PCP
Total
Placebo
10
40
50
Study
drug
5
45
50
Risk Ratios: Putting it All Together
 Absolute Risk of PCP if given placebo:
10/50 = 0.2 or 20%
 Absolute Risk of PCP if given study drug:
5/50 = 0.1 or 10%
 Relative risk of PCP if given study drug:
0.1 / 0.2 = 0.5 or 50%
Difference in absolute risk of PCP if given
study drug:
0.1 - 0.2 = -0.1 or 10% reduction
PCP
No PCP
Total
Placebo
10
40
50
Study drug
5
45
50
Risk Ratios: Putting it All Together
Odds of PCP if given placebo:
10:40 = 1:4 or 0.25
Odds of PCP if given study drug:
5:45 = 1:9 or 0.11
Odds ratio of PCP if given study drug:
0.11 / 0.25 = 0.44
PCP
No PCP
Total
Placebo
10
40
50
Study drug
5
45
50
Other Terms
Incidence: The number of new cases of a
particular disease or condition over a
defined period of time (e.g., new HIV
infections occurring in 2009).
Prevalence: The overall number of cases
of a particular disease over a defined
period of time (e.g., total number of people
living with HIV in 2009).
Presenting Data
A variety of graph styles can be used to
present data
Used to convey the importance of data
quickly
Graphs should be simple and easy
Presenting Data: Graphs
Pie Chart
New HIV/AIDS cases in 2005, by race
Compare part of a whole at a given point in time.
Line Chart
Estimated number of deaths among adults with AIDS, 1985–1999, United States
To find and compare trends (changes over time)
Bar Graph
Women Aged 18 and Older who Have Ever Been Tested for HIV, by
Race/Ethnicity, 2007
Used to compare frequencies (percentage of women testing for HIV) in
different categories (race/ethnicity)
Bar Graph
Adults Aged 18 and Older who Have Ever Been Tested for HIV, by Age and Sex,
2007
Used to compare two frequencies (percentage of men and women testing for
HIV) in different categories (age)
Histogram
AIDS cases, by age and sex, reported 1981–2000, United States
A bar chart representing a frequency distribution; heights of the bars represent
observed frequencies
Box-and-Whiskers Plot
Total abdominal fat among patients on ARV treatment with lipodystrophy, on
ARV treatment w/out lipodystrophy and HIV-negative controls
A convenient way of graphically depicting five sets of data: the smallest observation
(sample minimum), first quartile, second quartile (median), third quartile, and
largest observation (sample maximum).