Statistic and Public Health

Dr. MPH José Ivo O. Contreras Briceño

Statistics

What are Statistics? One single item or datum in a collection of items A quantity that is computed from a sample A branch of mathematics concerned with

collecting, organizing, summarizing and analyzing data.

Origins of the Term

Originally, “statistics” referred to the collection of information about and for the “State”

Reasons for Studying Statistics

Decision making We must have some information In healthcare we use statistics to:

Find out why patients come to the facility Cost of taking care of patients Quality of care given Required by accrediting agencies Required by third party payors Prioritizing needed services Maintain physician specialty mix

How do they get to the knowledge?

Must have the data Unprocessed facts and figures

Data leads to information Data that have been deliberately selected,

processed, and organized to be useful Information leads to the facts

A piece of information presented as the truth Facts lead to knowledge

What we know

Descriptive Statistics versus Inferential Statistics

Descriptive Statistics Describe what the data show

Inferential Statistics Help us make inferences or draw conclusions

from a small group of data to a large group

Types of Statistics/Analysis

Descriptive Statistics

Frequencies Basic measurements

Inferential Statistics Hypothesis Testing Correlation Confidence Intervals Significance Testing Prediction

Describing a phenomena

How many? How much?

BP, HR, BMI, IQ, etc.

Inferences about a phenomena

Proving or disproving theories

Associations between phenomena

If sample relates to the larger population

E.g., Diet and health

Descriptive Statistics

Descriptive statistics can be used to summarize and describe a single variable (aka, UNIvariate) Frequencies (counts) & Percentages

Use with categorical (nominal) data Levels, types, groupings, yes/no, Drug A vs. Drug B

Means & Standard Deviations Use with continuous (interval/ratio) data

Height, weight, cholesterol, scores on a test

Sample vs. Population

Population Sample

Descriptive Statistics

Class A--IQs of 13 Students

102 115

128 109

131 89

98 106

140 119

93 97

110

Class B--IQs of 13 Students

127 162

131 103

96 111

80 109

93 87

120 105

109

An Illustration:

Which Group is Smarter?

Each individual may be different. If you try to understand a group by remembering the qualities of each member, you become overwhelmed and fail to understand the group.

Descriptive Statistics

Which group is smarter now?

Class A--Average IQ Class B--Average IQ

110.54 110.23

They’re roughly the same!

With a summary descriptive statistic, it is much easier to answer our question.

Descriptive Statistics

Types of descriptive statistics: Organize Data

Tables Graphs

Summarize Data Central Tendency Variation

Descriptive Statistics

Types of descriptive statistics: Organize Data

Tables Frequency Distributions Relative Frequency Distributions

Graphs Bar Chart or Histogram Stem and Leaf Plot Frequency Polygon

Descriptive Statistics

Summarizing Data:

Central Tendency (or Groups’ “Middle Values”) Mean Median Mode

Variation (or Summary of Differences Within Groups) Range Interquartile Range Variance Standard Deviation

Mean

Most commonly called the “average.”

Add up the values for each case and divide by the total number of cases.

Y-bar = (Y1 + Y2 + . . . + Yn) n

Y-bar = Σ Yi n

Median

2. If the recorded values for a variable form a symmetric distribution, the median and mean are identical.

3. In skewed data, the mean lies further toward the skew than the median.

Mean

Median

Mean

Median

Symmetric Skewed

Mode

The most common data point is called the mode.

The combined IQ scores for Classes A & B:80 87 89 93 93 96 97 98 102 103 105 106 109 109 109 110 111 115 119 120

127 128 131 131 140 162

BTW, It is possible to have more than one mode!

A la mode!!

Descriptive Statistics

Summarizing Data:

Central Tendency (or Groups’ “Middle Values”) Mean Median Mode

Variation (or Summary of Differences Within Groups) Range Interquartile Range Variance Standard Deviation

RangeThe spread, or the distance, between the lowest and

highest values of a variable.

To get the range for a variable, you subtract its lowest value from its highest value.

Class A--IQs of 13 Students

102 115

128 109

131 89

98 106

140 119

93 97

110

Class A Range = 140 - 89 = 51

Class B--IQs of 13 Students

127 162

131 103

96 111

80 109

93 87

120 105

109

Class B Range = 162 - 80 = 82

Interquartile Range

A quartile is the value that marks one of the divisions that breaks a series of values into four equal parts.

The median is a quartile and divides the cases in half.

25th percentile is a quartile that divides the first ¼ of cases from the latter ¾.

75th percentile is a quartile that divides the first ¾ of cases from the latter ¼.

The interquartile range is the distance or range between the 25th percentile and the 75th percentile. Below, what is the interquartile range?

0 250 500 750 1000

25% of cases

25% 25% 25% of cases

Variance

A measure of the spread of the recorded values on a variable. A measure of dispersion.

The larger the variance, the further the individual cases are from the mean.

The smaller the variance, the closer the individual scores are to the mean.

Mean

Mean

Standard Deviation

To convert variance into something of meaning, let’s create standard deviation.

The square root of the variance reveals the average deviation of the observations from the mean.

s.d. = Σ(Yi – Y-bar)2

n - 1

Standard Deviation

For Class A, the standard deviation is:

235.45 = 15.34

The average of persons’ deviation from the mean IQ of 110.54 is 15.34 IQ points.

Review:1. Deviation2. Deviation squared3. Sum of squares4. Variance5. Standard deviation

Standard Deviation

1. Larger s.d. = greater amounts of variation around the mean.

For example:

19 25 31 13 25 37

Y = 25 Y = 25

s.d. = 3 s.d. = 6

2. s.d. = 0 only when all values are the same (only when you have a constant and not a “variable”)

3. If you were to “rescale” a variable, the s.d. would change by the same magnitude—if we changed units above so the mean equaled 250, the s.d. on the left would be 30, and on the right, 60

4. Like the mean, the s.d. will be inflated by an outlier case value.

Standard Deviation

Note about computational formulas: Your book provides a useful short-cut formula for

computing the variance and standard deviation. This is intended to make hand calculations as

quick as possible. They obscure the conceptual understanding of

our statistics. SPSS and the computer are “computational

formulas” now.

INFERENTIAL STATISTICS

Inferential statistics can be used to prove or disprove theories, determine associations between variables, and determine if findings are significant and whether or not we can generalize from our sample to the entire population

The types of inferential statistics we will go over: Correlation T-tests/ANOVAChi-square Logistic Regression

Type of Data & Analysis

Analysis of Categorical/Nominal Data Correlation T-tests T-tests

Analysis of Continuous Data Chi-square Logistic Regression

Chi-square

When to use it? When you want to know if there is an association between

two categorical (nominal) variables (i.e., between an exposure and outcome) Ex) Smoking (yes/no) and lung cancer (yes/no) Ex) Obesity (yes/no) and diabetes (yes/no)

What does a chi-square test tell you? If the observed frequencies of occurrence in each group

are significantly different from expected frequencies (i.e., a difference of proportions)

Measures of Population Health

Mortality rate

Is a measure of the number of deaths (in general, or due to a specific cause) in a population, scaled to the size of that population, per unit of time. Mortality rate is typically expressed in units of deaths per 1000 individuals per year; thus, a mortality rate of 9.5 (out of 1000) in a population of 1,000 would mean 9.5 deaths per year in that entire population

The crude death rate

The total number of deaths per year per 1000 people

The perinatal mortality rate

The sum of neonatal deaths and fetal deaths (stillbirths) per 1000 births.

The maternal mortality ratio

The number of maternal deaths per 100,000 live births in same time period.

The maternal mortality rate

The number of maternal deaths per 1,000 women of reproductive age in the population (generally defined as 15–44 years of age) .

The maternal mortality ratio

The number of maternal deaths per 100,000 live births in same time period.

The maternal mortality rate

The number of maternal deaths per 1,000 women of reproductive age in the population (generally defined as 15–44 years of age) .

The infant mortality rate

The number of deaths of children less than 1 year old per 1000 live births.

The child mortality rate

The number of deaths of children less than 5 years old per 1000 live births.

The standardised mortality ratio (SMR)

This represents a proportional comparison to the numbers of deaths that would have been expected if the population had been of a standard composition in terms of age, gender, etc

The age-specific mortality rate (ASMR)

This refers to the total number of deaths per year per 1000 people of a given age (e.g. age 62 last birthday).

Morbidity Rates

Morbidity rates refer to the number of people within a certain unit of the general population who have a certain disease or condition. The unit of population is generally 100,000, although this may vary depending on location and the condition in question. Morbidity rates are used to help determine the overall prevalence of a specific illness, as well as where the most instances of the condition occur when compared to the population as a whole.

Life Expectancy

Summarizes all age-specific mortality rates

Estimates hypothetical length of life of a cohort born in a particular year

This assumes that current mortality rates will continue

Potential Years of Life Lost (PYLL)

PYLL = ( “normal age at death” – actual age at death). Doesn’t much matter what age is chosen as reference; typically 75

Attempts to represent impact of a disease on the population: death at a young age is a greater loss than death of an elderly person

Focuses attention on conditions that kill younger people (accidents; cancers)

All-causes or cause-specific PYLL

Measures of Impact of Interventions to Reduce Inequalities

Population attributable risk: The reduction in mortality that would occur if everyone experienced the rates in the highest socioeconomic group

Population attributable life lost index: The absolute or proportional increase in life expectancy if everyone experienced the life expectancy of the highest SES group

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