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Definition of Biostatistics
- Science that studies biological phenomenons from a quantitative
- point of view (quantitative analysis
- of biological phenomenons)
- n GATHERING OF DATA
- n DATA PROCESSING
- n ANALYSIS AND INTERPRETATION
- n VALIDITY AND GRADE OF TRUST TRIALS
- n ANY CHARACTERISTIC, STUDIED ON A POPULATION THAT
- CAN CHANGE AND WHOSE CHANGE CAN BE MEASURED.
- n Examples: age
- (by order or name)
- (continuous or non continous)
Definition of qualitative variable
- characteristic of a population
- that due to its peculiarity , can not be measured with numbers (it can not be
- quantified by numbers).
- Examples: sex, race,
- religion, civil status, level of
- academic studies
variables: classification according to number of possible values it can
- n DICOTHOMIC (choosing between two): the
- studied variable can only have one value without hierarchy
- between different values (ex.: man/woman; son/daughter).One value excludes
- the other.
- n POLICOTHOMIC OR MULTICOTHOMIC (choosing between more than two): the studied variable can have multiple
- either with or without hierarchy among
- them (socioeconomical level (low, medium, high ), blood
- groups ( A/B/AB/0), colour of the hair
- (black, brown, blonde)
variables classification depending on the
existence of an order (
- Ordinal variable: variable where its values show an order,
- sequence or natural progression.
- days of the week, months of the
- progression or sequence:grade of undernourishment (light, moderate,
- severe), answer to a treatment (good/ bad ), socioeconomical level (low,
- medium, high), alcohol consumption (light, moderate, severe), dental hygiene (good/intermediate/bad)
- Nominal variable: variable where its values
- do not show hierarchy ( order, sequence or natural progression):
- Ex.: names
- of people, races, blood groups, civil status, types
- of teeth( incisor, canine, premolar, molar)
Definition of quantitative variables
- of a population that can be measured with numbers.
- n Ex.:number of children, number of teeth
Quantitative variables classification
- non continuous
of quantitative continuous variable.
- n It can have a whole (entire) or fractioned value (inside a numeric scale) (they refer to items that show a
- n Ex.: age, depth of a gum pocket (4mm, 5,5 mm, normal:3mm), mouth opening (3,5 cm, 2,7 cm )
of quantitative non continuous
- n It can
- only have a whole (entire) value (inside a numeric scale) (they refer to items that can not
- be divided)
- n Ex.: number of teeth (20/32)
of variables according to cause
- n Independent: variable
- causing the effect (Streptoccoccus
- mutans causes dental decay)
- n Dependent: variable due to
- an independent variable (dental decay is caused by Streptoccoccus mutans)
- (dental pain is due to
- sore due to unadjusted dental prosthesis)
of “confusion variable”
- variables that have an influence on the effect, but they are not the main
- stress can increase dental pain due to pulpitis. (stress is a confusion
- variable) deficient dental hygiene can increase
- (but the main cause are bacteria of the mouth), deficient dental hygiene is a
- auftreten, muss aber nicht, wenns auftritt verstärkt es den depending
confusion, depending, indepedendent variable
- variable: stress
- dental pain
- bacteria of the mouth
- deficiet dental hygiene
- parameter, we measure how often a disease occur in a population
- prevalence, -> morbidity,
- percentage, proportion, ratio, relative risk, rate
of incidence and incidence rate
- n Incidence: number of new
- cases of a disease in a certain period of time (ex.: 100 new cases of
- influenza per week)
- n Incidence Rate: number of
- new cases of a disease in a certain period of time/total population X 100 (
- ex.: Incidence Rate of influenza in the population of this city is 8%)
of prevalence and prevalence rate
- n Prevalence: total number of cases (new and previous) in a determined period
- of time.
- n Prevalence Rate: total number of cases ( new and
- previous) in a determined period of time/ total population X 100
- n Ex.: prevalence of influenza infection is 5%( it
- means that 5% of total population is affected)
of “absolute frecuency”
- n They quantify the importance of a disease in a
- community ( total number of people affected).
- n Ex.: absolute frequency of Influenza in the
- population of that city is 850 cases.
- n disadvantage: Absolute data do not provide
- information about the probability to develop the disease (relative risk).
of “relative frequency”
- provide a more complete information about the event we are studying and about
- the risk of the event or disease to
- because they compare absolute data with other data ).
Types of relative frequencies
- ratios and rates
- n Relation between 2 events of the same type, in a
- different geographical area
- n Ex.: number of car accidents in Madrid/ number of
- car accidents in Spain;
- n Number of influenza cases in Valencia/ number of
- influenza cases in Spain.
- n Fraction of total population affected by a disease
- or event, in relation to total population x 100
- (ex.: 35% of adults over 50 years old have
- n Relation between two events of the same type, one
- of them exposed to the risk factor, and the other one non exposed to the risk factor.
- n Each event can be expressed as an absolute or
- relative frecuency.
- n Ex.: number of children with dental decay taking
- sugar/number of children with dental decay not taking sugar.
- n The most common ratio in epidemiological studies
- is RELATIVE RISK (RR).
n Relative risk is a ratio
- n It intends to show the relation between risk
- factors and appearance of diseases.
- n Ex: relative risk to develop cancer of the
- mouth associated with unadjusted dental
- n Ex.: relative risk to develop periodontitis
- associated with deficient oral hygiene.
- n Rate: number of events in relation to total
- population X constant (100-1000)
- n Ex.: mortality rate: number of people died in one
- year/total population X 1000
- n Ex.: birth rate: number of children born alive
- during one year/total population X 1000
- n Ex.: children mortality rate: number of children
- under one year old died during one year/total of born alive in one year X 1000.
- n Rates give us a more complete information about
- the event we are studying, than absolute numbers.They allow us to compare data from different
- populations. Ex.: we can compare mortality rate in Africa (13,2 per 1000 ) and
- in Europe (11,8 per 1000)
types of rate
- - Raw Rate: referred to total population.
- Ex.: mortality rate in Spain is 8/1000. e.g. birth rate, mortaliy rate
- - Specific Rate: referred to a certain part
- of total population. Ex.: mortality rate in age group 40-50 years old in that
- country is 4/1000.
- mortality by age group, morbidity by cause of the disease
define relative risk
relative risk = morbidity rate in the group of exposed people / morbidity rate in the goup of non exposed people -> a/a+b / c/c+d
a/a+b: people with the disease in relation to total of people exposed to the risk factor
c/c+d: people with the disease in relation to total of people non exposed to the risk factor
RR= 1 indicates that the probability to develop the disease is the same in both groups (exposed and non exposed)
RR> 1 indicates that exposed group has higher probability to develop disease than non exposed
- association, random errors (bias), misleading errors (sesgos), confusion
- Show if an
- association exist or not between differen variables
- Absence of
- error due to random (the larger the sample, the more precision; criteria =
of “null hypothesis”
- (Ho): it
- does not exist association or relation
- between 2 studied variables.
of “alternative hypothesis”
- (Ha): it exists association or relation between two
of “hypothesis test”
- = test of
- statistical significance = comparison between the 2 hypothesis
- appears at
- the end of scientific articles when the author is trying to demonstrate that
- his results have a “quality"
- statistical significance -> result is trustable/true
test: how do they work?
- We look at the size (magnitude) of the
- difference ( in the result) between the 2 groups we are studying.
- - we reject Null Hypothesis (=no association
- between 2 variables)
- - we accept Alternative Hypothesis
- - enough evidence to doubt about Null
- - result observed is not compatible with Null
- - it is unprobable to obtain a result like
- the one observed if Null Hypothesis would be true
- - It is unprobable ( unlikely) that the
- result observed would be due to random
- - “P” is minor 0,05 ( p<0.05 )
of “p” value
- to accept “Alternative hypothesis” as being true, when the true hypothesis
- could be “null hypothesis”
- accept/reject a hypothesis has a riskt what we quantify as p value
- The smaller
- the p value, the greater the statistical significance/the more secure is the
- alternative hypothesis
- we have a security of 95% of alternative
- hypothesis being true
Interpretation of “p” value<0.01
- we have a
- security of 99% of alternative hypothesis being true
Interpretation of a small “p” value
- the smaller
- the “p” value is, the greater is the statistical significance of the result of
- the study
Interpretation of “p” value>0.05
- random can
- not be excluded as the cause of the association between 2 variables, that is,
- we can not reject Null hypothesis
- that says
- that both variables are not associated
statistical significance depend on?
- of the difference (the larger the
- difference, the higher the statistical significance), size of the sample (the
- larger the size, the higher the statistical significance)
What is the
relation between “magnitude of the difference” and “statistical
- the larger
- is the difference in the result observed at both groups we are studying, the
- easier is to demonstrate statistical
What is the relation between “size of the
sample” and “statistical significance”?
- the larger
- the size of the sample, the easier is to detect differences in the result
- obtained in both groups we are studying, that is, the easier is to detect
- statistical significance in the result of our study
error in association between variables
- positive, False negative
of error Type I ( false positive)
- This means
- that we say that “it exists a relation between 2 variables”, but that is
- We make
- this error when we reject Null Hypothesis and we are wrong
- we accept
- Alternative Hypothesis but we are wrong.
- Example: We
- make a study and our results show us that there is a relation between
- sweets and
- dental decay found at children. But at this particular case, we are wrong
of error Type II ( false negative)
- This means
- that we say that “it does not exist a relation between 2 variables”, but we
- are wrong
- We make
- this error when we accept Null Hypothesis as real, but it is false.
- we accept
- Null Hypothesis but we are wrong
- Example: We
- make a study and our results show us that there is not a relation
- bad oral
- hygiene and periodontitis found on adults. But in this particular case, we
of random error. Examples
- To happen
- by chance
- Ex.: one
- person could have a cancer by random: he is not exposed to risk factors, he
- is not genetically predisposed, he has not family history related to that
- disease…but cancer just happens.
- In the
- sample that we have chosen out of the general population, there exist a
- certain biological characteristic
- that could influence the result of the study.
- Ex.: a
- sample of people receiving an antihypertensive treatment have responded very
- well because they had a previous excellent condition of their vascular system
- (arteries and veins), and not only because the medicine we have given to them
- has such a fantastic effect to reduce hypertension.
- error (sesgo): in the study we are carrying out we introduce a condition in the observers or in the method of study
- we are using , that will alter the result of the study, thus , giving us a
- wrong information (false result)
- Ex.: If we
- want to diagnose dental decay in children, through the method of detecting a
- “white spot” on the enamel of teeth, and we are using an observer who has
- visual deficit , we are introducing a misleading error in the study.
- Variables that can affect the result of the
- study, but they are not the main cause of the result observed.
- oral hygiene can be a confusion variable when we study periodontitis, where
- the main cause of the disease are the bacteria of the mouth ( and not the
- lack of dental hygiene ).