3. Inferential statistics
• involves making generalizations from a sample to a
population
◼ Estimation
◼ Point Estimation
Mean / proportion
etc.
◼ Interval Estimation
i.e. Confidence interval of
point estimate
◼ Hypotheses Testing
◼ Comparison between
the treatments
◼ Association
◼ Etc.
4. Why Use Statistics?
• Descriptive Statistics
• Identify patterns
• Leads to hypothesis generating
• Inferential Statistics
• Distinguish true differences from random variation
• Allows hypothesis testing
5. Population
• The entire collection of individuals or objects about which
information is desired.
• Populations are determined by our sphere of interest.
• It may be infinite or finite.
• Fixed number of values- finite
• Endless number of values – infinite
• Ex. all human beings, all families joint or nuclear, women of 15- 45
yrs. of age or only a married women
• Such population invariably give qualitative data.
6. • A statistical population may also be birth weight, Hb levels,
thermometer readings, number of RBCs in the human body,
such population mostly gives quantitative data.
7. Sample
• A subset of the population, selected for study in some
prescribed manner.
• Defines as a part of a population.
• Often, a sample of the population is taken, data
collected from it, & inferences about the population are
made based on the analysis of the sample data.
• Sampling unit: each member of a population.
8. • Data collected from a sample that is not representative of the
population will often result in inferences that consistently
overestimate or underestimate some population characteristic;
these are called biased samples.
• On the contrary, unbiased samples are statistically similar to their
parent population, & inference on a population based on unbiased
samples are more reliable than those based on biased samples.
9. • A random sample of n observations is a sample with n
observations, selected in such a way that every such sample of the
population has the same probability of being selected.
• These samples are considered to be unbiased.
• The field of sampling theory deals with the process of selecting
random samples, collecting data from these samples, & analyzing it
to develop inferences about the population as a whole.
10. Variable
• any characteristic whose value may change from one individual
to another.
• A quantity that varies within the limits such as X and notation for
orderly series as X1, X2, X3,….Xn.
• The suffix n is the symbol for number in the series.
• ∑ (sigma) stands for summation or results or observation.
11. Observation
• Observation: an event & its measurements such as bp
(event) & 120mm Hg (measurement)
• observational units: the source that gives observations
such as objects, person, etc.
• In medical statistics the term individuals or subjects is
used more often.
12. Data
• Observations on single variable or simultaneously on two
or more variables.
• A set of values recorded on one or more observational
units.
Experiment: A planned activity whose results yield a
set of data.
Statistic: A numerical value summarizing the sample
data.
13. Parameter:
• A numerical value summarizing all the data of an entire
population such as mean, standard deviation, standard error,
correlation coefficient, proportion, etc.
• This value is calculated from the sample and is often applied
to population but may not be a valid estimate of population.
• Though not desirable, parameter & statistic are often used as
synonyms.
14.
15. Parametric test
• Test is one in which population constants as described above are
used such as mean, variance, etc.
• Data tend to follow one assumed or established distribution such
as normal, binominal, Poisson, etc.
16. Non- Parametric test
• Tests such as X2 test, in which no constant of a population
is used.
• Data do not follow any specific distribution and no
assumptions are made in non-parametric tests,
• Ex – to classify good, better & best you allocate arbitrary
numbers or marks to each category.