Introduction to Statistics

Introduction to Statistics

• A process involved in conducting a statistical study includes preparation, analysis, and conclusion.
• Statistical thinking involves critical thinking and the ability to make sense of data, not just complicated calculations.
• Statistics is the science of planning studies/experiments, obtaining data, organizing, summarizing, presenting, analyzing, and interpreting data to draw conclusions.

Data

• Data are collections of observations like measurements, genders, or survey responses.
• A population is a complete collection of all measurements/data being considered, which inferences are made about.
• A census involves collecting data from every member of a population.
• A sample refers to a subcollection of members selected from a population.
• For instance, in a survey of 410 HR professionals, a sample of 148 felt job candidates were disqualified from social media.
• The population in this case is all HR professionals, while the sample consists of the 410 surveyed.

Statistical and Critical Thinking

• Prepare the data by understanding its context and the study's goal.
• Examine the data source for potential bias that may influence results.
• Evaluate the sampling method to determine if it's unbiased or if it may skew participation.
• Analyze the data by graphing and exploring the data.
• Look for outliers, determine key statistics, data distribution, missing data, and subject refusal rates.
• Use appropriate technology to assist in result obtainment.
• Conclude the process by assessing the statistical and practical significance of the results.

Data Preparation

• Includes shoe print lengths and heights of eight males, useful in estimating a criminal's height at burglary scenes.
• An example goal could be determining the relationship between shoe print length and male height, based on survey data.
• A reasonable hypothesis is taller males have larger shoe print lengths.
• The data originates from Data Set 9 "Foot and Height" and was randomly selected, indicating a reputable source and sound sampling.

Voluntary Response Sample

• A Voluntary Response Sample/Self-Selected Sample is when respondents decide whether or not to be included.
• Common examples: internet, mail-in, and telephone call-in polls, all of which have a high possibility of bias.
• For example, 67% of 186,000 Nightline viewers wanted the United Nations to move out of the U.S.
• Another survey of 500 randomly selected individuals found only 38% wanted the United Nations to move.
• Results can vary greatly and the smaller poll of 500 is more reliable than Nightline's, due to its superior sampling method.

Data Analysis

• Includes graphing and exploring data, along with correct use of statistical methods, common sense, and sound statistical practices.

Conclusion

• Requires the ability to distinguish between statistical and practical significance.
• Statistical significance in a study is typically achieved when the likelihood of an event occurring by chance is 5% or less.
• For example, getting 98 girls in 100 random births is statistically significant due to its low likelihood.
• Getting 52 girls in 100 births does not statistically mean it could easily occur.
• Practical significance considers if the treatment or finding is effective enough to warrant its use, using common sense.
• For example, the Atkins program resulted in an average loss of 2.1 kg after one year, which is statistically significant.
• Many dieters do not feel that 2.1kg is that significant a loss so the diet lacks practical significance.

Analyzing Data: Potential Pitfalls

• When drawing conclusions, make statements clear, even to those unfamiliar with statistics.
• When collecting data from people, take measurements directly, rather than relying on self-reporting of data.
• Word survey questions carefully, as results can mislead.
• The "order of questions" on surveys can skew the responses.
• Nonresponse: when someone refuses/is unavailable to respond.
• Low Response Rates: Decreases reliability and increases bias among respondents if sample size is small.
• Watch out for misleading percentages, especially references exceeding 100%.

Types of Data

• It is important to know and understand the meaning of statistics and parameters.
• The type of data is a critical factor in determining the statistical methods to use.

Parameter

• A numerical measurement describing a characteristic of a population.
• Example: There are 250,342,875 adults in the United States which is the parameter.
• A survey of 1,659 adults found that 28% own a credit card.

Statistic

• A numerical measurement describing a characteristic of a sample.

Quantitative Data

• Also known as numerical data.
• Includes numbers representing counts or measurements such as weights of supermodels.

Categorical Data

• Also known as qualitative or attribute data.
• It consists of names/labels and not numbers, which represent counts or measurements.
• For example, male/female genders are measured in professional athletes.

Discrete Data

• Consists of quantitative data where the number of values is finite/countable.
• Examples include coin tosses until getting tails, the number of students in a class, and the number of lectures in a syllabus.

Continuous Data

• Consists of numerical data resulting from infinitely many possible quantitative values.
• It has an uncountable collection of values, like distances, blood pressure, or the lifetime of a light bulb.

Levels of Measurement

• Measurement levels are nominal, ordinal, interval, and ratio.
• Nominal: Consists of names, labels, and categories only, which cannot be arranged in any order.
• Ordinal: It can be arranged in a certain order, but value differences cannot be determined/are meaningless.
• Interval: Arranged in order and value differences are meaningful, but with no natural zero starting point.
• Ratio: Meaningful order, differences, and a natural zero point where zero indicates none of the quantity are present.

Summary - Levels of Measurement

• Nominal: Categories only.
• Ordinal: Categories with some order.
• Interval: Differences but no natural zero point.
• Ratio: Differences, and a natural zero point.

Big Data

• Refers to extremely large and complex datasets that exceed traditional software analysis capabilities.
• Requires software run simultaneously on multiple computers.
• Google analyzes GPS data to provide live traffic maps.
• Netflix uses data on viewing records for original programming and movie acquisition.
• Internet searches for flu symptoms can help forecast potential flu epidemics.

Data Science

• Involves statistics, computer science, and software engineering.
• It covers relevant fields in sociology or finance to support data analysis.
• Examples of Jobs According to Analytic Talent, there are 6000 companies hiring data scientists.
• Facebook, IBM, PayPal, The College Board, and Netflix are hiring data scientists.

Missing Data

• A data value is missing completely at random if the likelihood of its being missing is independent of its value or any other values in the data set.
• A data value is missing not at random if the reason that it is missing is related to the value being missing.

Correcting for Missing Data

• Cases can be deleted, very common way for dealing with missing data, or missing data values can be imputed

Collecting Sample Data

• Key concept: Sample data should be collected appropriately because bad collection leads to data uselessness regardless of the analysis amount.

The Gold Standard

• Randomness, coupled with placebo/treatment groups, "gold standard" because of its effectiveness.
• A placebo is a harmless/ineffective pill, medicine, or procedure used for psychological benefit or for comparison with other treatments.
• Placebos have no medicinal effect, examples include sugar pills.

Basics of Collecting Data

• Statistics are driven by the data collected.
• Normally obtained via observational studies and experiments.

Experiment

• Involves applying a treatment to individuals and observing the effects
• The individuals are called experimental units or subjects.

Observational Study

• Involves observing/measuring specific characteristics without modifying the individuals.
• An observational study could be observing past data to conclude ice cream causes drownings.
• It could be that temperature is the lurking data that actually causes drowning as more people swim in hotter temps along with increased ice cream sales.
• Experiments, compared to observation, are clearly better than previous study results.

Design of Experiments

• Replication requires that an experiment is repeated on more than one individual.
• Replication requires sample sizes to be large enough to see effects of treatments.

Blinding

• Blinding ensures that subjects don't know whether they are receiving a treatment/placebo to get around the placebo effect.

Double-Blind

• Occurs on two levels.
• The subject doesn't know whether he or she is receiving the treatment or a placebo
• The experimenter does not know whether he or she is administering the treatment or placebo.

Randomization

• Randomness is used to create similar groups.

Simple Random Sample

• A sample of n subjects is randomly selected in such a way that every possible sample of the same size n has the same chance of being chosen.
• A simple random sample is called a random sample.

Systematic Sampling

• Involves selecting every kth element in the population after choosing a starting point.

Convenience Sampling

• Uses data that are easily accessible.

Stratified Sampling

• Involves subdividing a population into subgroups/strata based on shared characteristics.
• A sample is then selected from each.

Cluster Sampling

• The population is divided in areas, the clusters that are randomly selected.
• All of the members are chosen from said clusters.

Multistage Sampling

• Collecting data by using a mix of several sampling methods.
• Pollsters select sample in different stages, it may use different sampling methods.