Untitled Quiz

Introduction to Statistics

• Statistics is a field of study dealing with the collection, analysis, interpretation, presentation, and organization of data.
• It is used to understand patterns, trends, and relationships within data, often used to make predictions or decisions.

Types of Data

• Categorical Data: Data that fits into categories or groups, like gender, color, or type.
• Quantitative Data: Data that can be measured numerically, like height, weight, or temperature.

Sampling

• Sampling is a process where a researcher selects one or more cases from a larger group (population) for study.
• Important for studying populations too large to collect data on every member.
• Crucial for generalizing findings to the entire population.

Sampling Methods

• Simple Random Sampling (SRS): every member of the population has an equal chance of being selected. Can be with or without replacement.
• Systematic Sampling: Every kth member of a population is selected.
• Stratified Random Sampling: The population is divided into subgroups (strata). Then random samples are drawn from each stratum.
• Cluster Sampling: A sampling method where the population is divided into groups (clusters). Then entire clusters are randomly selected.
• Convenience or Accidental Sampling: The researcher selects the most accessible individuals or cases.

Data Collection Methods

• Questionnaires: A structured set of questions used to collect data from individuals. Can be answered in person, by mail, phone, or online.
• Recording: Recording data collected through observation.
• Qualitative Methods: Methods used to find information through observation, watching, listening, or reading.

Sample Size

• Sample size is the number of individuals selected for observations.
• Precision (Acceptable amount of error)
• Population Homogeneity (Variability in pop.)
• Sampling Fraction (relative number of elements in sample to pop.)

Sampling Fraction Adjustment

• n' (adjusted sample size) = n (estimated sample size without adjustment) / [1+(n/N)]
• N: population size

Non-Probability Sampling

• Availability sampling: Uses readily available and accessible participants.
• Snowball sampling: Participants refer other participants to take part.
• Quota sampling: Samples are selected to match characteristics of the population across multiple subgroups.
• Purposive sampling: Selects participants based on their specific characteristic.

Spurious Relationships

• A spurious relationship exists where two variables appear to have a relationship, but that relationship is actually caused by a third variable.
• Controlling for other variables is important for understanding the true relationship.

Data Display

• Graphs: Used to present and visualize the distribution of data.
  • Bar charts: Useful for displaying categorical data.
  • Pie charts: Useful for displaying categorical data (parts of one whole).
  • Histograms: Used for frequency distribution of quantitative data.
  • Time series plots: Used to show how a variable changes over time.
  • Dot plots: Useful for graphically representing data
  • Stem plots: Display individual data points in a systematic way.

Variables

• Individuals: Objects or entities being observed. Can be people, animals or things.
• Variables: Characteristics of an individual. Can take various values or categories.
  • Quantitative: Measured numerically. Examples: Height, weight, temperature.
  • Categorical: Fits into categories. Examples: Eye color, gender.
• Categorical types: Nominal (unordered categories), ordinal (ranked categories)

How to Determine Variable Type

• Ask what is being measured of each individual.
• Is it a numerical value, or a descriptive category?

Measures of Center

• Mean: Average of all values in a data set.
• Median: Center point of a data set when ordered.
• Mode: Most frequent value in the data set.

Measures of Spread

• Range: Difference between the highest and lowest values.
• Interquartile Range (IQR): range between third and first quartile of a data set.
• Standard Deviation: Average distance between each data point and the mean.
• Variance: Sum of squares of deviations from the mean, divided by degrees of freedom.
• Semi-Interquartile Deviation: Half the difference between the third and first quartiles.

Box Plots

• Box plots visually display the five-number summary (Min , Q1, Median, Q3, Max) of a set of data.
• Helpful for identifying outliers.

Outliers

• Outlier: An observation that is substantially different from most of the other data points.
• Potential Issues
• How the outlier influences the calculated mean and standard deviation.

Choosing a Summary Statistic

• Use the mean and standard deviation for symmetrical distributions without outliers.
• Use the median for non-symmetrical distributions and those with outliers.

Hypothesis Testing

• Table showing the possible outcomes of a hypothesis test is included.
• Includes Type I and Type II errors for rejecting or accepting the null hypothesis.

Confidence Intervals

• Specific methods for calculating 96% and 70% confidence intervals (CI) using a given standard deviation and mean are included.
• Confidence Intervals (CI) give a range within which a true population value is estimated to lie with a specified confidence level.

Z-scores and Probabilities

• Explains z-scores transformation of normal distributions, and how to interpret percentiles.
• Includes z-score ranges for different grades (A, B, C, etc.)
• Explains how to interpret z-score values from tables of percentiles.

Probability

• A quantitative assessment of the likelihood of an uncertain event occurring.
• Always between 0 and 1 (inclusive), [0,1].

Sensitivity, Specificity, PPV, and NPV

• Sensitivity: Percentage of true positives (correct positive results).
• Specificity: Percentage of true negatives (correct negative results).
• Positive Predictive Value (PPV): Percentage of true positives among positive test results.
• Negative Predictive Value(NPV): Percentage of true negatives among negative test results.
• Important in evaluating the usefulness of tests (e.g. screening tests).