Overview

Statistics, in short, is the study of data. It includes descriptive statistics (the study of methods and tools for collecting data, and mathematical models to describe and interpret data) and inferential statistics (the systems and techniques for making probability-based decisions and accurate predictions.

Statistics as a subset of mathematics

As one would expect, statistics is largely grounded in mathematics, and the study of statistics has lent itself to many major concepts in mathematics: probability, distributions, samples and populations, the bell curve, estimation, and data analysis.

Types of Statistics

  • Descriptive Statistics
  • Inferential Statistics

Descriptive Statistics

Descriptive statistics allow you to characterize your data based on its properties. There are four major types of descriptive statistics:

  • Measures of Frequency
    • Count, Percent, Frequency
    • Shows how often something occurs
    • Use this when you want to show how often a response is given
  • Measures of Central Tendency
    • Mean, Median, and Mode
    • Locates the distribution by various points
    • Use this when you want to show how an average or most commonly indicated response
  • Measures of Dispersion or Variation
    • Range, Variance, Standard Deviation
    • Identifies the spread of scores by stating intervals
    • Range = High/Low points
    • Variance or Standard Deviation = difference between observed score and mean
    • Use this when you want to show how "spread out" the data are. It is helpful to know when your data are so spread out that it affects the mean
  • Measures of Position
    • Percentile Ranks, Quartile Ranks
    • Describes how scores fall in relation to one another. Relies on standardized scores
    • Use this when you need to compare scores to a normalized score (e.g., a national norm)

Inferential Statistics

When you have quantitative data, you can analyze it using either descriptive or inferential statistics. Descriptive statistics do exactly what it sounds like – they describe the data. Descriptive statistics include measures of central tendency (mean, median, mode), measures of variation (standard deviation, variance), and relative position (quantiles, percentiles). There are times, however, when you want to draw conclusions about the data. This may include making comparisons across time, comparing different groups, or trying to make predictions based on data that has been collected. Inferential statistics are used when you want to move beyond simple description or characterization of your data and draw conclusions based on your data. There are several kinds of inferential statistics that you can calculate; here are a few of the more common types:

  • t-tests
  • ANOVA (Analysis of Variance)
  • Regression

We will provide the detailed specifications of each of type in coming posts.Until then, Keep learning