inferential statistics

Examples of inferential statistics in the following topics:

• Descriptive or Inferential Statistics?

  • Descriptive statistics and inferential statistics are both important components of statistics when learning about a population.
  • Descriptive statistics are distinguished from inferential statistics in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
  • This generally means that descriptive statistics, unlike inferential statistics, are not developed on the basis of probability theory.
  • Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented.
  • The conclusion of a statistical inference is a statistical proposition.

• Inferential Statistics

  • The mathematical procedure in which we make intelligent guesses about a population based on a sample is called inferential statistics.
  • More substantially, the terms statistical inference, statistical induction, and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from data sets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation.
  • The mathematical procedures whereby we convert information about the sample into intelligent guesses about the population fall under the rubric of inferential statistics.
  • Inferential statistics are based on the assumption that sampling is random.
  • Discuss how inferential statistics allows us to draw conclusions about a population from a random sample and corresponding tests of significance.

• Basic Inferential Statistics

  • These values are called statistics.
  • The reason the normal distribution is so important is because most inferential statistics are based on the assumption that the variable we are measuring is normally distributed.
  • What type of inferential statistics we use will inevitably depend on our research question and our type of data.
  • There are many types of inferential statistical tests, but perhaps the simplest is the t-test, which determines whether there is a significant difference between two means.
  • However, there are many other types of inferential statistics that can be used, some of which test differences in means (t-tests), others which test differences in variances (analysis of variance), and others which use more sophisticated statistical models (General Linear Models).

• Introduction to describing one network

  • Most social scientists have a reasonable working knowledge of basic univariate and bivariate descriptive and inferential statistics.
  • Second, many of tools of standard inferential statistics that we learned from the study of the distributions of attributes do not apply directly to network data.
  • The standard formulas for computing standard errors and inferential tests on attributes generally assume independent observations.
  • Instead, alternative numerical approaches to estimating standard errors for network statistics are used.
  • So, let's begin with the simplest univariate descriptive and inferential statistics, and then move on to somewhat more complicated problems.

• Inferential Statistics for b and r

  • State the assumptions that inferential statistics in regression are based upon
  • Although no assumptions were needed to determine the best-fitting straight line, assumptions are made in the calculation of inferential statistics.
  • As applied here, the statistic is the sample value of the slope (b) and the hypothesized value is 0.

• Applications of Statistics

  • Statistics also provides tools for prediction and forecasting.
  • This is called descriptive statistics .
  • Statistical models can also be used to draw statistical inferences about the process or population under study—a practice called inferential statistics.
  • Inferential statistics uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.
  • Probability is used in "mathematical statistics" (alternatively, "statistical theory") to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.

• Introduction: Applying statistical tools to network data

  • All of these concerns (large networks, sampling, concern about the reliability of observations) have led social network researchers to begin to apply the techniques of descriptive and inferential statistics in their work.
  • Descriptive statistics have proven to be of great value because they provide convenient tools to summarize key facts about the distributions of actors, attributes, and relations; statistical tools can describe not only the shape of one distribution, but also joint distributions, or "statistical association."
  • So, statistical tools have been particularly helpful in describing, predicting, and testing hypotheses about the relations between network properties.
  • Inferential statistics have also proven to have very useful applications to social network analysis.
  • In this chapter we will look at some of the ways in which quite basic statistical tools have been applied in social network analysis.

• A note on statistics and social network data

  • Where statistics really become "statistical" is on the inferential side.
  • Inferential statistics can be, and are, applied to the analysis of network data.
  • The other major use of inferential statistics in the social sciences is for testing hypotheses.
  • The key link in the inferential chain of hypothesis testing is the estimation of the standard errors of statistics.
  • There is, however, nothing fundamentally different about the logic of the use of descriptive and inferential statistics with social network data.

• What Is a Sampling Distribution?

  • The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
  • Inferential statistics involves generalizing from a sample to a population.
  • A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.
  • The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size $n$.
  • This statistic is then called the sample mean.

• Introduction to small sample hypothesis testing for a proportion

  • In this section we develop inferential methods for a single proportion that are appropriate when the sample size is too small to apply the normal model to ˆ p.