      Introduction to Inferential Statistics          Social science deals with two main concepts as far as statistics are concerned: population and sample. Population refers to the total number of objects, groups, individuals or any other thing being studied while a sample is a subset selected from the overall population. Many studies rely on samples because they are more manageable, less time consuming and cheaper. Inferential statistics help researchers to make generalizations about a population based on the sample studied. They are used to reach conclusions that go beyond the immediate data in question.

The challenge

Inferences are prone to errors because they are made from a relatively small subset of a population. Since the results cannot be said to be a complete representation of the characteristics of a population, they are usually expressed in form of probability. For example, they may give a probability of 93 percent.

A sample may not be representative of the target population because of two problems:

• Sampling errors that occur by chance
• Sample bias, which stems from inadequate design

What Inferential Statistics Do

Since sample bias is a problem with the research design, inferential statistics does not attempt to correct it. The statistics are instead used to address sampling errors, and they are typically used to test hypotheses.

The calculations help in determining the probability and margin of error, which are important in accepting or rejecting hypotheses. If the value of probability is smaller than required, the hypothesis is rejected because it means the sample is not truly representative of the population. The probability or p value gives an estimate of how often the results can be obtained by chance if the hypothesis used is true.

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Inferential statistics analyze at least two variables, and the types of variables determine the type of inferential statistics applied. The type of analysis using two variables is known as bivariate analysis while that using more than two variables is called multivariate analysis.

The statistics help researchers determine how strong the relationship between independent and dependent variables is. If a hypothesis positively relates wages to age, for example, age will be the independent variable while wages will be the dependent variable.

Types and Examples of Variables

• Ratio/Interval, such as wage or age
• Nominal, such as gender
• Ordinal, for example class grades

Common types of tests include:

• Chi-square
• T-test
• Correlation
• Analysis of Variance
• Analysis of Covariance
• Cluster Analysis
• Factor Analysis
• Discriminant Function Analysis
• Multidimensional Scaling
Major inferential statistics are in a family of statistical model called General Linear Model.

When Can Inferential Statistics be used?

• When there is a complete list of members of a population
• When researchers take a random sample from the population
• When the researchers can determine that the sample size is sufficiently large using pre-established formula

While there are various types of inferential statistics, they all determine how different variables compare to one another. Calculations can be done either by hand or computer.