# Inferential Statistics in Psychology

Inferential statistics is a tool for studying a given population. Even if you don’t follow a theoretical model, you’d surely be able to take a sample of one, watch it, and describe it. Thus, this field seeks to answer the question: **can you infer the behavior of the whole population using only information from a small part of it**?

Thus, inferential statistics in psychology allows you to validate or refute the conjectures of descriptive statistics. That is, both validating a possible model for the population and estimating parameters of that model.

This way, you could say that inferential statistics is the area of statistics that deals with generalizing the results obtained from a sample. To do so, it uses probability distributions as a base and facilitates error, then interprets it as a confidence measure, associated with the results.

“Facts are stubborn things, but statistics are pliable.”-Mark Twain-

## The objective of inferential statistics

Its goal is to generate models and predictions associated with the phenomena, taking into account that the observations are random. On one hand, **its use focuses on creating patterns of the data**. On the other hand, it extracts inferences about the population under study.

Inferences can take several forms:

- Yes/no answers (hypothesis testing).
- Estimates of some numerical characteristics (estimation).
- Forecasts of future observations.
- Association descriptions (correlation).
- Modeling of relationships between AWS SAM variables (regression analysis).

## Characteristics of inferential statistics

### Extrapolation and generalization

Inferential statistics are concerned with extrapolating data from a population. How to make generalizations about it, so to speak. **Its method of operation consists of taking data on a sample of a population, **usually because the cost of taking data from the entire population would be high. The problem is if there’s an error in the population sample.

Thus, inferential statistics establish conclusions one can rely on to a certain extent in relation to the population the sample belongs to. These conclusions are associated with a confidence margin. Thus, the margin will depend on variables such as the relationship between the size of the sample and the population. It could also depend on the variability that exists in the population of the variables under study.

### Validity and realism in the observations

This is the most valid and realistic type of statistics for the exchange of information between researchers.

## Parts of inferential statistics

As we mentioned above, inferential statistics acts by means of parameter estimation and hypothesis contrasting.

### Parameter estimation

This consists of looking for the most probable values of a parameter in the population (the mean, for example). **There isn’t a lot of information about the population, so one can’t specify a value beyond a confidence interval**.

This interval will be accompanied by the probability that the parameter is in it. That is, the confidence level or its complementary (error probability). In addition, one of the values is considered to be the best estimate within this confidence interval. The best possible estimate, that is.

For instance, you want to estimate the population mean for a variable such as body mass. Thus, you obtain a sample of the population in which the value will be similar to that of your sample. However, the larger the sample you obtain from the population, the more the value you obtain will resemble that of the population.

Thus, **if you obtain a sample of 50o people from a population of 100,000 inhabitants, you’ll obtain an average body mass that’ll be closer to the average of the population** than if your sample contained only 200 people (the law of large numbers). Moreover, it’s likely for the value of the population to be higher or lower than that of the sample. This is because you must consider that the variable is drawn along the continuous “body mass” following a normal distribution.

### What’s the value of a parameter?

In order to estimate what the value of a given mean in a population is, you only need to define one number in the descriptive statistics. However, inferential statistics requires three numbers.

- The optimum estimation.
- The estimation error.
- The confidence level (or error-probability).

These three numbers comprise the confidence interval. **This is an interval in which there’s a certain level of confidence that the real value of the population will be included**. In terms of a mean, you obtain its upper and lower limits by adding and subtracting the estimation error from the value of the best estimate.

### Contrasting hypotheses

The second part of inferential statistics consists of contrasting hypotheses. That is, you must determine if a statement is true or not in the given population, in probabilistic terms. The most frequent types of contrasts are:

- Sample comparison. For example, tall people have a lower body mass index than short people.
- Association between variables. For example, body mass index and height are two related variables.

Thus, the need for inferential statistics in the field of psychology seems obvious (you can change the body mass for intelligence, memory, and attention in the examples). When making inferences, you must estimate how the general characteristics of a population will be. Thus, **researchers can reach important conclusions about populations**. For example, determining measures to take at a social level.