Inferential Statistics In Psychology

When we want to study a population two things can happen. The most common is that we do not know the theoretical model of it. However, we can surely observe it, take a sample and describe it. And the question is, using the information obtained from a small part of the population, can the behavior of all of it be inferred? Inferential statistics takes care of this .

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

In this way, we could say that inferential statistics is the part of statistics that deals with generalizing results from the results obtained in a sample. To do this, it is based on probability distributions and provides an error, which we can interpret as a confidence measure, associated with the results.

The objective of inferential statistics is none other than to generate models and predictions associated with the phenomena, taking into account that the observations are random. Its use focuses on creating patterns on the data, on the one hand, and on the other drawing inferences about the population studied.

These inferences can take several forms:

• Form of yes / no answers (hypothesis test).
• Estimates of some numerical characteristics (estimation).
• Forecasts of future observations.
• Association (correlation) descriptions.
• Modeling of relationships between Sam’s variables (regression analysis).

Characteristics of inferential statistics

Extrapolation and generalization

Inferential statistics deals with extrapolating data from a population. This is, so to speak, how to make generalizations about it. Its method of action consists of taking data on a sample of a population (usually because the cost of taking data from the entire population would be very high). The problem is in that step from the sample to the population the error appears.

Thus, inferential statistics establishes conclusions on which we can trust to a certain extent in relation to the population to which said sample belongs. These are conclusions associated with a confidence margin. This margin will depend on different variables, such as the relationship between sample and population size or the variability that exists in the population of the variables studied.

Validity and realism in the observations

It is considered the most valid and realistic type of statistic for the exchange of information between researchers.

Parts of inferential statistics

As we have introduced before, inferential statistics works by estimating parameters and testing hypotheses.

Parameter estimation

Parameter estimation consists of finding the most probable values ​​of a parameter in the population (for example, the mean). As the population as a whole is not known, a value beyond an interval (confidence interval) cannot be specified either.

This interval will be accompanied by the probability that the parameter is in it, that is, the confidence level. Or, its complementary ( probability of error ). Furthermore, within this confidence interval one of the values ​​is considered as the best estimate. That is, the best possible estimate.

Let’s say we want to estimate the population mean in a variable such as body mass. We obtain a sample of the population in which the value will be similar to that of the sample. However, the larger the sample that we have obtained from the population, the more likely it is that the value obtained will resemble that of the population.

Thus, if from a population of 100,000 inhabitants we obtain a sample of 500 people, we will obtain an average of the body mass that will be closer to the mean of the population than if we obtained a sample of 200 people (Law of large numbers). In addition, it is curious that the value of the population is just as likely to be greater or less than that of the sample. This is so because we consider that the variable is drawn along the continuum “body mass” following a normal distribution.

How do we answer the question of what is the value of a parameter?

To estimate what is the value of, for example, the mean in a population, a single number will be defined in descriptive statistics. However, inferential statistics will use three numbers. These are:

• The best estimate.
• The estimation error.
• The confidence level (or the probability of error):

These three numbers will form the confidence interval. It is an interval in which we have a certain level of assurance (“level of confidence”) that the real value of the population is included . Its upper and lower limits are obtained, when we refer to the mean, by adding and subtracting the estimation error from the value of the optimal estimate. 

Hypothesis testing

The second part of inferential statistics consists of hypothesis testing. That is, to determine if a statement is true or not in the population, in probabilistic terms. The most frequent types of contrasts are:

• Comparison of samples. Ex: our hypothesis may be that tall people have a lower body mass index than short people.
• Association between variables. Ex: our hypothesis may be that body mass index and height are two related variables.

Thus, the need for inferential statistics in the field of psychology seems obvious (in the examples, we can exchange body mass for intelligence, memory, attention …). By making inferences we estimate what the characteristics of a population will look like in general. This allows researchers to draw conclusions about populations, which can be very important, for example, in determining what action to take at the social level.