Understanding inferential statistics


Inferential statistics

Descriptive statistics describes data (for example: how many people have partners and how many do not? How many people have children and how many do not?) and inferential statistics allows you to make predictions (“inferences”) from that data (for example: if a person gets a partner, what are the chances that that person will get a child?). With inferential statistics, you take data from samples and make generalizations about a population.

There is a way to discover whether the difference in group means is caused by error variance or by systematic variance. Inferential statistics are used for this purpose. Inferential statistics refers to drawing conclusions. This method assumes that the independent variable has had an effect, when the difference between the means of the conditions is larger than is expected based on chance alone. Therefore, we compare the group means that we found with the group means that we expect to find if there is only error variance. Unfortunately, this method does not provide certainty. We are only able to determine the chance that the differences in group means are caused by error variance.

Testing hypotheses

Scientists try to test their hypotheses by analyzing different group means. First, they formulate a null hypothesis. This hypothesis states that the independent variable did not have an effect on the dependent variable. On the contrary, there is an experimental hypothesis which states that the independent variable did have an effect on the dependent variable. The experimental hypothesis may (directional) or may not (non-directional) indicate a direction of the effect. A directional experimental hypothesis is called one-sided. With a one-sided hypothesis, the researcher indicates whether he expects the independent variable to cause a decrease or increase of the dependent variable. When the researcher does not have an indication of the direction of the expected effect, a two-sided hypothesis can be used. With a two-sided hypothesis, the direction of the effect is not indicated. Based on statistical analyses, the null hypothesis can be rejected or preserved (failing to reject the null hypothesis).

Rejecting the null hypothesis implies that the independent variable did have an effect on the dependent variable. By rejecting the null hypothesis, you indicate that there is a difference between the means. The independent variable thus had an effect, and there is some systematic variance. Rejecting the null hypothesis implies that the difference in group means is larger than expected on error variance only. When the null hypothesis is preserved, it does not mean per se that the independent variable did not have an effect on the dependent variable. Instead, it means that the effect that is found is not large enough to reject the null hypothesis. Whether a null hypothesis is rejected, is dependent upon the confidence interval, which is controlled by the researcher (the researcher determines the significance level). It is important to understand that not rejecting the null hypothesis does not mean that there is no effect.

Statistics: Magazines for encountering Statistics

Statistics: Magazines for encountering Statistics

Startmagazine: Introduction to Statistics
Stats for students: Simple steps for passing your statistics courses

Stats for students: Simple steps for passing your statistics courses

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Stats of studentsTheory of statistics

  • The first years that you follow statistics, it is often a case of taking knowledge for granted and simply trying to pass the courses. Don't worry if you don't understand everything right away: in later years it will fall into place and you will see the importance of the theory you had to know before.
  • The book you need to study may be difficult to understand at first. Be patient: later in your studies, the effort you put in now will pay off.
  • Be a Gestalt Scientist! In other words, recognize that the whole of statistics is greater than the sum of its parts. It is very easy to get hung up on nit-picking details and fail to see the forest because of the trees
  • Tip: Precise use of language is important in research. Try to reproduce the theory verbatim (ie. learn by heart) where possible. With that, you don't have to understand it yet, you show that you've been working on it, you can't go wrong by using the wrong word and you practice for later reporting of research.
  • Tip: Keep study material, handouts, sheets, and other publications from your teacher for future reference.

Formulas of statistics

  • The direct relationship between data and results consists of mathematical formulas. These follow their own logic, are written in their own language and can therefore be complex to comprehend.
  • If you don't understand the math behind statistics, you don't understand statistics. This does not have to be a problem, because statistics is an applied science from which you can also get excellent results without understanding. None of your teachers will understand all the statistical formulas.
  • Please note: you will have to know and understand a number of formulas, so that you can demonstrate that you know the principle of how statistics work. Which formulas you need to know differs from subject to subject and lecturer to lecturer, but in general these are relatively simple formulas that occur frequently and your lecturer will tell you (often several times) that you should know this formula.
  • Tip: if you want to recognize statistical symbols you can use: Recognizing commonly used statistical symbols
  • Tip: have fun with LaTeX! LaTeX code gives us a simple way to write out mathematical formulas and make them look professional. Play with LaTeX. Wit that, you can include used formulas in your own papers and you learn to understand how a formula is built up – which greatly benefits your understanding and remembering that formula. See also (in Dutch): How to create formulas like a pro on JoHo WorldSupporter?
  • Tip: Are you interested in a career in sciences or programming? Then take your formulas seriously and go through them again after your course.

Practice of statistics

Selecting data

  • Your teacher will regularly use a dataset for lessons during the first years of your studying. It is instructive (and can be a lot of fun) to set up your own research for once with real data that is also used by other researchers.
  • Tip: scientific articles often indicate which datasets have been used for the research. There is a good chance that those datasets are valid. Sometimes there are also studies that determine which datasets are more valid for the topic you want to study than others. Make use of datasets other researchers point out.
  • Tip: Do you want an interesting research result? You can use the same method and question, but use an alternative dataset, and/or alternative variables, and/or alternative location, and/or alternative time span. This allows you to validate or falsify the results of earlier research.
  • Tip: for datasets you can look at Discovering datasets for statistical research

Operationalize

  • For the operationalization, it is usually sufficient to indicate the following three things:
    • What is the concept you want to study?
    • Which variable does that concept represent?
    • Which indicators do you select for those variables?
  • It is smart to argue that a variable is valid, or why you choose that indicator.
  • For example, if you want to know whether someone is currently a father or mother (concept), you can search the variables for how many children the respondent has (variable) and then select on the indicators greater than 0, or is not 0 (indicators). Where possible, use the terms 'concept', 'variable', 'indicator' and 'valid' in your communication. For example, as follows: “The variable [variable name] is a valid measure of the concept [concept name] (if applicable: source). The value [description of the value] is an indicator of [what you want to measure].” (ie.: The variable "Number of children" is a valid measure of the concept of parenthood. A value greater than 0 is an indicator of whether someone is currently a father or mother.)

Running analyses and drawing conclusions

  • The choice of your analyses depends, among other things, on what your research goal is, which methods are often used in the existing literature, and practical issues and limitations.
  • The more you learn, the more independently you can choose research methods that suit your research goal. In the beginning, follow the lecturer – at the end of your studies you will have a toolbox with which you can vary in your research yourself.
  • Try to link up as much as possible with research methods that are used in the existing literature, because otherwise you could be comparing apples with oranges. Deviating can sometimes lead to interesting results, but discuss this with your teacher first.
  • For as long as you need, keep a step-by-step plan at hand on how you can best run your analysis and achieve results. For every analysis you run, there is a step-by-step explanation of how to perform it; if you do not find it in your study literature, it can often be found quickly on the internet.
  • Tip: Practice a lot with statistics, so that you can show results quickly. You cannot learn statistics by just reading about it.
  • Tip: The measurement level of the variables you use (ratio, interval, ordinal, nominal) largely determines the research method you can use. Show your audience that you recognize this.
  • Tip: conclusions from statistical analyses will never be certain, but at the most likely. There is usually a standard formulation for each research method with which you can express the conclusions from that analysis and at the same time indicate that it is not certain. Use that standard wording when communicating about results from your analysis.
  • Tip: see explanation for various analyses: Introduction to statistics
Statistics: Magazines for understanding statistics

Statistics: Magazines for understanding statistics

Startmagazine: Introduction to Statistics
Understanding data: distributions, connections and gatherings
Understanding reliability and validity
Statistics Magazine: Understanding statistical samples
Understanding variability, variance and standard deviation
Understanding inferential statistics
Understanding type-I and type-II errors
Statistiek: samenvattingen en studiehulp - Thema
Statistics: Magazines for applying statistics

Statistics: Magazines for applying statistics

Applying z-tests and t-tests
Applying correlation, regression and linear regression
Applying spearman's correlation
Statistiek: samenvattingen en studiehulp - Thema

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Statistics: Magazines for understanding statistics

Startmagazine: Introduction to Statistics
Understanding data: distributions, connections and gatherings
Understanding reliability and validity
Statistics Magazine: Understanding statistical samples
Understanding variability, variance and standard deviation
Understanding inferential statistics
Understanding type-I and type-II errors
Statistiek: samenvattingen en studiehulp - Thema
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