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# Distribution Psychology

There's a natural order to how we do things, driving a car, for instance. You need to start the engine for a car to move. However, the following steps depend on the type of car, e.g. is it automatic or manual? The same can be said about data handling and analysis. Before we can identify what statistical tests can be used, we need to find the distributions of data.

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Distribution in psychology is one of the initial steps of analysing data. If you put a car in reverse, your vehicle will move backwards; if in first gear, it will move forward. The type of distribution of data also affects the direction of analysis.

• We will start by looking at the distribution psychology definition and the characteristics of distributions.
• Then moving on to look at the types of distributions and what their shapes are covering normal distribution and skewed distribution psychology; this will include examples of positively skewed distributions and negatively skewed distributions to help your understanding.
• In addition, the differences between normal distribution: psychology and skewed distribution: psychology will also be covered.

## Distribution Psychology Definition

When researchers collect data, the majority of the time, researchers aim to use statistical tests to empirically test if their data findings support or reject the hypotheses they proposed at the start of the study.

However, there are two types of parametric tests:

1. Parametric tests
2. Nonparametric tests

But how do researchers know when to use which test? One of the answers is distribution. When data has a normal distribution, a parametric test is used, and data with skewed distributions use nonparametric tests.

Ideally, researchers aim to use parametric tests as they are more sensitive and are more likely to find significant findings.

Nonparametric tests are only really used when data is not normally distributed.

Now that we've figured out the uses of distributions in psychology let's understand what the data analysis method means.

The distribution psychology definition is a probability distribution that measures the spread of data. From this, researchers can identify the proportion of data that varies/ differs from the average; most commonly, the mean and standard deviation is reported when measuring distributions.

## Characteristics of Distribution

Distribution graphs have numerous names, such as the bell curve graph or Gaussian distribution graph. Let's take a look at the characteristics of a distribution graph:

• Shape - The distribution graphs should resemble a bell with its tail extending to each side of the chart. The highest point of the graph is where there is the highest likelihood of the phenomenon occurring.
• Central tendency - The mean, median and mode are important figures used to understand and interpret distribution graphs. The graph can be used to identify how much each value differs from the average. The mean, median and mode values are usually the same in a normally distributed graph.
• Variability - From distribution graphs, researchers can calculate how much each data point varies from the average.

## Types of Distributions in Psychology

Now that we know what distributions mean let's look at the different types and how we can identify them.

• Normal distribution - the graph resembles a bell shape; the highest point of the chart should be at the centre of the chart, the left and right-hand sides of the graph should be symmetrical, and the tail should extend to each side of the graph.
• Positively skewed distribution - the mean, median and mode of distribution are positive, so the graph has a long tail extending to the right, and the highest point of the graph is shifted to the left.
• Negatively skewed distribution - the mean, median and mode of distribution are negative, so the graph has a long tail extending to the left, and the highest point of the graph is shifted to the right.

### Frequency Distribution Psychology

In psychology, distributions can mean many things. The types of distribution we are focusing on are based on probability. However, frequency distributions are used to understand data. For instance, how often something is observed.

Imagine a research project investigating 100 people of various ages. The researcher can't understand how common specific ages are by looking at each case. Instead, the data is organised using frequency distribution.

An example of how frequency distributions in psychology may look is shown in the table below.

 Age Frequency 20 20 23 20 24 35 27 7 30 18

If you total the frequency, it adds up to 100, the number of participants in the experiment.

Frequency distributions are related to the probability distribution. From frequency distributions, the researcher can identify outliers and whether the data centres around the averages (central tendency values); these factors contribute to whether data is normally distributed.

## Normal Distribution

Let's look at what a normal distribution graph looks like to interpret what the graph shows.

Figure 1 - Graph depicting a normal distribution.

The graph shows that the highest point of the curve is in the middle of the graph, and both sides of the chart are symmetrical. But what does it mean?

The mean, median and mode are the same, as the distribution is symmetrical half of the scores are above the average, and the other half are below the average. The mean is equal to 0, and the standard deviation to 1.

Standard deviation (SD) is how much something deviates/ differs from the average.

In normal distributions:

• 99.7% of observations fall within + or - 3 SD of the mean.
• 95.4 of observations fall within + or - 2 SD of the mean.
• 68.2% of observations fall within + or - 1 SD of the mean.

These are known as the empirical rules of normal distribution.

A smaller SD means that the data is less varied, so the data is less likely to have outliers affecting the reliability and validity of findings.

### Example of Normal Distribution in Psychology

Suppose in a psychology test. These were the average results of the class:

 Mean Median Mode 25 26.5 25

These findings suggest a normal distribution because the mean, median, and mode are approximately the same. And so, if this were plotted onto a graph, it would probably take the shape of a bell curve.

When the mean, median and mode are approximately the same, then this suggests that the dataset does not have many outliers.

## Skewed Distribution Psychology

The two types of skewed distribution charts we will cover are positive and negative.

Figure 2 - Examples of a negative and positive skewed distribution graph.

Let's start by understanding negatively skewed charts.

Typically the scores will mostly be larger numbers and fewer smaller figures. And the mean will fall to the left of the median, which will cause the tail to extend to the left. The data is skewed when all of the central tendency values are not equal to 0.

Let's use test scores to understand negative skewness. On average, students are less likely to score under 50% on typical tests. Thus, the average is likely to be higher, which shifts the average to the right. However, they may be a lot of variance in scores, making the median differ from the mean. In essence, this describes negatively skewed data.

On the other hand, positively skewed data is the opposite. The majority of the numbers will be smaller rather than larger. The mean will fall to the median's right, causing the graph's tail to extend to the right. The findings would suggest a lower probability of occurrence of the phenomenon investigated.

## Positively Skewed Distribution and Negatively Skewed Distribution Examples

Let's take a look at an example of a positively skewed distribution graph average data output:

 Mean Median Mode 28 23 18

The mode and median are below the mean.

 Mean Median Mode 17 26 30

These suggest a negative skew since most people scored high as the mode and median are higher here.

Do these results indicate anything?

If we look at the examples above, the positively skewed shape indicates that the participants scored lower on average, so perhaps the test was too hard. Similarly, the negatively skewed graph shows higher scores, so maybe the test was too easy. The mode is the highest point that illustrates the distribution.

We can then suggest making the test harder or easier, depending on the distributions above.

## Distributions - Key takeaways

• Distribution is a probability distribution that measures the spread of data.
• From distributions, researchers can identify the proportion of data that varies/ differs from the average; most commonly, the mean and standard deviation is reported when measuring distributions.
• There are three major characteristics of distributions shape, central tendency and variability.
• The three distributions covered are normal, negatively skewed and positively skewed distributions.
• Normal distribution and frequency distributions are related.

#### Flashcards in Distribution Psychology 22

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What are the types of distribution in psychology?

There is normal distribution psychology, in addition to positively skewed distribution and negatively skewed distribution.

What is distribution in psychology?

The distribution psychology definition is a probability distribution that measures the spread of data.

What is frequency distribution in psychology?

Frequency distribution measures how often a value occurs in a data set. Frequency distributions are usually presented in tables.

How do you achieve a normal distribution curve in psychology?

A normal distribution in psychology can be achieved by collecting data with few outliers, and the figures centre closely to the measures of central tendency.

What is skewed distribution psychology?

Skewed distribution in psychology means that the values are spread quite far from the average, and many outliers are present. There are two types: positively and negatively skewed distributions.

Why is normal distribution important in psychology?

Because it determines later statistical tests that can be used. For example, parametric tests can only be used when a normal distribution is found. In contrast, non-parametric tests are used when positively or negatively skewed distributions are found.

What is frequency distribution in psychology?

Frequency distributions in psychology are used to measure how often a variable occurs and are usually displayed on a table.

## Test your knowledge with multiple choice flashcards

Would the distribution be normal, positive skewed, or negative skewed for these results: mean 17, median 26, mode 30?

What does a positive skew look like?

Would a negative skew be seen if most participants received lower or higher scores?

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