Psychological Statistics Overview

A table or graph showing how often each value appears in a dataset.

Lists each value and its frequency in a dataset.

Groups data into ranges and shows the frequency of each range.

A graph representing a frequency distribution, with data values on the x-axis and frequency on the y-axis.

Techniques used to analyze and interpret data.

Statistical test comparing means of two groups.

Statistical test comparing means of more than two groups.

Summarizing data using measures like mean, median, and mode.

The variable that is changed or manipulated in an experiment to see its effect on another variable.

The variable that is measured in an experiment and is expected to change in response to the independent variable.

Variables that are kept constant during an experiment to ensure the relationship between the independent and dependent variables isn't affected by outside influences.

Data that describes qualities or attributes, often collected through observations or interviews.

Data that consists of numbers obtained from counts or measurements.

Quantitative data that can only take on specific, separate values, often whole numbers representing categories.

Quantitative data that can take on any value within a range.

A statistical test used to compare the means of two related groups, often when the same individuals are measured twice (e.g., before and after a treatment).

In a hypothesis test, this means there is enough evidence to conclude that there is a statistically significant difference between the means of the groups being compared.

In a hypothesis test, means there is not enough evidence to conclude a significant difference between the means of the groups being compared.

ANOVA is used to compare multiple groups when you want to see if there are statistically significant differences between their means.

A system of notation used to describe the factors and levels in an experiment. For example, a 2x3 factorial design has two factors with three levels each.

A researcher wants to know if different teaching methods affect student test scores. They compare the average scores of students using three different methods using ANOVA to see if there's a significant difference.

A teacher wants to see if a new teaching method improves student test scores. They compare the average scores of students before and after using the new method.

A decile is a statistical value that divides a dataset into ten equal parts. Each decile represents 10% of the data, offering a more detailed analysis than quartiles (which divide into four parts) or percentiles (which divide into 100 parts).

Kurtosis describes the peakedness or flatness of a distribution. A higher kurtosis indicates a sharper peak and heavier tails, meaning more extreme values. A lower kurtosis suggests a flatter peak and lighter tails, indicating more even distribution.

A mesokurtic distribution has a kurtosis of 3, indicating a typical bell-shaped curve with a moderate peak and data evenly distributed around the mean. Most values cluster near the average, leading to a balanced number of outliers.

A leptokurtic distribution has a kurtosis greater than 3, characterized by a sharp peak and heavy tails. This means there is a higher likelihood of extreme values, making it riskier.

A platykurtic distribution has a kurtosis less than 3, featuring a flatter peak and light tails. This suggests the data is more evenly spread with fewer outliers.

A percentile is a statistical measure that divides a dataset into 100 equal parts. Each percentile represents a specific point within the data distribution, indicating the percentage of values that fall below it.

To find deciles, first order the data points from smallest to largest. Then, divide the dataset into ten equal parts, marking the points that separate each tenth. Each point represents a decile, indicating the value below which the corresponding percentage of the data falls.

Deciles are valuable for analyzing data distribution and identifying outliers. They have various applications in fields such as finance (analyzing investment performance and risk), education (evaluating student performance and comparing schools), and more.

Statistical tests used when data doesn't meet the assumptions of parametric tests (like normality or equal variances). They work with ordinal or nominal data, are less sensitive to outliers, and can be used with smaller datasets.

Use non-parametric tests when your data is:

1. Not normally distributed
2. Ordinal or nominal
3. Contains outliers
4. Has a small sample size

A non-parametric test used to compare the means of three or more independent groups. It determines if there are statistically significant differences between them.

A test that relies on the ranking of data, rather than assuming a specific distribution. This makes them less sensitive to outliers and suitable for various data types.

Non-parametric tests offer several advantages:

1. Fewer assumptions about data distribution
2. Robustness to outliers
3. Versatility across different data types

A small p-value (less than 0.05) suggests a significant difference between at least two groups. A large p-value (greater than 0.05) indicates no significant difference.

A small p-value (less than 0.05) suggests a significant difference between at least two of the groups being compared. This means that the observed differences are unlikely to have occurred by chance, and likely reflect a real difference.

A large p-value (greater than 0.05) indicates that there is no statistically significant difference between the groups being compared. The observed differences are likely due to random variation.

A non-parametric test comparing two related groups when data is not normally distributed. It's like a paired t-test for non-normal data.

A non-parametric test comparing means of three or more related groups (repeated measures) when data is not normally distributed. It's like a repeated measures ANOVA for non-normal data.

Use it when comparing two related groups with non-normal data. Think of it as a paired t-test alternative for non-normal data.

Use it when comparing three or more independent groups with non-normal data. Think of it as an ANOVA alternative for non-normal data.

Use it when comparing three or more related groups (repeated measures) with non-normal data.

A test used to compare frequencies of categorical variables. It determines if there's a significant difference in how often things occur in different categories.