PSY-259 ~ Ch. 4-6

Scatterplot

A graph showing the relationship between two dependent variables for a group of individuals.

Standard Deviation

A measure representing the average difference between the scores and the mean of a distribution.

Distribution

A set of scores.

What is APA style and why is it important?

APA style is a set of rules for writing research reports. It provides a consistent structure for research reports to help readers easily understand the report of the study and quickly find information they are looking for.

Calculation Summary: Mean

Add up the scores in the data set and divide by the total number of scores.

Outlier

An extreme high or low score in a distribution.

How do the mean, median, and mode compare for different distributions?

Because the mean is the average of the scores, it will be more influenced by extreme scores than the other measures. Thus, for a skewed distribution, the mean will be closest to the extreme scores, followed by the median and the mode, which will be closer to the middle of the distribution. For symmetrical distributions, however, the three measures will provide the same value that is in the middle of the distribution.

How can I create graphs using software?

Both Excel and SPSS can be used to create the graphs described in this chapter. The details are described by graph type. In Excel, however, you often must calculate some descriptive statistics before you can graph the data.

What can we learn about a distribution from measures of central tendency?

Central tendency measures provide a description of the typical score in a distribution.

Calculation Summary: Mode

Count the frequencies (i.e., how often each score appears) of the scores—the mode is the score(s) with the highest frequency in the data set.

How do I choose the best way to present my data?

First, you should consider whether a graph or table is the best way to present data. This choice will depend on what aspects of the data you wish to highlight to your audience. If you choose a graph, then consider the types of variables you have in your study design to choose between the graph types.

Calculation Summary: Median

For data sets with an odd number of scores, put the scores in order from lowest to highest and then find the middle score. For data sets with an even number of scores, put the scores in order from lowest to highest and then average the two middle scores.

What are the different ways I can present data from a study?

Frequencies from a data set can be presented in frequency distribution tables and graphs. You can also present the descriptive statistics from a data set in tables and graphs to illustrate the differences (or similarities) across groups or conditions. Categorical variables should be displayed in pie charts or bar graphs, and continuous variables should be displayed in line graphs.

Line Graphs

Graphs of data for continuous variables in which each value is graphed as a point and the points are connected to show differences between scores (e.g., means).

Three Main Measures of Central Tendency:

Mean, Median, and Mode.

What can we learn about a distribution from measures of variability?

Measures of variability provide some information about how much the scores in a distribution differ from one another.

Continuous Variables

Measures with number scores that can be divided into smaller units.

Discrete Variables

Measures with whole number scores that cannot be subdivided into smaller units.

What are the differences between pie charts, bar graphs, and line graphs?

Pie charts show values as portions of a circle ("pie slices"). Bar graphs show the values for levels of a variable or response categories as the height the bars in the graph. Line graphs show the relationship between values on a continuous scale. Bar and line graphs often include a measure of the variability in the data if the x-axis contains an independent or grouping variable.

Central Tendency

Representation of a typical score in a distribution.

Mean

The average score for a set of data.

Range

The difference between the highest and lowest scores in a distribution.

Interquartile Range

The difference between the scores that mark the middle 50% of a distribution.

How are the mean, median, and mode used as measures of central tendency?

The mean is the average, the median is the middle score, and the mode is the most common score. Each of these measures gives us summary value for the scores in a distribution, but in different ways.

Which measure of central tendency should I use when describing a distribution?

The mean is the most commonly used measure of central tendency; thus, it is often reported for comparison with other data sets. However, with skewed distributions, it is best to provide the median in addition to or instead of the mean. The mode is useful when describing data sets with many scores at the high and low ends of the scale or when reporting data on a nominal scale.

Median

The middle score in a distribution, such that half of the scores are above and half are below that value.

Mode

The most common score in a distribution.

Degrees of Freedom

The number of scores that can vary in the calculation of a statistic.

How are the range and standard deviation used as measures of variability?

The range measures the difference between the highest and lowest scores in a distribution to provide you with a sense of how much of the measurement scale the scores cover. The standard deviation conceptually measures the average distance between the scores and the mean of the distribution. This measure provides you with a sense of how much the scores differ from the center of the distribution.

How do the range and standard deviation compare for different distributions?

The range only uses the two most extreme scores in the distribution, so it is a fairly imprecise measure of variability. It does not provide any information about the scores between these two extremes. The standard deviation uses all the scores in its calculation, so you are getting a more precise measure of variability from the standard deviation.

Variance

The squared standard deviation of a distribution.

Why does the standard deviation calculation differ for samples and populations?

The standard deviation is the average of the differences between the scores and the mean. For a population, this value is calculated using N to determine the average. However, the sample, as a representative of the population, will have lower variability than the whole population because you are not obtaining scores from every member, only a subset of the population. Thus, we adjust the standard deviation calculation for a sample to account for its lower variability and still provide a good estimate of the variability in the population the sample represents. We do this using n − 1 (which are the degrees of freedom) in our calculation of the average of the deviations between the scores and the mean.