Psych Statistics Chapter 5-6

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.

Continuous variables:

measures with number scores that can be divided into smaller units

categorical variables

measures with responses as categories that cannot be divided into smaller units

abstract section:

provides a paragraph summary of the study

discussion section

provides a review of the results along with possible future directions and general conclusions from the study

results section

provides descriptive and inferential statistics and a description of the analyses performed on the data

methods section

provides the details of the participants, design, materials/stimuli/apparatus, and procedure for the study

sampling error: the difference between our _______ statistics and those that we would get from the ________ population

sample, whole

The choice between the range, interquartile range, and standard deviation measures of variability primarily depends on the ________ ____ ________________used to collect the data

scale of measurement

Low variability means that the scores are very ________ and clustered around a middle value

similar

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

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.

Adding up squared deviations will give us a value known as the sum of squared deviations or just sum of __________

Adding up these squared deviations will give us a value known as the sum of squared deviations or just sum of squares

Discrete Variables

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

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.

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.

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.

Pie Charts

Graphs of categorical variables where proportions are represented as a portion of the pie

Bar Graphs

Graphs of data for categorical variables where the bar height represents the size of the value (e.g., mean)

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)

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

Categorical Variables

Measures with responses as categories that cannot be divided 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.

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

Degrees of Freedom

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

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.

To calculate the___________________________, you must locate the scores that mark the middle _______ of the distribution by finding the bottom _______ of the scores and top 25% of the scores

interquartile range, 50%, 25%

The standard deviation is the _________difference between the _______and the mean of a __________. It tells us about how ________ out the scores are around the mean, while the mean tells you about the representativeness of the distribution.

average, scores, distribution, spread,

Variability means that things _______ in some way

differ

Interquartile range can be used instead for distributions with _________ scores

extreme

If you are using a nominal data scale, __________ cannot be quantitatively measured for your distribution, so none of these measures is appropriate

variability

A range is the best measure of __________ when there is no extreme ___________in the distribution and when the data do not use _________ data scale.

variability, outlier, nominal

High variability means scores are ________ spread out across the scale

widely