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Scales of Measurement: A Review Whenever a variable is studied, there is an definition of the variable that has two or more |
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The levels of the variable are described using one of these scales of measurement: nominal, , interval, and ratio. |
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The type of measurement scale used determines the types of used to analyze the results of the study. |
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Analyzing the Results of Research Investigations Depending on the way that variables are studied, there are basic ways of describing the results. |
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Comparing group , scores of individuals on two variables, and group means. |
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After describing the data, the next step would be to perform a analysis to determine whether the relationship or differences are statistically . |
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Frequency DistributionsWhen analyzing the results, it is useful to start by constructing a distribution that shows the number of individuals that receive each possible or response on a variable. |
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It is also useful to examine the associated with this number and/or graphically depict the frequency distribution. |
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Frequency distributions can be depicted in several types of graphs.
For example, a chart divides a circle into sections that represent relative and a bar graph uses a separate and distinct for each piece of information. |
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Another graph is the frequency uses a line to represent the frequencies. |
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By examining frequency distributions, we can directly observe how participants , see what are most frequent, look at the shape of the distribution, and tell whether there are any outliers. |
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Moreover, in an experiment, we can the distribution of scores in the groups. |
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Descriptive Statistics and Graphing Relationships In addition to examining the distribution of scores or responses, statistics can be computed. |
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Descriptive statistics allow researchers to make precise statements about the . |
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There are statistics needed to describe the data. |
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One number is needed to describe the tendency of the scores. |
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This can be one of three central tendency measures: the mean, the , and the mode. |
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In addition to central tendency, a single number is needed to describe the of the scores or how widely the distribution of scores is spread. |
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In addition to central tendency, a single number is needed to describe the of the scores or how widely the distribution of scores is spread. |
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The three measures of variability are the standard , the variance, and the . |
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To graph the relationship between the independent and dependent variables, a graph is commonly used. |
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The of the independent variable are represented on the horizontal axis, and the dependent variable values are shown on the vertical axis. |
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For each , a point is placed along the y-axis that represents the mean of the group and a line is drawn to connect the points. When the graph is completed, it presents a visual picture that describes the relationship between the variables. |
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Correlation Coefficients: Describing the Strength of Relationships A correlation is a statistic that describes how variables are related to one another. |
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A Pearson correlation coefficient, symbolized as , is used when both variables are or ratio scale. |
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The values of the correlation coefficient range from to 1.00 (plus or minus). |
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The nearer a correlation is to (plus or minus), the stronger the relationship. |
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In addition to the r value indicating the strength of the relationship, the sign (plus or minus) of the r indicates the of the linear relationship. |
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When the sign is positive, both variables covary in the direction and when the sign is negative, both variables covary in directions. |
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Since, the Pearson correlation coefficient is designed to detect only relationships, it is important to construct a and view the pattern of the data first. |
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If the pattern is not linear but curvilinear, another type of coefficient must be used to determine the strength of the relationship between the variables. |
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