Question | Answer |
Observed Score | A score obtained from a measurement instrument. - Has strong meaning when compared with other scores. |
How do we calculate a centred score? | Subtract the mean from the observed score. Negative when below the mean; positive when above the mean. |
Sum of squares (SS) - What is it a measure of? - How is it calculated? | - A measure of variability. - Calculated by squaring the centred scores and then adding them together. |
When is the sum of squares (SS) larger? | When the scores fall farther from the mean. |
Sum of products (SP) - What is it a measure of? - How is it calculated? | - Measure of the relationship between two variables. - It is calculated by multiplying the centred score on one variable by the centred score on the other variable, and then adding these products together. |
When is SP positive? Negative? | - Positive when an increase in one variable is associated with an increase in the other variable. - Negative when an increase in one variable is associated with a decrease in the other variable. |
Independent vs. Dependent variable | The dependent variable is the variable one wants to predict (Y), and the independent variable is the variable one uses to predict it (X). |
What does a sum of squares and products (SSP) table provide? | It conveniently provides a way of summarizing information about the variables. |
Degrees of freedom (df) | Number of scores in a set that can vary freely. |
True/False: The sum of centred scores is always 0. | True |
How is variance calculated? | SS/(N-1) (N - 1 = degrees of freedom) |
How does the standard deviation relate to the variance? | It is the square root of the variance. |
What is the purpose of taking the square root of the variance? | To undo the initial squaring of the centred scores. - Providing an estimate of variability that relates directly to the original unit of measurement. |
True/False: The ratio between N-1 and N approached unity as N increases. | True |
Standard scores - What are they? - What is a common form? | - Centred scores that have been scaled relative to the standard deviation. - z score |
What does a z score indicate? | A z score indicates the number of standard deviations that an observed score is away from the mean. - z scores have a mean of zero (like centred scores). |
Simple correlation | A standardized measure of relationship that ranges in value from −1 to 1. |
When is a simple correlation positive? When is it negative? | It is positive when an increase in one variable is associated with an increase in the other variable, and it is negative when an increase in one variable is associated with a decrease in the other variable. |
How is the simple correlation calculated? | Simple correlation is equal to the standardized sum of products divided by its degrees of freedom. |
What is the standardized sum of products? | The standardized sum of products is simply the sum of products calculated using z scores rather than centred scores. |
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