PSYCH 240: EXAM 1
48 Cards in this Set
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Descriptive Statistics
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to summarize and describe a set of numbers
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Inferential Statistics
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to draw conclusions and make inferences based on the scores collected in a study but going beyond them
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Variable
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any characteristic that varies among individuals (like height)
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Value
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possible number or category that a score can have
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Nominal (categorical) Variable
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variable that has values that are names or categories
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Numeric (quantitative) Variable
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variable that has values that are numbers
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Rank-order (ordinal)
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numeric variable in which values give relative position of things measured (like place in a race or differences between small, medium, and large)
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Equal-Interval
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numeric variable in which differences between values correspond to differences in the underlying thing being measured (age)
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When making histograms...
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put the frequencies on the y-axis and the values of a numerical variable on the x-axis
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Frequency Polygon
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a histogram made by joining the middle-top points of a histogram's columns, special line graphs
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Compare histograms to bar graphs
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Histograms- y-axis is frequencies, x-axis is numeric, no gaps between the columns, inherent order, can interpret shape
Bar graphs- y-axis is variables, x-axis is frequencies, gaps between columns, no inherent order, cannot be interpreted
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Name modalities
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unimodal-one peak
bimodal- two peaks
multimodal- two or more peaks
rectangular- approximately equal
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What does skewed to the left mean?
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low distribution in lower numbers, negatively (look at tail)
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What does skewed to the right mean?
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low distribution in higher numbers, positively (look at tail)
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Mean
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The arithmetic average, best guess in long run, sensitive to outliers, balances the scores, but not in the middle (most of the time)
M=∑x÷N
1. Add up all the scores
2. Get total number of scores
3. Divide the sum by the number of scores in total
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Deviation scores
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distances from the mean
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Mode
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Most frequent score in distribution, preferred measure measure of central tendency for nominal variables
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Median
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middle score when arranged from lowest to highest
1. Sort numbers from lowest to highest
2. Calculate the position of the middle scores using (N+1)÷2
3. Determine the value of the middle score by counting inwards towards the middle of the sorted numbers
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When are mean, median, and mode the same?
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When the graph is symmetrical
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Resistance to outliers
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Median and mode are resistant to outliers. The mean is not.
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Which measure of central tendency should we use
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use the mean, unless there are extreme outliers, then use the median. Use the mode for nominal variables
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Variability
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how spread out or scattered the scores in a distribution are; the great the variability, the more spread are the scores
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Variance
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"how spread out scores are around the mean"
the average of each score's SQUARED deviation from the mean
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Calculating Variance
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∑(x-M)2÷N=SD2
1. Calculate the mean
2. Calculate the deviation scores (M-Raw score)
3. Square the deviation scores
4. Sun of the squares
5. Divide that sum by the total number of scores
Top part of formula is the Sum of Squares (SS), CAN NEVER BE NEGATIVE
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Standard deviation
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the positive square root of the variance. It is the average amount that scores differ from the mean. The standard deviation expresses variability in the same unit as the raw data
CAN NEVER BE NEGATIVE
SD=√SD2
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Why do we usually prefer the standard deviation as a measure of variability?
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Variance= average of each score's SQUARED deviation from the mean
Standard deviation= average amount that scores differ from the mean
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Resistant to outliers part 2
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Variance and standard deviation are NOT resistant to outliers because they consider all scores- avoid using them for skewed deviations
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Z Score
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describes distance of single score to mean in standard deviation units. The number of standard deviations a score above or below the mean,
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Converting raw scores into Z scores
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Z=(X-M)÷SD
1. Calculate M and SD, if not provided.
2. Plug in numbers into formula
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Converting Z scores into raw scores
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X=Z×SD+M
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Correlation
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relationship between two interval variables.
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Describing the relationship between 2 variables
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describe type, direction, and strength of the relationship. Also look out for outliers
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Types of relationships
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Linear- pattern of dots fall roughly in a straight line *will only use linear
Curvilinear- pattern of dots fall roughly on a curve
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When do we get a positive, negative, or 0 Z score?
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Positive= raw score above M
0= raw score equal to M
Negative= raw score below M
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Positive linear relationships
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values on both variable go in the same direction
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Negative linear relationships
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values on the two variables go in opposite directions
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Strength of a relationship
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determined by how closely the points follow a clear form
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Pearson Correlation coefficient
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measures the direction and strength of a linear relationship between the two equal interval variable X and y
r=∑ZxZy÷N
r is the average of the cross-products of Z scores
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Cross Products of Z scores
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the result of multiplying a person's Z score on one variable by the person's Z score on another variable
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Calculating r
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1. Convert raw scores into Z scores if necessary
2. Multiply to get cross products
3. Sum up the cross products
4. Divide by N
5. Describe the results IN WORDS
*remember to state strength and direction of the relationship and to express relationship in words
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Interpreting r
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r ranges from -1 to +1
The closer r is to 1, the stronger the relationship/ correlation.
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Why use Z scores to calculate r?
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Z scores are used since they bring the scores of the two variables onto the same scale.
If Z scores within a pair tend to have:
1. the same signs: positive correlation
2. different signs: negative correlation
The strength of the correlation is determined by how consistent these trends…
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r and outliers
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r is not resistant to outliers
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Predicting scores
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If there is a relationship between 2 variables, then we can predict the criterion variable (Y) from the predictor variable (X).
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Predicting Z scores from Z scores
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Zy= β×Zx
β=r
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Prediction error
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prediction error= observed value-predicted value
r2 expresses the proportion of variance(or variability) in one variable can be explained by the other variable. *proportion of variance accounted for*
r2 expresses by what proportions the variability of our errors in predicting Y can be r…
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Scatter Plots
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1. Draw the axes and decide which variable goes on which axis
*The variable that is doing the predicting or causing goes on the horizontal axis
2. Determine the range of values to use for each variable and mark them on the axes
3. Mark a dot for each pair of scores
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β
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standardized regression coefficient
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PSYCH 240: UNIT 3 & 4