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Psych Stats Ch. 1

QuestionAnswer
Discrete Variables variables that can only take certain values
Continuous Variables variables that can take ANY value within its specified range
Categorical variables Nominal and ordinal scales
Quantitative variables Interval and ratio scales
nominal scale A categorical variable. the data can only be categorized The only comparisons that can be made between variable values are equality and inequality. There are no “less than” or “greater than” relations among the classifying names, nor operations such as
ordinal scale A categorical variable. the data can be categorized and ranked Comparisons of greater than/less than can be made, and equality/inequality. However, operations such as conventional addition and subtraction are still meaningless.
Interval Scale Quantitative Variable. the data can be categorized, ranked, and evenly spaced no absolute zero point I Temperature on the Fahrenheit or Celsius scale. I Comparisons and arithmetic operations of addition/subtraction are meaningful, but not multipl
Ratio Scale Quantitative variable. the data can be categorized, ranked, evenly spaced, and has a natural zero. have absolute zero point. Weight, height, GPA. Comparisons and arithmetic operations of addition/subtraction, multiplication/division all meaningful
Parameter a numerical value that describes the population. I Ex: The average IQ of all US adults is 100
Statistic numerical value that describes the sample. I Ex: The average IQ of 50 sampled USU college students is 110
Overall Range Overall range = highest value – lowest value
Categorical Variables Bar plot/Dot chart
Quantitative Variables Histogram, Cumulative percentage plot/ogive
Pie Charts Humans bad at judging relative areas=bad at correctly interpreting pie charts
Dot Charts x-axis: frequency or relative frequency y-axis: Categories
Frequency Distribution (Distribution) What values a variable can take and how often it takes these values Describe distribution Numerically/ Graphically
Frequency Table Arrange data values with corresponding frequencies Column 1=Limits/Class Limits, 9 classes w/ interval widths of 5 Summarize quantitative or categorical variables Good frequency table=5-15 classes, and no categories with 0 frequencies
Frequency Raw number of individuals How often value happens
Relative Frequency Number of individuals divided by sample size Percent/Proportion
Cumulative Frequency Frequency up to and including the frequency for that category Past columns as well as present columns
Percentile Point Pth percentile=value greater than P percent of all the other cases/individuals in the distribution Whole number between 130 and 170, can't be 130.5
Percentile Rank Rth percentile=Proportion of cases in the distribution that are less than the specified value 0 to 99, can't be 100 or negative 1
Meaning of symbols mean formula x with line over it: sample mean. Weird Greek 3 symbol: sigma, add things up. n: sample size. everything on left side: add up all values starting with 1 (i=1) and stop at nth value. X: individual data value. i: index, ith individual ex.) x1, x2, x3)
μX population mean of X
N N: population size
is mean or median less sensitive to outliers? Median. Thus, the median is a better measure of the center of skewed distributions than the mean.
order of mean, median, and mode least to greatest in a negatively skewed graph. mean, median mode
order of mean, median, and mode least to greatest in a positively skewed graph. mode, median, mean
order of mean, median, and mode least to greatest in a symmetrical graph. mean, median, and mode are equal.
what is mode greatest frequency
score transformation a process that changes every score in a distribution to one on a different scale
what happens to mean, median, and mode when each data value is mulitplied, divided, subracted, or added by the same constant variable? the exact same thing happens to the mean, median, and mode.
measures of variability numerical expressions of the spread of a distribution. AKA the extent to which individual observations are scattered vs. clustered together.
The relation between measure of variability and the distribution larger the variability, wider the distribution
5 number summary minimum, Q1, Q2 (median), Q3, maximum
What is IQR interquartile range. Like the range, the IQR also measures variability using percentiles. IQR = Q3 − Q1 the spread in the center of the distribution
What is S-IQR Like the range and IQR, the S-IQR measures variability using percentiles. S-IQR = (Q3−Q1)/2
positively skewed box plot longer whisker for large values and/or the median is closer to the bottom side of the box
negatively skewed box plot longer whisker for small values and/or the median is closer to the top side of the box
degree of freedom the number of sample observations that are “free to vary” while keeping the same statistic value(s) n-1 when one thing is changed. n-2 when 2 things are changed, etc.
sample variance estimated variance of the variable X based on a sample of n values, given by __ S^2=[∑ni=1(Xi − X )^2]/(n −1)
how to calculate sample variance first calculate mean __ X then subtract each variable by the mean and square them and add them together. ex.) (x1-mean)^2 + (x2-mean)^2 etc. then, divide it by number of values minus 1 (degree of freedom)
Standard deviation Sd (S) the square root of the variance (S^2) The average distance a data point is from the mean
how is S-IQR and IQR, and SD and Variance affected by outliers? S-IQR and IQR are more robust (not very affected by outliers) and SD and S^2 are affected by outliers
When each variable is added/subtracted, IQR, SIQR, variance, SD will... stay the same
When each variable is multiplied/divided, IQR, SIQR, variance, SD will... spread (increase) when multiplied and decrease when divided
z score standardized values that express how many standard deviations a raw score is above or below the mean. z = (X−mean)/SD
The mean of any distribution of scores converted to z-scores is always 0.
The standard deviation of any distribution expressed in z scores is always 1
Transforming raw scores to z-scores changes the value of the mean to... and SD to..., What does it do to the shape of the distribution? mean: 0; SD: 1; shape of the distribution does not change
Created by: nathalieward
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