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PA (from mochi_venti's reviewer) > Stats > Flashcards

Stats Flashcards

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1
Q

What are the two main purposes of statistics?

A

Description and inference

Statistics provide summaries of data and allow logical deductions about unobservable events.

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2
Q

What is exploratory data analysis?

A

An analysis approach that identifies general patterns in the data; Gathering data

It involves collecting data to understand patterns and trends.

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3
Q

What is confirmatory data analysis?

A
  • Evaluating data against rigid statistical rules
  • It tests hypotheses or predictions based on collected data.
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4
Q

Define descriptive statistics.

A
  • Methods used to provide a concise description of quantitative observations from a sample
  • It summarizes data from a small group to represent a larger population.
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5
Q

Define inferential statistics.

A
  • Methods used to make inferences from a sample of a population
  • It estimates characteristics of a larger group based on sample observations.
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6
Q

What is a continuous variable?

A

Measured using a continuous scale with values that can take on an infinite number of values

It can be represented with any degree of precision.

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7
Q

What is a discrete variable?

A

Measured using a discrete scale with values that can only take certain specific values

There are no decimals or fractions involved.

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8
Q

What does ‘error’ refer to in measurement?

A

Collective influence of all factors on a test score beyond those specifically measured

Error is always present in continuous scales.

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9
Q

What are the three properties of scales of measurement?

A

Magnitude, Equal Intervals, Absolute Zero

These properties determine how measurements are interpreted.

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10
Q

What is a nominal scale?

A

Simplest form of measurement for classification or categorization

Data are qualitative and mutually exclusive.

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11
Q

What is an ordinal scale?

A

Permits classification and rank ordering but lacks equal intervals or an absolute zero

It ranks observations but does not quantify the differences between them.

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12
Q

What is an interval scale?

A

Contains equal intervals between numbers but lacks an absolute zero

It allows for meaningful arithmetic operations but not ratios.

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13
Q

What is a ratio scale?

A

Has magnitude, equal intervals, and an absolute zero

All mathematical operations are permissible.

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14
Q

What is a frequency distribution?

A

A way to organize scores to reflect how frequently each value was obtained

It can be presented in tabular or graphic form.

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15
Q

Define a histogram.

A

Graph with vertical lines at true limits of test scores forming contiguous rectangles

Scores are placed on the horizontal axis, frequency on the vertical.

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16
Q

What is a percentile rank?

A

Indicates what percent of scores fall below a particular score

It provides insight into the relative standing of a score within a distribution.

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17
Q

What is the difference between percentile and percentile rank?

A

Percentile is a specific score below which a percentage of scores fall, while percentile rank indicates the percentage of scores below a specific score

They are similar but serve different purposes.

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18
Q

What is the arithmetic mean?

A

Sum of observations divided by the number of observations

It is the most common measure of central tendency for interval or ratio data.

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19
Q

What is the median?

A

Middle score in a distribution

It is found by ordering scores and locating the middle number.

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20
Q

What is the mode?

A

Most frequently occurring score in a distribution

There can be more than one mode in a distribution.

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21
Q

What does variability indicate?

A

How scores in a distribution are scattered or dispersed

It reflects the degree of spread in the data.

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22
Q

What is the range?

A

Difference between the highest and lowest scores

It provides a quick measure of score dispersion.

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23
Q

What is the interquartile range?

A

Difference between Q3 and Q1, representing the middle 50% of the distribution

It is useful for understanding variability in skewed distributions.

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24
Q

Define standard deviation.

A

Square root of the average squared deviation around the mean

It indicates the average distance of scores from the mean.

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25
What is skewness?
Nature and extent of symmetry absence in a distribution ## Footnote It indicates the direction of data skew.
26
What does positive skew indicate?
Few scores at the high end of the distribution ## Footnote It may suggest that the test was too difficult.
27
What does negative skew indicate?
Few scores at the low end of the distribution ## Footnote It may suggest that the test was too easy.
28
Define kurtosis.
Steepness of a distribution in its center ## Footnote It describes the shape and tails of the distribution.
29
What is a normal curve?
Bell-shaped, symmetrical distribution highest at its center ## Footnote It approaches the X-axis asymptotically.
30
What are standard scores?
Raw scores converted to a standardized scale for easier interpretation ## Footnote They indicate how a score relates to the mean in terms of standard deviations.
31
What is a z-score?
Indicates how many standard deviation units a raw score is from the mean ## Footnote A positive z-score means above the mean, while a negative z-score means below.
32
What is a T-score and its formula
T = 10z + 50, with a mean of 50 and SD of 10 ## Footnote It transforms z-scores into a different standardized scale.
33
What is a correlation coefficient (r)?
Index of the strength of the relationship between two variables ## Footnote Its sign and magnitude provide information about the relationship's direction and strength.
34
What does a correlation of +1 or -1 indicate?
A perfect relationship between two variables ## Footnote Positive correlation means both increase/decrease together; negative means one increases while the other decreases.
35
What is correlation?
An expression of the degree and direction of correspondence between two things ## Footnote Correlation can be positive, negative, or nonexistent.
36
What does a positive correlation indicate?
Both variables simultaneously increase or decrease ## Footnote Represented by a plus (+) sign.
37
What does a negative correlation indicate?
One variable increases as the other decreases ## Footnote Represented by a minus (-) sign.
38
What is the significance of the correlation coefficient being +1 or -1?
Indicates a perfect relationship between the two variables ## Footnote No error exists in the correlation.
39
What does an r value of 0 signify?
Absolutely no relationship exists between the two variables ## Footnote Correlation does not imply causation.
40
What is Pearson r?
Pearson correlation coefficient or Pearson product-moment coefficient of correlation ## Footnote It is used when both variables being correlated are continuous.
41
What does the coefficient of determination (r^2) indicate?
How much variance is shared by the X and Y variables ## Footnote It is calculated by squaring the correlation coefficient and multiplying by 100.
42
What is a null hypothesis in correlation testing?
The hypothesis that there is no relationship between the variables ## Footnote This is rejected if evidence shows a significant association.
43
What is Spearman Rho?
Rank-order correlation coefficient or rank-difference correlation coefficient ## Footnote Used when sample sizes are fewer than 30 pairs of measurements.
44
What does Biserial Correlation express?
The relationship between a continuous variable and an artificial dichotomous variable ## Footnote Example: College GWA and passing or failing board exams.
45
What is Point Biserial Correlation?
Expresses the relationship between a true dichotomous variable and a continuous variable ## Footnote Example: Sex and board exam ratings.
46
What does the Phi Coefficient measure?
The relationship between true and artificial dichotomous variables ## Footnote Example: Sex and passing the final exams.
47
What is Tetrachoric Correlation?
Expresses the relationship between two artificial dichotomous variables ## Footnote Example: Passing mock boards and actual board exams.
48
What is a scatterplot?
A simple graphing of the coordinate points for values of the X-variable and the Y-variable ## Footnote It indicates the direction and magnitude of the relationship.
49
What is an outlier in a scatterplot?
An extremely atypical point located at a relatively long distance from the rest of the points ## Footnote Outliers can hint at deficiencies in testing or scoring procedures.
50
What is meta-analysis?
A family of techniques used to statistically combine information across studies ## Footnote It produces single estimates of the data under study.
51
What does regression analysis do?
Makes predictions about scores on one variable from knowledge of scores on another variable ## Footnote It uses the regression line to minimize the squared deviation.
52
What is the formula for the regression line?
Y’ = a + bX ## Footnote Where Y’ is the predicted value for Y, a is the intercept, b is the slope, and X is the score on X.
53
What is a residual?
The difference between the observed and predicted score (Y - Y’) ## Footnote The best-fitting line keeps residuals to a minimum.
54
What is the Standard Error of Estimate?
Standard deviation of the residuals ## Footnote It measures the accuracy of prediction.
55
What does the Coefficient of Determination tell us?
The proportion of total variation in scores on Y explained by X ## Footnote Example: Correlation of .40 indicates 16% of the variation in Y is explained by X.
56
What is the Coefficient of Alienation?
Measure of non-association between two variables ## Footnote It is the opposite of the coefficient of determination.
57
What is the shrinkage effect in regression?
Decrease observed when a regression equation is applied to a different population ## Footnote The proportion of variance may decrease when applied to a new group.
58
What is multivariate analysis?
Considers relationships among combinations of three or more variables ## Footnote It shows the relationship between many predictors and one outcome.
59
What is multiple regression?
Used to find the best prediction of a certain outcome from three or more variables ## Footnote It involves finding the correlation between the criterion and a composite of predictors.
60
What is discriminant analysis?
Finds a linear combination of variables that provides maximum discrimination between categories ## Footnote Used when there are multiple categories.
61
What is factor analysis?
Used to study interrelationships among a set of variables without reference to a criterion ## Footnote It is essential in grouping test items into domains or subscales.
62
What property of scales can nominal perform?
Mode
63
What property of scales can ordinal perform?
Mode, and median
64
What property of scales can interval perform?
Mode, median, arithmetic mean
65
What property of scales can ratio perform?
Mode, median, arithmetic mean, and geometric mean.
66
What mathematical equation can nominal perform?
None. Its only purpose is to classify and categorize variables.
67
What mathematical equation can ordinal perform?
Order, rankings
68
What mathematical equation can interval perform?
Order, addition, and subtraction
69
What mathematical equation can ratio perform?
Order, addition, subtraction, multiplication, and division.

PA (from mochi_venti's reviewer) (6 decks)

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