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3340 Data Analysis > Week 8-11 (Quantitative) > Flashcards

Week 8-11 (Quantitative) Flashcards

1
Q

Descriptive Statistics

A
  • Numbers that describe the data
  • Frequencies
  • Central tendency
  • Measures of dispersion
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2
Q

Inferential Statistics

A
  • Numbers that make inferences/predictions
  • Calculations depend on the study
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3
Q

Frequency

A

How many times each value appears for a given variable

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4
Q

Mode

A

Most frequent value in a data set

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5
Q

Median

A

Middle value of data set

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6
Q

Mean

A

The mean is the average or norm

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7
Q

Measures of Dispersion

A
  • Variables can vary from their centre or central tendency
  • Variation can be explained by two terms
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8
Q

Range

A

Difference between the lowest & highest value

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9
Q

Standard Deviation (SD)

A

Average difference between each values & the mean

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10
Q

Large Standard Deviation (SD)

A

Data is spread out

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11
Q

Probability

A
  • Chance of something happening
  • Allows inferences/predictions about what is likely to happen
  • Normal distribution for interval & ratio data
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12
Q

Normal Distribution

A

Probability distribution in which the mean, median, mode are equal

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13
Q

Normal Curve

A
  • Most variable form a normal distribution
  • Assumption for inferential statistics
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14
Q

Z Score

A
  • Statistic used to measure distance of raw scores from the mean
  • Unit of measure is in standard deviation
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15
Q

SD & Z Scores

A
  • Express raw score as a percentile
  • Determine likelihood of getting a particular score
  • Compare 2 scores from different normal distributions - standardizations
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16
Q

Skewness

A
  • Asymmetrical distribution in which 1 tail is longer than the other
  • Outliers to the right = positive skew
  • Outliers to the left = negative skew
  • Mean, median, mode not equal
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17
Q

Kurtosis

A

How narrow is the peak of the distribution

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18
Q

Null Hypothesis (H0)

A

Observations are the result of chance

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19
Q

Alternative Hypothesis (H1)

A

Observations are result of a real affect - something else happened

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20
Q

P-Value

A

Probability that a test statistic will result by chance

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21
Q

Threshold Value (a)

A

Acceptable probability of rejecting a true null hypothesis

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22
Q

Rejecting Null Hypothesis

A

P-value lower than the pre-determined value a
Between .05-.001

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23
Q

Hypothesis Testing

A
  1. State the null hypothesis & alternative hypothesis
  2. Identify a statistic to assess the truth of the null hypothesis
  3. Compute the p-value
  4. Compare the p-value to a predetermined threshold value (a)
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24
Q

P=0

A

Impossible to be chance

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25
Q

P=0.001

A
  • Very unlikely
  • 1 in 1000
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26
Q

P=0.05

A
  • Fairly unlikely
  • 1 in 20
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27
Q

P=0.5

A
  • Fairly likely
  • 1 in 2
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28
Q

P=0.75

A
  • Very likely
  • 3 in 4
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29
Q

P=1

A

Absolutely certain it is due to chance

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30
Q

Statistical Significance

A
  • A result NOT attributed to chance
  • Reject null hypothesis
31
Q

Type I Error

A
  • Null hypothesized is incorrectly rejected
  • Concludes there is a significant relationship when there is not
32
Q

Type II Error

A
  • Fail to reject a null hypothesis that is actually false
  • Concludes there is no relationship when there is
33
Q

Confidence Intervals

A
  • Specific range within which the population parameter is expected to lie
  • Narrower = more precise findings
  • Common to use 95%
34
Q

Clinical Significance

A
  • Practical importance of a treatment effect
  • Not always the same as statistical significance
35
Q

Nominal

A

Differentiates between items based only on qualitative classifications

36
Q

Ordinal

A

Provides a rank order with no degree of difference between them

37
Q

Interval

A
  • Allows for the degree of difference between items
  • Zero is not truly zero
38
Q

Ratio

A

Has a meaningful zero value

39
Q

Alpha Level

A
  • Cutoff for value for p
  • P should be less than a to reject H0
40
Q

Non-Parametric Tests

A
  • Use categorical data
  • Ordinal or nominal
  • Normal distribution not applicable
  • Chi-square test
41
Q

Parametric Tests

A
  • Use continuous data
  • Interval or ratio
  • Normal distribution is applicable
  • Population parameters (means/SDs) can be estimated
  • T-test, ANOVA, correlation
42
Q

Chi-Square Test

A
  • Compares expected frequency with observed frequency of the data
  • Examines relationship among categorical variables
43
Q

Chi-Square Data Type

A
  • Categorical - nominal
    • Frequencies - counts or percentages
  • Data can be put in a contingency table
44
Q

Chi-Square Relationship of Interest

A
  • Goodness of fit (observed vs expected) - 1 variable
  • Test of independence/association - 2 variables
45
Q

Degrees of Freedom (df)

A

Number of scores that are free to vary when calculating a statistic

46
Q

Goodness of Fit - 1 Variable*

A
  • 1 independent categorical variable
  • Tests how well an observed distribution corresponds to an expected probability
  • Represented by the H0
47
Q

Test for Independence/Association - 2+ Variables*

A
  • 2+ independent categorical variables
  • Tests whether categorical variables are associated with 1 another
48
Q

Chi-Square Assumptions

A
  • Frequency data
  • Adequate sample size - 5+
  • Measures must be independent
  • Categories are set before testing based on theory
  • No assumptions about the underlying distribution of the data
49
Q

Chi-Square Limitations

A
  • Does not indicate strength of an association
  • Yes or no statistically significant relationship
  • Sensitive to the sample size
50
Q

T-Test

A

Used to compare means of 2 groups

51
Q

T-Test Assumptions

A

2 groups that are compared should have approx. normal distributions with similar SDs

52
Q

Independent vs Paired Samples

A
  • T-tests can be done with independent or paired/dependent samples
  • Not the same as dep & indep variables
  • Calculations are different
53
Q

Independent Samples

A

Both samples are randomly selected within population of interest

54
Q

Paired Samples

A

Individuals in 1 sample are matched with those in the other sample

55
Q

Two-Tailed Test

A
  • Tests for any difference between means
  • Non-directional
  • Means are significantly different if 1 mean is within the top/bottom 2.5% of the other samples probability distribution (p<0.05)
56
Q

One-Tailed Test

A
  • Tests for a difference in a particular direction
  • Less stringent in the direction of interest
  • Rejection region for H0 is all in 1 tail of the curve
  • Will not give a significant result in other direction
  • Should be used only when change in opposite direction is nearly impossible
57
Q

ANOVA

A

Compare means of 3+ groups

58
Q

Interpreting T-Test

A
  • Compare test statistic to critical value for a given alpha
  • If test statistic > value it means p<a
59
Q

ANOVA Function

A

Calculates ratio of variation between treatments to the variation within treatments

60
Q

ANOVA H0

A

All means of treatment group are equal

61
Q

ANOVA H1

A

At least 1 mean of treatment group is different

62
Q

ANOVA Hypothesis

A

Can only determine whether a difference exists

63
Q

Why ANOVA

A
  • Allows testing of several null hypotheses at 1 time without increasing error
  • <2 groups can’t compare means with t-test without increasing risk of type I error
64
Q

ANOVA Musts

A
  • Use interval/ratio data/quasi-interval
  • In practice ordinal data are used if scales are symmetric
  • Groups being compared have similar SDs
  • Independent/dependent samples
65
Q

Independent Sample

A

Randomly selected within population of interest

66
Q

Dependent Sample

A
  • For repeat measures
  • Examining a change over time in samples - time related
67
Q

Repeat Measures

A

Increases likelihood of finding significant differences where they exist

68
Q

Position/Carry-Over Effects

A
  • Order of treatment may affect outcome
  • Previous treatment continues to have effect during the next treatment
  • Minimized by randomly assigning treatment order
69
Q

SD Calculation

A

Average difference between each value & the mean

70
Q

Variance Calculation

A

Average of the squared differences from the mean

71
Q

F-Distribution

A
  • Skewed to right
  • F-values can be 0 or +
  • Different F-distribution for each pair of degrees of freedom
72
Q

MANOVA

A
  • M=multivariate
  • Data comes from independent samples
  • 2 outcome variables
73
Q

Post Test

A
  • Determine which means are significantly different from the others
  • Different tests: Tukey, Bonferroni, Fisher’s
74
Q

Tukey Test

A

Best of all pairwise comparisons are of interest

3340 Data Analysis (3 decks)

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