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PSYC 217 > Midterm 2 - Chapter 12 > Flashcards

Midterm 2 - Chapter 12 Flashcards

1
Q

When do we need stats in the research process?

A

After collecting data - need to summarize & communicate findings

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2
Q

2 types of stats:

A
  1. Descriptive Statistics
  2. Inferential Statistics
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3
Q

How should we most efficiently present research:

A

Want to convey maximum information using minimum space

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4
Q

Purpose of descriptive statistics?

A

Summarizes mass of data points
- Understanding and interpretation
- Visual displays, appropriate calculations

In experiments can calculate within each
- condition/group
- Mean, standard deviation…

In correlation designs
- For each variable, calculate mean, standard deviations, etc
- For every pair of variables, calculate a correlation coefficient (also a descriptive statistic)

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5
Q

3 Types of Descriptive Statistics

A
  1. Measures of Central Tendency (Mean, Median, Mode)
  2. Measures of Variability (Range, Variance, Standard Deviation)
  3. Measures of Relationship (Correlation, Multiple Regression, Multiple Correlation, Partial Correlation)
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6
Q

Scales of Measures

A
  • Nominal
  • Ordinal
  • Interval
  • Ratio
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7
Q

Nominal

A

Group or categorization
- No order or direction
- Summarized by proportion/percentages or the mode

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8
Q

Ordinal

A

Ranked order (1st, 2nd, 3rd..)
- Uneven spaces between “scores”

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9
Q

Interval

A

Numerical scales in which intervals have the same interpretation throughout but no true zero (e.g. temp in celsius - 0 deg still indicates a temperature)

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10
Q

Ratio

A

An interval scale with a true zero reference point (e.g. 0 pounds)
- Summarized with the mean or median and standard deviation

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11
Q

Measures of central tendency

A
  • Describe what’s happening at middle of data
  • What’s “normal”?
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12
Q

3 measures of central tendency:

A

Mean, Median, Mode

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13
Q

Mean

A

= arithmetic average

  • What we usually use!
  • Uses information from every single score
  • Add up all scores in each group and divide by the
    number of scores in each group
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14
Q

Downsides of Mean:

A

□ Affected by outliers (i.e., extreme scores)

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15
Q

Upsides of mean:

A

□ With increasing sample size, each extreme score has less effect on the mean.
□ Maximizes use of all of our data.
□ Has mathematical properties that enable us to
use it in statistical analysis.

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16
Q

Outliers - With increasing sample size, the mean is

A

Less affected by outliers

□ Main idea here - check for outliers if you only have a small sample, but try to get a large sample

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17
Q

Median

A

= score that divides group in half

  • 50% of the scores above, 50% below
  • Used if there are extreme scores (outliers)
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18
Q

How to find median:

A

Put scores in order. Count number of scores.

If odd #: identify the middlemost score.

If even#: identify two middle scores, take average of them.

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19
Q

When is median useful?

A

Whenever it’s most descriptively informative to report the value for which equal numbers of people score higher
and lower (e.g. income)

  • Also, when you can spot an outlier
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20
Q

Mode

A

= most frequently occurring score

  • Sometimes no mode; sometimes more than one
  • Usually used for nominal or ordinal variables
  • Put the scores in order – look for most frequently occurring score(s)
  • May be none, or more than one
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21
Q

When is mode useful?

A

Whenever it’s most descriptively informative to
report the most frequently occurring score (e.g.: employee salary distribution)

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22
Q

Measures of Spread:

A
  • Variability
  • Standard Deviation
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23
Q

Variability:

A

The spread in a distribution of scores

AMOUNT of spread is often measured by Standard Deviation

How much each score deviates from the mean

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24
Q

Possible Measures of Variability

A

□ Range (max – min)
□ Variance
□ Standard Deviation

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25
Q

Issues with range

A

can be too simplistic

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26
Q

Issues with variability:

A

not very descriptive

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27
Q

Standard Deviation

A

□ A measure of variability that enables reference to the Normal Distribution so it’s meaningful (as opposed to variance).
□ Defines what’s “normal” for that variable

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28
Q

How to calculate variance:

A
  • Find out how much each score deviates from the mean (mean of 5, 0 = 5)
  • Square each number
  • Add up these numbers
  • Divide by TOTAL number of scores being calculated MINUS 1 (not the total of the numbers, but how many there are - 7, 3: not 10, but 1)
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29
Q

One half of the bell curve, SD of +/-1, SD of +/- 2, SD of +/- 3

A
  • 50%
  • 68%
  • 95%
  • 99.7%
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30
Q

How to calculate Standard Deviation:

A

SQUARE ROOT of variance

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31
Q

Measures of Relationship:

3 types of Descriptive Stats

A
  • Correlation
  • Multiple Regression
  • Multiple Correlation
  • Partial Correlation
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32
Q

Correlation (r) and r-squared

A

□ +/- = “direction” of relationship - Positive or negative?
□ Number = “strength” of relationship?
(How closely is one set associated with other set?)

For linear relationships!!
- r = 0 could mean no relationship OR a non-linear relationship!

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33
Q

Correlations - Restriction of range

A

Correlations can be misleading if the full range on both variables is not measured

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34
Q

Multiple Correlation (R) and R-squared

A

Expressing correlation as a percentage:
- r2 = a proportion
- r2 = .28 means that 28% of the variance in scores is shared by MC and written portions.
- r2 = .28 means that 28% of the variance in MC scores is predicted by written scores & vice versa

Measures the proportion of variance in the dependent variable that can be explained by the independent variable in a regression model.

35
Q

Amount of Shared Variance

A

If r2 = 0, there is NO shared variance!
If r2 = 1, there is 100% shared variance (goes from 0-1 only)

36
Q

READINGS

A
37
Q

In which type of scale are the intervals between each rank order NOT equal?

A

Ordinal scale

38
Q

In which type of scale ARE the intervals between each rank order equal?

A

Interval Scale (differences between 90-95 are the same as 115-120)

39
Q

When it’s difficult to know whether an ordinal or interval scale is being used, what should we do?

A

Treat variables as a interval scale. because when ordinal scales are averaged across many instances, they take on properties similar to an interval scale

40
Q

Data measured on __ and __ scales can be summarized using __

A

interval; ratio; MEAN

41
Q

Variables measured on interval and ratio scale are often referred to as…

A

continuous variables - the values represent an underlying continuum

42
Q

Interval and ratio scales can be treated the same way..

A

Statistically

43
Q

Why should we first explore variables separately?

A

Allows us to get a sense for what the data for each of our variables look like and also identify any possible errors that might have occurred during data collection

44
Q

Graphing frequency distributions

A

Frequency Distribution: indicates # of p’s select each possible category/scale on a variable

EX: a poll asks 100 people how many pets they have. They find that 38 people have no pets, 25 have one pet, 17 have two pets, 6 have three pets, and 14 have four or more pets.

45
Q

Pros of Graphing frequency distributions:

A
  • See what scores are most common/uncommon
  • See shape of distribution
  • Identify OUTLIERS: scores that are unusual, unexpected, very different from scores of other participants
46
Q

Bar Graph:

A

Uses a separate and distinct bar for each piece of information

Used for comparing group means and percentages

47
Q

Types of Frequency Distributions:

A
  • Bar Graphs
  • Pie Charts
  • Histograms
  • Frequency Polygons
48
Q

Pie Charts

A

Divide a whole circle that represents relative percentages

Useful in representing data on a nominal scale

49
Q

Histograms:

A

Uses bars to display a frequency distribution for a continuous variable (e.g. continuous, increasing amounts of a variable)

50
Q

How do histograms differ from bar graphs:

A
  • Histograms: bars touch each other, reflecting a continuous variables (ie on x axis)
  • Bar Graph: gaps between each bar, helping communicate that values on x-axis are nominal categories
51
Q

Normal Distribution

A

A distribution of scores that is frequently observed, and rather important for stats

Majority of scores cluster around the mean

Only possible for continuous variables (interval or ratio)

52
Q

Standard Deviation:

A

How scores spread out from the mean, on average

53
Q

Breakdown of normal distribution/deviation:

A
  • 68%: fall within 1 standard deviation above and below the mean
  • 96% fall within 2 standard deviations above/below mean
54
Q

Frequency Polygons:

A

Alternative to histograms - use a line to represent frequencies for continuous variables

Helpful when you want to examine frequencies for multiple groups simultaneously

55
Q

Descriptive Statistics:

A

Calculating statistics to describe or summarize our data

56
Q

2 main types of descriptive stats:

A

1: measures of central tendency - capture how participants scored overall, across the entire sample
2: measures of variability - how differently the scores are from each other, or how widely they’re spread out or distributed

57
Q

Central Tendency

A

Tells us what the scores are like as a whole, or how people scored on average:
- Mean (represented by X in calculations, M in reports)
- Median (Mdn in scientific reports)
- Mode (for variables that employ an interval, ratio, or ordinal scale)

58
Q

Variability

A

Characterizes the amount of spread in a distribution of scores, for continuous variables

59
Q

Comparing Group Percentages

A

e.g. - wanting to know how groups differ in the ways they respond to questions

  • Can calculate percentages for each group and compare
60
Q

Comparing group means

A

e.g. wanting to see how groups, on average, responded and comparing these numbers

61
Q

Graphing Nominal Data

A

Common way to graph relationships between variables when one variable is nominal is to use a bar graph or line graph

62
Q

When are bar graphs used compared to line graphs?

A

Bar graphs - when values on x-axis are nominal

Line graphs - when values on x axis are numeric

63
Q

Describing Effect-Size Between Two Groups

A

Effect-Size: describing relationships among variables in terms of size, amount, or strength; helps determine how large effects are

64
Q

Effect Size - Cohen’s d:

A

Cohen’s d: comparing two groups on their responses to a continuous variable
- Difference in means between two groups, standardized by expressing it in units of standard deviation

  • In a true experiment, the Cohen’s d value describes the magnitude of the effect of the IV on the DV
  • When studying naturally occurring groups, describes magnitude of effect of group membership on a continuous variable
65
Q

Smallest possible value for Cohen’s d:

A

0 - no effect, no max value

66
Q

Different analyses are needed when you don’t have distinct groups you wish to compare, but rather..

A

have a range of scores to investigate in terms of their relationship with other scores

67
Q

What data is appropriate for correlational designs?

A

Correlation coefficient: statistic describing whether, how, and how much two variables relate to one another (many different types)

68
Q

Pearson R Correlation Coefficient

A
  • r = 0 to 1 (NOT a percentage or probability)
  • tells us the direction of the relationship
69
Q

How can R be graphed - Scatterplots

A
  • Scatterplot: each pair of scores is plotted as a single point in a graph
  • Perfect relationships = perfectly diagonal lines (however, remember measurement errors!)
  • Whenever relationships aren’t perfect, if you know a person’s score on the first variable, you can’t perfectly predict what that person’s score will be on the second variable
70
Q

Pros of scatterplots:

A
  • Provide ways of seeing how variables relate to one another
  • Allow researchers to detect outliers
71
Q

Important Considerations:

A
  • Restriction of Range
  • Curvilinear Relationship
72
Q

Important Considerations - Restriction of Range:

A
  • If the full range of possible scores isn’t sampled, but instead restricted, the correlation coefficient produced with these data can be misleading - LESS variability in the scores and thus, less variability that can be explained or predicted by the other variable
  • The issue can occur when people you’re sampling are all very similar on one or both of the variables you are studying
73
Q

Important Considerations - Curvilinear Relationship

A

Pearson Correlation only designed to detect linear relationships - if relationship is not linear but curvilinear, the correlation coefficient will fail to detect this relationship

Another type of statistic must be used to determine the strength of the relationship

74
Q

Correlation Coefficients as Effect-Sizes

A

Correlation coefficients not only allow us to examine relationships between continuous variables, they are also indicators of effect size

75
Q

Correlation Coefficients as Effect-Sizes - Square Value of R

A

By multiplying R by itself, it lends itself to a simple interpretation: THE PROPORTION OF VARIANCE BEING EXPLAINED - AKA Squared Correlation Coefficient

76
Q

Regression

A

Regression: advanced way of examining how variables relate or covary (a statistical technique); analyzes relationships among variables

77
Q

The Regression Equation

A

Y = a + bX
(Y = criterion variable: score we wish to predict, X = predictor variable: known score, a = y-intercept, b = slope of line)
The same as an equation for drawing a straight line - the line that best summarizes all of the data points

Can be used to make specific predictions

78
Q

Multiple Correlation

A

(symbolized as R, distinguished from Pearson r)

Provides correlation between a combined set of predictor variables and a single criterion variable (as any phenomenon is likely determined by many factors, accounting for these permits a greater accuracy of prediction)

79
Q

Squared Multiple Correlation Coefficient

A

R squared can be interpreted in the same way as the Squared Correlation Coefficient (r squared)

R squared tells you the proportion of variability in the criterion variable that is accounted for by the combined set of predictor variables

80
Q

Regression is more powerful than correlation because…

A

it can be expanded to accommodate more than one predictor to predict the criterion variable - this expanded model is AKA multiple regression, allowing us to examine the unique relationship between each predictor and the criterion

In contrast to multiple correlation, which only provides a single value for the relationship between the combined set of predictors and the criterion variable

81
Q

Order of Interpreting Data Analysis:

A
  1. Correlation Coefficient
  2. Multiple Correlation
  3. Multiple Regression
82
Q

What technique helps address the third variable problem?

A

Partial Correlation: provides a way of statistically controlling for possible third variables in correlational

Estimates what the correlation between the two primary variables would be if the third variable were held constant - in other words, if everyone responded to this third variable in the exact same way

83
Q

What can you do with a calculated partial correlation?

A

With a calculated partial correlation, you can compare with the original correlation to see if the third variable was influencing the original relationship

84
Q

Advanced Modelling Techniques:

A
  • Structural Equation Modelling (SEM): examines models (an expected pattern of relationships among numerous different variables) that specify a set of relationships among many variables

PSYC 217 (18 decks)

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