Midterm #2 Flashcards
(99 cards)
1
Q
What type of theorists tend to this traits are fixed?
A
Entity theorists (fixed mindset) The kind of person someone is is something that is basic and can't be changed
2
Q
What type of theorists tend to think traits are changeable?
A
Incremental theorists (growth mindset) Everyone, no matter the person can sig. change their basic characteristics
3
Q
Theories of intelligence and how much people study. When looking at the extent to which ppl have growth or fixed mindset associated with how much people study- how does univariate descriptive statistics vs bivariate data stats allow us to look at it?
A
Univariate descriptive stats= we can identify 2 variables and their scale of measurements. can plot the variables separately- can calculate CT and variability and check the distribution of the variables.
Bivariate allows us to look at the correlation- examines how strong and in what way the 2 variables are related
4
Q
What are 2 ways to describe data from one variable?
A
- graph the association
- numerically describe the association (Mean, SD etc)
5
Q
What 2 things can we do to look at a bivariate relationship?
A
To assess the association or relationship between 2 variables we can
1) Graph the association (scatterplot)
2) Numerically describe the association (correlation coefficient, r)
6
Q
When drawing a scatterplot, what variable goes on the x or y axis?
A
If we have a theory of which variable predicts the other- then the predictor goes on the x-axis, and what is being predicted about/caused goes on the y.
If no theory, it doesn’t matter.
7
Q
What 3 things do we look for in a scatterplot?
A
- Direction
- Shape
- Strength
8
Q
What does the direction of a scatterplot tell us?
A
The relationship- how the values of one variable systematically change relative to those on the other variable?
9
Q
What does a positive relationship look like?
Give 2 examples
A
When both variables systematically change in the same direction.
- Can increase- the taller you get the larger your shoe size.
- Can decrease- the less you study, the lower your GPA
10
Q
What does a negative relationship look like?
A
When the variables systematically change in the opposite direction.
eg. the more money you spend, the lower your bank balance will be.
11
Q
2 shapes of the relationship you can see in a scatterplot.
A
- Linear
2. Curvilinear
12
Q
3 terms we use to describe the shape of a scatterplot graph.
A
Weak, moderate, strong
13
Q
What is a 4th way (other than looking at the shape, direction and strength)?
A
Superimpose a quadrant to look at the relationship by drawing a line of mean for the y and x axis. You can then determine for each quadrant if participants are above or below the mean on y and x.
14
Q
If there are more data points above the mean on both and below the mean on both what does this suggest?
A
There is a positive relationship between the 2 variables.
15
Q
What does the Pearson r describe?
A
It describes a linear relationship between 2 continuous (or somewhat continuous) variables.
16
Q
What is the Pearson r used for? What kind of data?
A
Interval or ratio
17
Q
What are the 5 steps to calculating Person r?
A
- Describe ea/ variable
- plot the data and compute the mean and SD for x and y - Compute deviation scores (y-Ymean) and (x-Xmean)
- Compute sums of products (SP)
- Compute Covariance (COV)
- Compute the Correlation Coefficient r
18
Q
What does the numerator in the Pearson r represent/measure?
A
Measures the degree that 2 variables covary
19
Q
What does the denominator of Pearson r represent?
A
Adjusts covariability by amount of variability in each variable.
20
Q
How do you determine the sums of product?
A
You multiply 2 deviation scores together and add up all the deviation scores
SP= ∑(X − XM)(Y −YMean )
21
Q
How do you compute covariance?
A
Average the summed products by dividing by N
22
Q
What does covariance determine?
A
It determines the average extent to how much these 2 variables are varying apart/together from their respective means across the entire group of scores.
23
Q
What is important to note about covariance?
A
It isn’t standardized. The magnitude of covariance depends on units of measure- you need to convert covariance to standard scores.
24
Q
How do you compute the correlation coefficient? What does this do?
A
Divide covariance by product of SD for each variable. This transforms covariance to a scale, giving direct info about the relationship between the variables regardless of the units of measure for each variable.
25
When interpreting the correlation coefficient what are the general guidelines for the numerical value of the number.
No relationship=
26
Give an example of how you would write up an interpreted graph using Pearson r?
There was a strong positive relationship between a
growth mindset (M = 4.00, SD = .71) and estimated
hours studied per week (M = 13.00, SD =4.34) for 5
participants, r=.82. The more participants had a
growth mindset, the more hours they estimated that
they studied per week
27
Growth mindset= 5.5, 3.5, 5, 5.5, 5.5
Hours studied= 7, 11, 15, 20, 12
Hours= SD=4.34
Growth Mindset SD=0.78
SP= 3.00
Cov=3.00/5=0.6
r=0.1786
28
When looking at cross product pairs (covariance) if some pairs vary in the same direction, but some vary in opposite direction what does this mean?
The value for covariance is close to 0.
29
Researcher is studying the relationship of sleep to mood. She asked 6 students in her morning seminar 2 questions:
1. How many hours did you sleep last night?
2. How happy do you feel right now on a scale of 0=not at all to 8=extremely?
1. Hours=5, Mood=2
2. Hours=7, Mood= 4
3. Hours=8, Mood=7
4. Hours=6, Mood=2
5. Hours= 6, Mood=3
6. Hours=10, Mood=6
What is Pearson r? How do you write it up?
Hours, M=7, SD=1.63
Mood, M=4, SD=1.92
SP=16
COV=16/6=2.6667
r=2.6667/(1.63)(1.92)=0.85
There was a strong positive relationship between
number of hours of sleep the night before (M = 7.00,
SD =1.63) and mood (M = 4.00, SD = 1.92) for 6
participants, r=.85. The more sleep students got the
night before, the happier they were the morning after.
30
What value of r would we want?
We have a measure extraversion and we want to make sure all the items on the measure capture the same thing.
Example items:
-I like to have a lot of people around me.
-I laugh easily.
-I really enjoy talking to people.
-I like to be where the action is.
-I often feel as if I'm bursting with energy.
-I am a cheerful, high-spirited person.
A) -0.6
B) 0.08
C) 0.35
D) 0.85
D) 0.85
| b/c reliability
31
We want to examine the relationship between extraversion and number of positive status updates on Fb in a month.
```
What is the lowest value of r that would suggest a positive relationship?
A) -0.6
B) 0.08
C)0.35
D) 0.85
```
C) 0.35
32
What 3 things are included when interpreting reliability?
test-retest, inter-rater & inter-item reliability
33
What is the difference between interpreting the correlation coefficient for reliability and human behaviour?
reliability= 0.85< is desired
0.75-0.84 is mod. acceptable
<0.65 is not desirable
For human behaviour, lower correlations are acceptable
-can use the general guidelines to specify weak, moderate and strong correlations
No relationship |0.30| to |0.50|
Strong relationship > |0.5
34
```
We want to examine the relationship between extraversion and the intensity of smile in Fb profile pictures. What is our desired correlation between coders in their rating of smile intensity?
A) -0.6
B) 0.08
C) 0.35
D) 0.85
```
D) 0.85
35
When would you use pearson r?
When both variables are interval/ratio
36
When would you use spearman rho?
When one or both of the variables are ordinal
- weak curvilinear relationship in interval/ratio data
- Heteroscedasticity in interval/ratio data
37
When would you use point biserial?
When one variable is nominal and the other is interval/ratio
38
When would you use phi?
When both variables are nominal. Two dichotomous variables.
39
How do you compute spearman rho?
1. Rank scores on each variable from low to high
2. Assign ranks of 1 to N to the scores
3. Put the data back into their original pairs and replace their scores with assigned ranks
4. Carry out the Pearson correlation on the ranked data
5. Result: "pearson on ranks"
40
What is a disadvantage of spearman rho?
Ranks only tell you the order in which Ps scores but doesn't tell you the magnitude of difference among values
41
What kind of correlation would you use if you're looking into how does spending money on others affect your happiness?
Group 1: Spend money on self
Group 2: Spend money on others
Point biserial Correlation
42
What kind of correlation would you use if you're looking at If a couple is more likely to divorce if their parents were divorced?
Phi
43
What correlation coefficient should you use for the following scenario:
Do people's words with friends rankings on the leaderboard correlate with their GRE verbal scores?
Spearman rho because WWF=ordinal
44
What does the restricted range refer to?
Refers to cases in which the range over which X or Y varies is artificially limited.
The correlation may increase when the restriction of results eliminates some curvilinear relationship in the data.
45
What is an example of how correlation may increase when sampling from a restricted range?
You examine the relationship between height and age between the age of 0-70.
This is curvilinear because it rises to about 17years of age and then levels of or declines.
Correlation would be stronger if we restricted the range of ages to 4-17.
46
When would the correlation increase or decrease when restricting the range?
The correlation may increase when the restriction of results eliminates some curvilinear relationship in the data.
The correlation may be reduced when restricting the range of X and Y.
47
Possible relationship between university GPA and scores on a standard achievement test for a sample of students?
Not everyone gets into uni so GPAs are are only available for students who had relatively high scores on the standardized test. University students only get 400 or more on the test.
48
Data in which the sample of observations could be subdivided into two distinct sets of the basis of some other variable
Heterogeneous subsamples
Group A tends to be really high on both variables (x and y) whereas Group B tends to be really low on both variables
Can get a strong relationship when there isn't really one there
49
What is an example of a heterogenous subsample?
Subjective well-being vs individualism comparing american cultural context to japanese cultural context.
(Jap=high w-b with low individualism, Amer=high indiv with high w-b)
50
Does moving in childhood affect well-being? (3)
Numbers f childhood moves for extraverts unrelated to well being, number of childhood moves for introverts negatively related to well-being.
(extraversion/introversion=3rd variable)
51
What is sampling variation?
Each sample will vary somewhat.
| Values for mean, median, mode may differ for each sample.
52
What is heteroscedasticity?
A skew in one or both variables, high value of SD in variable with skew.
53
How does heteroscedasicity effect r?
A variable with skew results in a high value of SD.
Higher values of SD means a lower r.
r=covariance/(SDx)(SDy)
Therefore, heteroscedascity in the data results in a smaller r.
54
What is an example of heteroscedasticity?
The relationship between age and annual income.
Teens mostly earn minimum wage, but as age increases (20,30,40+ years) some will shoot up in the income brackets whereas others may not
55
Does the size of r depend on hypothesis testing vs. descriptive statistics?
Descriptive- if you're just describing a dataset, size of N doesn't directly influence a magnitude of Pearson r provided you randomly sampled from the population.
Hypothesis- when you do a test of how meaningful the value of r is, size of N will be important.
56
When does the size of N matter for descriptive measures?
Only for the variation (range) of correlation values. Because a small N means you are less confident in your r value.
57
Variable that is used to predict scores of individuals on another variable. On X axis.
Advertising budget.
Predictor variable
58
A variable that is predicted. On Y axis. Album sales.
Criterion variable
59
What variable is on the Y axis for a regression scatter plot?
Criterion- dependent variable.
60
What variable is on the X axis for a regression scatter plot?
Predictor- independent variable.
61
What is Ŷ?
Predicted score
62
If we want to predict album sales based on the advertisement budget we allot for a particular record, which variable is the criterion variable?
a) Advertisement budget
b) The record being promoted
c) The artist being promoted
d) The album sales
d) The album sales
63
What is the goal of regression?
Mathematically 'fit' (define) a line that best describes the present data and then use this line to predict behaviour for a new group of participants.
Regression line= the straight line of best fit
64
How do we find the best fitting line?
Find the line that makes predictions about album sales that are as little off from the true scores as possibles.
65
What is 'error' in regression?
The difference between a predicted score and a person's actual score
66
How do we determine the best-fitting line?
The line that minimizes the sum of squared errors of prediction
67
What is the equation to determine if the regression line minimizes the errors?
Sum of squared errors= Σ(Y-Ŷ)^2
68
What does the regression line reflect?
The linear relationship between 2 variables
69
What does slope indicate in regression?
Slope indicates the amount of change in Y that accompanies one unit of increase in X
70
In linear regression the symbol b-y is used to refer to the ________ and the symbol a-y is used to refer to the ________.
a) slope and intercept
71
Which coefficient will tell you the direction of the relationship (pos vs neg)?
B-y (slope)
72
The formula for a regression equation is:
Ŷ = -2+3X
What would Ŷ be for a person scoring 4 on X?
10
73
Suppose it is possible to predict a person’s score on
the next midterm (Ŷ) from their score on the first
midterm (x). The regression equation is: Ŷ =9 + 2X.
What is the person’s predicted score on the 2nd
midterm this person got a 40 on the first one?
89
74
How many coordinates do you need to plot the regression line?
Two!
1) Y intercept
2) The given X and predicted Ŷ coordinates
Can always plug in your own X value if don't have one
75
P Widget Test Score Widgets per Hour
1 1 2
2 1 4
3 2 4
4 2 6
5 2 2
6 3 4
7 3 7
8 3 8
9 4 6
10 4 8
11 4 7
```
X-mean= 2.6364
SD-x= 1.06794
```
```
Y-mean= 5.2727
SD-y= 2.09299
```
solve for r and b-y, and a-y
then put in an equation
X-mean=2.6364
SD-x= 1.0679
Y-mean= 5.2727
SD-y=2.0929
```
SP= 18.0904
Cov=SP/N= 1.6446
```
SD-ySD-x=2.2350
r=0.7358
b-y= 1.4420
a-y= 1.4710
Ŷ=1.4710+(1.4420)X
76
Why is the regression line also called the "least squares" regression?
Because this mathematically defined line minimizes the errors associated with trying to predict information
77
Where do the X and Y regression lines intersect?
At their means
78
What is Σ(Y-Ŷ)^2?
A minimum.
79
Assume that the regression predicting Grad School GPA from student GRE scores is Ŷ = .15 + .27(X). This means that there was an:
a) increase in GPA of .15 for every 1 point increase in
GRE score.
b) increase in GPA of .27 for every 1 point increase in
GRE score.
c) decrease in GPA of .27 for every 1 point increase in
GRE score.
d) decrease in GPA of .15 for every 1 point increase in
GRE score.
b) Increase in GPA of 0.27 for every 1 point increase in GRE score.
80
What is (Y-Ŷ)?
A residual or difference between an observed Y-value and a predicted Y value on a regression line.
Measures error of prediction around the regression line or how far off are we in our ability to predict.
81
In a previous section we also computed deviations from a value. What type of measures were we computing when we looked at deviations?
Variability
82
What does standard error of estimate do?
It's computing the standard deviation of prediction errors in linear regression.
SD sub Y-Ŷ
83
If there is a relationship between X and Y (and r doesn't equal 0) will SD sub Y-Ŷ be smaller or bigger than SD sub Y? Why?
Smaller. It reduces because you are using another variable of information rather than just one. With 2 sources of predictions you can see the distance between regression line and the actual values.
It allows more room to explain variation.
84
What happens if r=0 when comparing SD sub Y and SD sub Y-Ŷ?
They will equal one another!
85
Ŷ = 33.54 + 4.767(x)
X (hours/week) Y (test scores)
```
8 75
2 50
4 45
9 60
10 95
```
what is r? What is SD sub Y−Ŷ? solve the short and long ways.
X mean=6.6
SDx=3.0725
Y mean=65
SDy=18.1659
r=0.8062
SD sub Y-Ŷ=10.75
86
If Record executives ask us how many albums TSwift will sell if the company sells 500,000$ promoting her album what would be our best guess if we don't have an accurate model between album sales and advertising budget?
Our best guess would be the mean number of album sales from the previous data. No matter if we spend $1 or $50000
87
How do we determine the variability of prediction? How can we measure how much better our ability is to predict album sales based on the regression line compared to when we just use the mean album sales?
(when r=0?)
We can take the difference between total and unexplained variability.
Total variability-unexplained variability=explained variability
88
What is unexplained variability?
The degree of inaccuracy when applying the straight line that best fits the data. This is the difference between the observed value for Y and the predicted vale for Y (Ŷ). (Y-(Ŷ)
89
What is total variability?
Differences between observed data and mean value of Y. (Y-Ymean)
90
What is explained variability?
The difference between the mean value of Y and the regression line.
(Ŷ-Ymean)
91
What is total variability?
Total variability= explained variability(Ŷ-Ymean).+unexplained variability (Y-Ŷ).
92
How do you explain total variability= regression/prediction + error?
Total variability= how much variability do we have in album sales across 200 difference albums?
Regression/prediction= how much variability in album sales can we explain from the ad budget
Error= how much variability is due to other factors? (Variability we can't explain from the ad budget)
93
Why do we use a proportion of variability instead of SS-subR?
Because SS-subR is not easily interpretable as it is in squared units.
Proprtion=explained variability (SS-subR)/Total Variability (SS-sub T)
94
What is r^2?
Proportion of explained variability or predicted variability.
r^2= explained variability/total variability
95
What is 1-r^2?
Proportion of unexplained variability.
| 1-r^2=Error/total Variability
96
Assuming there is a correlation between X and Y, and given the total variability in the dataset: What is the term that represents the proportion that represents error in prediction?
Unexplained variability
97
Assuming there is a correlation between X and Y, and given the total variability in the data set: What is the term that represents the proportion that represents error in prediction?
Explained variabilty
98
How do you determine proportion of explained variability?
Explained variability (SSr)/Total Variability (SSt)
99
How do you determine proportion of unexplained variability?
Unexplained variability (SSE)/Total Variability (SST)
