content tests

The measurement of psychological variables and constructs
- Like what we can use to measure things like strength

A variable that cannot be observed directly
- Like working memory, face recognition

A definition of a variable or construct in terms of exactly how it will be measured
- like an individual questionnaire measuring extroversion

No relationship between the different possibilities
- # of people that are happy, sad, or neutral or other
Like how often fruits occur in a certain category - no relation between banana and apple other than them being fruits

There is a natural, meaningful way to order the different possibilities but that is it.
Eg) Rank the emotions in terms of which you currently feel from most to least dominant - you don't know the distance of difference between these things but you know one is ranked differently than the other.
If three people won gold, silver, bronze - you'd know fastest to slowest is gold, silver, bronze but you don't know HOW much faster

The numerical value is genuinely meaninful and the differences between the numbers are intepretable but there is a no natural 0.
- Person A and B are 10 IQ points different from one another
- You cannot say that a person with an IQ of 120 is 2x smarter than one with an IQ of 60
○ These values don’t have a natural zero
○ 20 deg C is not 2x warmer than 10 deg? - bc there is no natural zero bc 0 deg doesn't mean no kinetic energy
You'd have to use Kelvins to make that claim - bc at 0 K there is no movement

Numerical values genuinely meaninfyl, differences between values are meaninful and has a natural 0.
- We can sort from largest to smallest and then report the ranking
People that are from 0-25 years old are the young group, 50+ is senior

for any two values that you can think of, it’s always
logically possible to have another value in between

take on a set of possible values (with nothing
meaningful in the middle)

Unimodal: One mode/peal
Bimodal: Two modes/peaks (but only has one true peak)
Symmetrical: Mode at centre
Positively skewed: Mode towards left and rest of values towards right
Negatively skewed: Mode towards right and rest of values towards left

Proportion would not change height of bars
When moving from frequency to proportion

- The exact order the data came in
- We don't really care about the order, not useful organization

- Sorted data, more useful, best way to look at data

Histograms can be
made on continuous
data by discretizing
the continuous data
into discrete bins
- Involves converting continuous data into discrete data (discrete bins)

Used to identify a single valye close to all of the data points, the
sameness of the data
- Mean median mode

The differentness of the data, how different the numbers are

Mode is towards right, median after and the mean is furthest left

Mode is towards left, median right after, and the mean is furthest right

- In skewed data, you mostly focus on the median
○ Like in reaction time data
Mode is not reliable because it is skewed
- Mean gets pulled away from centre when a skew occurs
- Median stays close
Mode stays closest to the peak

- Reaction time data is represented with a positive skew because there is a physical limit as to how fast you can do this task

ts value exists in the data
- Represents greatest probability of
subjects having a score
- Can be used for nominal data
Depends how the data are
discretizedinned

Not affected by extremes
- Good for skewed distributions
No formula to easily calculate it
- Not as stable as the mean

More stable when sampling
- Easy to calculate with equations
Influenced by extreme values
- Value may not actually exist

Range:max-min
- Very susceptible to extreme values so you can get a very large range and gap with no data

IQR is the range between the first quartile and third quartile
(i.e., the range of the
middle 50% of the data)
- Gets rid of extreme valyes
This is how you get the true mean as you get rid of outliers - you split the data in half and then the halves into halves

Rank your data
2. Find the median of entire data, and use to cut data in half
• Note that this is straight forward for even numbers as each half will
have an equal number. For odd numbers, it’s common to
exclude the
median from each half.
3. Median of the lower half of the data = lower quartile (Q1)
4. Median of the upper half of the data = upper quartile (Q3)

Like the standard deviations, the average values all sum to 0

- Converting all the negative values to positive by squaring them and then summing them
- Sum of squared deviations: When all the deviations from the mean are squared and then summed

Variance = SS/N
- The average of the sum of squared difference scores from the mean
Eg) Data: 2, 5, 7, 11, 24, 19
SS = 262
Variance would be 262/6

Square root of the variance
Essentially sqrt(SS/N )

average difference/N

sqrt(average difference - mew truemean)^2/N)
- It is real data
- Mu is the true mean

average difference/n

sqrt(average difference - Xbar estimate)^2/n-1
- X bar is an estimate
- Everything else is true

- Removes bias
- More accurate, better value overall
- Won't affect large sample size

- Gives you uniased estmate
- We lose a degree of freedom because we use another estimate (X bar) in our calculation of s

For example, if we estimate the population mean μ, using the
sample mean, /X, of a sample with 50 observations, our df
would be 50
• If we estimate a population parameter using a statistic that
itself contains an estimate of a population parameter, we lose
one df
• For instance, the estimate of the population standard deviation,
σ, is the sample standard deviation, s. Since s contains, /X, it
has one fewer df than the estimate of the population mean. In
our example above of a sample with 50 observations, the df in
s would be 49
10

- Using raw data to make estimate - don't lose freedom
Using the estimate from the raw data to make an estimate - then you lose one degree of freedom

The z-score is a way of standardizing data to incorporate the
observation, mean, and standard deviation into a single value,
which will allow us to compare across distributions

Population or sample: (Individual score-mean of all scores)/SD

Z = (78-82)/1.4 = -2.8571 - your result-others


Z = (600-640)/30 = -1.3333

You were 2.86 SDs less accurate and 1.33 standard deviations faster in your responses

Recall that in our examples until now, I show the
actual distribution of the data.
• That allows us to not only see how far from the mean
we are in units of SD, but also, how much of the data
is similar to a given observation.
• But most often, you will only be given the mean and
standard deviation.
• And you won’t know if those numbers belong to a
wonky distribution like this...
WE NEED A NORMAL DISTRIBUTION

Truly continuous and never
ending
• Perfectly symmetrical
• Mean is the peak
• SD determines width of
distribution
• Total area under the curve = 1
Measures "fatness" of the curve not range
- We can make conclusions more easily
Makes our lives easier I guess

Shifts the curve horizontally without affecting the height or shape

Changing SD would change the peak though but area will always be 1 and changes the "spread"

You can know the probabilty of values more extreme than a certain criteron

Bins [50,55) -> include 50 but all values UP TILL 55 but not 55 itself
{curly brackets} are used to list a dataset

When n (sample size) is low, the distributions appear sporadic. When we say our data are 'normal' we are assuming that our n observations (samples) are from larger bell-shaped distribution. As sample size, increases, the distribution looks more like the populations.

When n is low, distributions appear sporadic. All values within a range are equally likely

- Many trials with 1 min or 30 secs
- One trial with 10 mins and wrong answer
You can get rid of this outlier

What is an experiment?
• A type of research study
• Different than descriptive and correlational researc
• Experimental research: looks at causal
• Does X cause/affect Y?
• X = Independent variable
• Y = Dependent variable
Does * cause affect Y ?

No, you cannot randomly assign people to a depressed group or make them depressed as an independent variable

Yes because you are aleady given a population of Asperger's syndrome

Yes, you can manipulate the independent variable (paying)

No, you cannot damage someone's parietal lobe

- Variables other than the IV and DV that need to be held constat across levels of the IV (like minimizing differences in instructions given to particiapants, want to make sure they're as similar as possible)

When an extraneous variable changes with the IV
- We don’t' have reason to believe that they will cause major differences
"What are people doing other than using instagram" - has a lot of confounding variables and would need lots of variation in experiments and you may never find an answer

The extent to which the IV truly had an effect on the DV
To make a causual conclusion, you need to get rid of confounding variables completely

Experimental studies have at lea
conditions
• Experimental condition(s) receive some level/form
• Referred to as treatment condition when in clinical trials
• Control condition
• Treatment & control are required for randomized c
trials (RCT)
- - Conditions you have expectations for
Need more than treatment and control

No treatment control
- Don't receieve treatment

Placebo control
- Recieve a placebo treatment

Waitlist control
- A group that recieves the treatment AFTER the main treatment group

Active/standard control
- When the standard treatment is given
Done in conditions where it is unethical to withhold someone from a treatment they are already receiving

Randomly assigning particiapnts to either treatment or control

All participants complete both the treatment and control conditions

Within-subject designs: carryover effects
• Practice effects: better performance in later condit
• Fatigue effects: worse performance in later conditi
• Context effects: performance depends on other cc
Condition A
Condition B
Condition C

Countering carryover effects
• Counterbalancing order of conditions between subjects ( each participant does a different condition first, second and the fatigue effects are cancelled out)
• Also, they may not be an issue if it's the focus of the study

- Random selection
- This may lead to unequal sample sizes, but these can be avoided by pseudorandomizing(block randomization)

- Biases due to an experimenter's biological, attitude
personality characteristics affect participant's behavuour
• Expectations affect how participants are treated
• Multiple experimenters may have subtle but important
differences in their procedure

Essentially you want the experimenter to to be as invisible as possible
- Participants will also do better if they get better instructions

• Create a written protocol of experimenter's role
• Create standard instructions for participants (have particiapants read their own instructions)
• Automate as much as possible (schedule breaks, minimze human interactions)
• Anticipate participant questions
• Train multiple experimenters together
• Distribute conditions equally between experimenters

In a single blind study, only the participants are blind to the condition they are in. A double blind study is one where the participants and the experimenters are also blind to the conditions

- Everything within reason should be take note of, like a random distraction messing with the participants task

- Do it so you know how it will look and it can help you find gaps in your study
- You collect data but don't

When the way an experiment was conducted
supports the conclusion that the independent variable caused
observed differences in the dependent variable. These studies
provide strong support for causal conclusions

When the way a study is conducted supports
generalizing the results to people and situations beyond those
actually studied.

The quality of the experiment’s
manipulations

Whether the statistics conducted in the study
support the conclusions that are made

Correlation investigates the relationship between a dependent
variable (Y i) and an independent variable (X i)
• Whether X or Y are dependent or independent depends on the
experimental design
• X = antidepressant dose, Y = mood state
• X = time slept night before exam, Y = exam performance

Historgrams tell us about distribution of each variable but not the relationships between variables

covxy= ((datapointx - mean of x) (datapointy - mean of y))/n-1
You don't lose two degrees of freedom because you are using the vairables from the same particiaonts

Correlation assesses if deviations from the mean in X are associated
with deviations from the mean in Y in a unitless, standard number
known as Pearson’s Product-Moment Correlation Coefficient,
r

r=covxy/sxsy in which "sxsy" is sqrt((xi-xbar)^2(yi-ybar)^2))
or
r = zxzy/n

Using mean of x and y which are 2 different and independent things so we use n-2
We lose 2 degrees of freedom because we are measuring 2

r = +1.00 when X and Y are perfectly positively correlated.
r = -1.00 when X and Y are perfectly negatively correlated.
r = 0 when there is no relationship between X and Y.
Some suggested interpretations:
• Weak: 0.1-0.3
• Moderate: 0.3-0.5
• Strong: >0.5

Linear: best fit line is
straight
• Nonlinear: best fit line is not
straightNote that correlation is only valid
for linear relations

Monotonic: as X increases, Y
either increases or decreases
without reversals
• Nonmonotonic: as X increases,
there is a reversal in Y one or
more times.

Pearson product-moment correlation coefficient (
r)
• Requires both variables to be continuous.
• Affected by normality of data and outliers.
• Assesses how
linear the correlation is
• Spearman’s correlation coefficient for ranked data (r s orρ)
• Requires both variables to be ranked/ordinal.
• Not as affected by normality and outliers.
• so if data are not normal / have outliers, can convert it to ranked and calculate
rs
• Assesses howmonotonic the correlation is

Spearman’s correlation coefficient
(rs ) is useful for data where the observations have been
replaced by their numerical ranks from lowest to highest

Nonlinearity – Pearson’s requires linear,
Spearman’s requires monotonic.
Anything beyond that, need to use other
tools.
• Extreme observations – outliers have
drastic effect on slope of the line, which
then affects it’s fit with the rest of the
data.
• Range Restrictions
• Heterogenous subsample

For example, there is a relationship
between school grade level and
knowledge of geography. But if you
only look at grades 1-3, you will not
see the correlation

Heterogenous subsamples are when sample could (should) be
subdivided into 2 distinct sets based on some other variable.
The relationship between variables may be obscured or enhanced by a
third variable.

The relationship could be causal: Caffeine leads to wakefulness
2. The relationship may be reversed: Happiness could lead to social relationships,
or the other way around.
3. The relationship could be partly causal: Early life adversity could cause mental
illness in later life, but only if there is a genetic vulnerability in the patient
4. There may be a third, confounding factor: Population size decreases as child
mortality decreases in a country; both are related to wealth
5. Both may be related to a third, causal factor: Family stability and physical
illness may be related because stress is related to both.
6. Variables may be changing over time: Bone density and memory are correlated,
mainly because both are decreasing as someone ages
7. Correlation may be a coincidence.
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We determine how successful construct
operationalization was
by assessing
reliability &
validity
• Operationalization: defining the specific way a construct is
measured.
• Reliability: the degree to which a measure provides consistent
results
• Validity: the degree to which a measure accurately assesses
the intended construct.
3

Test-retest reliability:
Is the measure as stable as
the construct it is supposedly
measuring?
Making the same measurement at a different time should provide consistent results

Internal consistency:
Consistency of responses
within a multi-item measure.
Measured using:
• Split-half correlation
• Cronbach’s alpha (see
tutorial 5)

- Cronbach's alpha: Takes one item from questionnaire and correlates it with another
- 5 items can generate 15 correlations
Cronbach's alpha is the average of those correlations

Inter-rater reliability:
Should have similar numbers with the same experimental conditions

do the
questions appear to reflect
the underlying construct

- If you're doing an experiment on stress, is it obvious to the participant that they are answering questions about stress?
Sometimes you may not want face validity and don't want the participant to know what is being asked of them

does the
scope of the measure capture
the scope of the construct
If you want to measure how well people can recognize emotions, don't just use one emotion

correlate with other expected
variables? (concurrent)
• predict the future value of another
variable? (predictive)
Measuring athleticism
- Strong: Expect you to do well in a range of sports
- Suppose you also use a questionnaire that asks participants how well they do in various sports (how much do these correlate? - concurrent?)
Predictive: Suppose they fill out the questionnaire first, you can look at it and predict that they would perform a certain way while actually playing the sport

does a
measure correlate with other
measures of the same
construct?

2 different questionnaires both measuring the same thing should have a correlation

2 measures reaching the same conclusion
But they don't have to be of the same format (one could be a questionnaire and another could be a task

does a
measure not correlate with
measures of distinctly different
constructs?

If you believe two different questionnaires are measuring two independent constructs, you should not see a correlation between the results