[Music]
A lot of people believe that women
and men are just different.
Women prefer to shop
and men to fish.
Women like pink and
men like blue.
These beliefs rely on ideas
about different genes
leading to different behaviors,
or the influence of hormones
causing these differences
making them hard-wired.
One of these beliefs
is that women are naturally poorer
at math and science than men.
To test whether such claims that 
everybody knows are true actually are,
scientists use
a standardized process
that generates evidence
meeting rigorous criteria
to be considered valid.
The process is intended
to limit the effects of bias
and beliefs that might influence
what we want to be true.
Everyone is biased to some degree.
Often these biases are unconscious.
The scientific method helps limit
the effects of these biases.
There is evidence
that men have better visual spatial
reasoning ability than women,
but that finding is not 100% consistent,
as some studies have shown
the reverse is true
Other studies have found women
have better verbal ability than men,
but those studies show only
small differences.
Consistent differences include
aspects of physical strength,
physical aggression,
and sexual attitudes and behaviors.
These differences may be due
to real differences
in brain structure and hormones
between women and men,
but the measured differences show
large overlaps between the sexes,
not two very separate groupings.
Additionally, what causes these
differences is unclear.
Until relatively recently the
educational opportunities for women
were much more restricted
than those for men.
And even today there are still fewer
women in traditionally male occupations
such as science and engineering,
where math ability is necessary.
Many studies in the mid-twentieth century
showed large differences in math
performance between girls and boys.
Many people are convinced that
it's an intrinsic difference,
and therefore cannot be changed,
while others believe the differences
are caused by environmental
and social factors
which can be changed.
One proposed cause for the observed
differences in math performance
is boys being better at
learning on their own,
which may be perceived sexual identity
rather than a difference
in learning strategy.
Another proposal uses the real
differences seen in brain structures
to explain the differences in
performance seen,
but the evidence showing these
anatomical differences also show
that while women and men may use
different methods of solving problems,
they both can and do solve them,
so performance ultimately
should be the same.
The perception that women cannot
match men's performance
can lead to employment disparities
where women are excluded from higher
paying, more prestigious jobs.
An infamous example of this kind of belief
comes from the then president of Harvard
University, Larry Summers.
In 2005, at the National Bureau
of Economic Research's
Conference on Diversifying the Science
and Engineering Workforce,
Summers explained why there are fewer
tenured women professors
in science and engineering
at top institutions, as quote
"different availability of
aptitude at the high end",
further asserting that there are
genetic differences between the sexes
leading to boys outperforming
girls in math and science.
It should be noted that these
quotes were taken from the
transcript of prepared remarks
provided by Summers himself
as there has been some controversy
about what he actually
said at the presentation.
Summers reiterated these common claims
made about science and engineering
participation and performance
differences between women and men.
The data being used to justify the claims
are older data that don't control for
the possible environmental differences.
The biggest stumbling block in
studying gender differences
expressed by many researchers
in the field
isn't that those observed
differences aren't real,
it's that the magnitude of the
differences
and their actual causes are unknown.
But many assume that the
differences are large and intrinsic.
To approach the pattern seen
more scientifically,
this video examines the available
evidence in one area
of perceived gender difference:
math performance.
First we'll examine if the
difference is real
and if yes, how big it is.
In addition we'll examine the claim
that there is more variance
at the "high end" of performance
favoring more men with
extraordinary ability in math.
Traits are often measured and then
their distribution is graphed.
Here the traits value is on the x-axis
and the number of individuals with that value
is on the y-axis.
This distribution is called normal
as there is a central peak
at the average value,
also called the mean,
and the trade is symmetrical
around that mean.
The spread of the trait can
be described as the variance.
One thing to be clear on is
what does "different" mean?
The two trait curves here
have different peaks,
which represent the mean of
whatever trade is being measured.
So in this case, there is
a real and large difference
between the two groups shown,
though there is overlap
between the extremes.
What about these two?
Here there is still a difference in
means but it is much smaller
and the degree of overlap
is much larger.
Depending on factors like sample size,
this difference can be considered quite
real, but it's by no means large.
These last curves show no
difference in means,
but the spread does differ a good deal,
so that the "ends" are
different between the groups.
The common claims assume that yes,
there is a difference
and specifically male performance
will be higher than female performance
and that male variance will also
be greater than female variance.
However, in science, we want to ensure
we're protecting ourselves
from bias so the alternative hypothesis
that, no, there are no differences,
must also be presented.
One tool that the mid-twentieth
century studies did not have
was a statistical method
called meta-analysis,
which can be used to identify
differences across data collected in
different studies and identify
how big those differences are.
Meta-analysis uses effect size
to measure how much
of a difference there actually is.
Effect size looks at the
distance between the peaks
and it also controls for
the spread of the peaks.
Effect size calculations
give a zero value when there's
no measured difference,
positive values when there's
better male performance,
and negative values when there's
better female performance.
By common convention,
effect sizes greater than 0.2
(either positive or negative)
are considered "real" differences.
Another measure, variance ratio,
compares the spread of the trait's
distribution to see if there are
differences at the "ends" of the
distribution.
Variance ratio calculations give
a value of 1 when the tails are equal.
Values greater than 1 have
higher male variability,
and less than 1 have higher
female variability.
The next slides show
various meta analyses regarding mass
performance in chronological order.
Hyde et al in 1990 collected data
from studies including
over 3 million individuals in
English-speaking countries.
When all the data were pooled,
the effect size was -0.05,
which shows a very marginal
difference in performance
and with female performance
higher than male performance.
Additional analyses showed age group
mattered a great deal
with older male subjects increasingly
outperforming female subjects.
In 1995, Hedges and Nowell
performed a meta-analysis
of U.S. high schoolers in the U.S.
and found effect sizes
ranging from 0.03 to 0.26 and
variance ratios between 1.05 to 1.20.
This shows boys outperforming girls,
as well as higher variability
in the boys scores.
With the passing of No Child Left
Behind in the U.S. in 2002,
curricula across the country
became more standardized
and also much more data
were being collected.
The National Assessment of Education Progress
found an effect size of 0.07 by 2008.
The study using the NAEP data
was another ambitious meta-analysis
from Hyde and Mertz in 2009,
using only 21st century data.
When pooling everything, effect size
was measured at 0.012,
and for 12th graders was only 0.06.
The variance ratios calculated were
between 1.11 and 1.21.
A 2010 study of more international data
showed effect sizes ranging from
-0.01 to 0.11, depending on the test.
Another 2010 study of international data
found an overall effect size of 0.05 and
a variance ratio of 1.07.
That 2010 study of Lindburg et al,
also produced this histogram
of effect sizes from the study,
included their samples.
Effect sizes between - 0.02 to 0.04
were most common,
which are well below that conventional
0.2 to be considered "real".
A similar plot of variance ratios
shows that there is a skew
towards greater male variability.
Hyde and Mertz created a theoretical
representation of their data
using the effect size and
variance ratios calculated
to examine that "high-end"
difference hypothesis more closely.
This here is what Larry Summers
was talking about.
There is a real difference between
variances in male and female performance,
but that difference would produce
about 2.15 men for every 1 woman
if we assumed the maximum
variance ratio seen.
That difference is likely exaggerated,
and it is also not representative
of the number of men versus women in
tenured positions at elite institutions
as Summers suggested.
There are about 4 men for
every 1 woman instead.
So what are the answers to our questions?
Are there differences in math
performance depending on gender?
These meta-analyses showed measured
differences ranging from
the effect sizes of -0.05 to 0.32,
but the overall trend is toward
smaller values,
especially less than 0.2,
that value of effect size meaning
there's a significant difference.
In the U.S., the high school
coursework chosen by girls
is becoming more and more similar
to what boys choose,
including more advanced
math and science courses,
which may explain why the measured
differences are getting smaller-
girls are simply learning more math.
So yes, differences have been measured
but they are quite small,
and they've been diminishing over time.
While measures of variance
do show boys performance being more
variable than girls,
for the most part those
differences are also small
though they have been
measured less often.
While there is more variance
in male performance in math
there are still many examples of women
who have extraordinary talent.
Ada Lovelace is heralded as the
developer of the first algorithm
in the 19th century, and the world's
first computer programmer
at a time when very few women were
educated at all much less in math.
Grace Hopper invented the first
compiler for computer code,
which allowed for more complex
programs to be developed.
And in 2014, the first time
since the awards inception in 1936,
the Fields Medal,
considered the Nobel Prize for
mathematics,
was awarded to a woman,
Maryam Mirzakhani.
What are the implications
of this research?
For one thing,
the widespread assumptions about gender
differences may not be based in evidence.
The arguments made about these
differences often create stereotypes
and implicit biases against both genders,
and in the case of math performance,
that women cannot perform
at the same level as men.
These stereotypes can cause individuals
to have poorer performance
than they would have otherwise.
This is called stereotype threat,
and is a well demonstrated phenomenon.
Now that girls experience
much of the same education
in primary and secondary schools
that boys do in the U.S.,
measured gender differences
in math performance
are essentially disappearing.
What is different about the
genders is boys are more likely to
feel confident about their
mathematical ability
and girls are more anxious
about math.
One thing is clear though,
girls are not bad at math.
[Music]
