UPDATED QUESTIONS AND CORRECT
ANSWERS
Larger samples: - CORRECT ANSWERS✅✅larger samples give better estimates (with less
error) of the population than smaller samples.
How do we decide if these results should be shared with others in the research community: -
CORRECT ANSWERS✅✅People have gotten together and agreed that if the chance
probability is 5% or less (which means the probability is 95% or greater that the results came
from real differences between the groups), then it's ok to share these results by publishing
them. This 5% value is in no way special. It is just a "good enough" standard that allows
research to move forward without making it too difficult to find differences if they exist.
inferential statistic - CORRECT ANSWERS✅✅help us make guesses about what is true in a
big set of things (usually people) by looking at the differences that show up in a small set of
things
Inferences never 'prove' what is correct, but rather offer statements that are likely to be true.
Importantly, inferential statistics allow us to determine how much error exists in our
statements, which is a huge leap over the kind of fuzzy judgments that would exist without
inferential statistics. In order to calculate inferential statistics, we need to first understand
descriptive statistics. In many cases, the easiest way to understand statistics is with the right
visualization of the conceptual elements
descriptive statistics - CORRECT ANSWERS✅✅we can use descriptive statistics to
quantify the performance values of the task. For example, we can describe the following
aspects of the performance scores...
The average score (called the mean)
The variability of the scores (which is how much the scores vary)
Modality - CORRECT ANSWERS✅✅just means that the picture has one "hump"
refers to how many HUMPS the distribution has.
,Symmetry - CORRECT ANSWERS✅✅just means that the picture is the same on the left as
it is on the right
Asymptoticness - CORRECT ANSWERS✅✅just means that the tails of the distribution go
to the end of the page (and actually to the end of infinity)
refers to how far the distribution extends out to the left and to the right.
Computational formulas - CORRECT ANSWERS✅✅are loved by students but are one of
the worst things ever created in the teaching of statistics. Formulas are "computational" when
they make the computation easier by combining/reducing steps. This does make the
computation easier, but it almost always completely obscures the concept described by the
original formula. Thus, the computational formula encourages students to learn how to solve
a problem without understanding what it is that they are doing. A far better way to test
students without giving them finger cramps is to use the original conceptual formulas and just
use very simple data.
The 30% 'probability' of rain tomorrow comes from two things that interact - CORRECT
ANSWERS✅✅the weather and the weatherperson making the prediction. The probability
rests solely on one thing: the knowledge of the weatherperson. If the weatherperson had a
complete understanding of all the forces that create weather, then they could predict that it
would (100%) or would not (0%) rain. The probability comes from the lack of knowledge or
ignorance.
If I flip a coin and then let it land on the floor, then what is the probability that the coin will
be a head? - CORRECT ANSWERS✅✅Intuitively, we say that the probability is 1/2
because there are two possible outcomes that are equally likely. In reality, there is no absolute
probability, only the probability that changes depending upon the knowledge of the observer.
Imagine three possible observers of the coin flip and see how the probability changes with
each observer..
Observer 1 is looking at the coin after it has fallen, so the probability of a head is either
100% or 0%, depending upon what observer 1 sees.
Observer 2 can't see the coin, so the probability of heads is 50%.
Observer 3, who observed the coin just before it landed (and saw a head facing up), has a
probability of something between 50% and 100% because the fact that the coin was facing up
increases the probability.
,Probability always depends upon an observer and an observed event, and that probability will
change as knowledge changes.
Monty Hall Problem - CORRECT ANSWERS✅✅It is always to your advantage to switch
your choice from your original choice to the 'switch door'.
Now what is the probability that your original choice was wrong? 1/3.
Therefore, the probability of the 'switch door' must be 1 - 1/3 = 2/3. Voila! The 'switch door'
is twice as likely to have a car than the door you originally chose.
7 choices, 3 doors you picked, 3 revealed by guy - CORRECT ANSWERS✅✅P(original
choice correct)=3/7=0.429
P(original choice wrong)=1-(3/7)=0.571
P(one of remaining closed doors correct)= P(original choice wrong)=0.571
On a game show, a car is hidden behind one of 8 doors. You randomly select 2 door.
The host knows where the car is and then shows you 3 door that has no car behind it.
What is the probability you win the car if you choose ONE of the remaining closed doors -
CORRECT ANSWERS✅✅P(original choice correct)=3/7=0.429
P(original choice wrong)=1-(3/7)=0.571
P(one of remaining closed doors correct)= P(original choice wrong)=0.571
Biased Sample - CORRECT ANSWERS✅✅A sample which is not typical or representative
of the larger set
Descriptive Statistics: - CORRECT ANSWERS✅✅Statistics that describe values of
populations or samples
Inferential Statistics - CORRECT ANSWERS✅✅Statistics that help us make
guesses/inferences about large sets of people (i.e. populations) from information gathered on
small sets of people (i.e. samples)
, Probability - CORRECT ANSWERS✅✅The likelihood of an event that results from an
interaction of the event and an observer
Sample: - CORRECT ANSWERS✅✅A small (usually) set of data collected in order to
make inferences (guesses) about a larger set of data (i.e. from a population)
Sample Size - CORRECT ANSWERS✅✅The number of people that are measured in a
sample
Inferential statistics are useful in that they tell us ... - CORRECT ANSWERS✅✅What is
likely to be true.
When do inferential statistics 'prove' things to be true? - CORRECT ANSWERS✅✅Never,
there is always the possibility of error.
What's wrong with using computational formulas? - CORRECT ANSWERS✅✅They
obscure the true meaning of concepts.
Why should statistical formulas NOT be given to students? - CORRECT
ANSWERS✅✅Because formulas represent conceptual information.
If you want your sample to have the highest probability of reflecting the characteristics of the
population, you should choose a _________________ sample size - CORRECT
ANSWERS✅✅large
A weatherman says there is a 30% chance of rain tomorrow, but in reality ... - CORRECT
ANSWERS✅✅There is either a 100% chance of rain or 0% chance of rain.
Where does probability come from? - CORRECT ANSWERS✅✅It only exists as an
interaction between an observer and an observed event.