Null + Simulations

According to the internet, about 2% of the world has green eyes. If I were to take a random sample of 1,000 people from around the world, what is the probability that my sample would contain fewer than 15 people with green eyes? # of coins POH How many runs Range

# of coins = 1,000 POH = 0.02 Runs = 10,000 Range - less than 15 (so 14 and below)

Suppose you knew that a basket ball player was an 82% free throw shooter, that is, for any given free throw that this player shoots, she has an 82% chance of making the shot. If this player takes 30 free throws one day after practice, what is the probability that she will make at least 20 of them? # of coins? POH? How many runs? Range?

30 coins poh = 0.82 runs = 10,000 range would start at 20 because it says what is the probability that she will make at least 20 of them (the x axis is her making that amount of shots, the y-axis is the probability of her making those, the higher the bar, the more likely)

Imagine an election in which 52% of the population supports Sasha, and 48% of the population supports Riley. On election day, 500 people turn out to vote, and every member of the population is equally likely to vote. Run this model to simulate an election and see how many people voted for Sasha. What would the number of coins be? Probability of heads? How many times would you run it?

500 coins Prob of heads = 0.53 Run 10,000 times

Suppose that there several M&M factories around the world. Most of which you don't know anything about. One is in NY and you have learned that the mix of colors in a bag of M&Ms from that factory is known to be about 24% blue, 13% brown, 16% green, 20% orange, 13% red, and 14% yellow. You open a 1 lb bag of M&Ms which has 500 M&Ms in it, and you count 71 red M&Ms inside. Does it seem reasonable that the bag was from the NY factory? (the distribution is shown on the other side to solve this problem)

71 red are from our 500 bag This graph shows the number of red m&ms that we would expect to come from bags that have 500 in them 58-73 are red that come from the NY based on the peak of the data less likely that the bag only had 49 or less or 82 or more red if it came from NY So the probability is that our bag came from NY

In statistics when we test a model we are testing: A possible origin story for the data we collected If we can verify that the model's details are all exactly correct To see if the data we collected can be trusted To see whether or experiment worked well

A possible origin story for the data we collected

A researcher believes that having students put their cell phones into airplane mode before studying for an exams will increase exam performance. What is the DV for this study? A. Students B. Airplane mode and not airplane mode C. Exam performance D. Cell phones E. Cell phone availability

C. Exam performance

A researcher believes that having students put their cell phones into airplane mode before studying for an exams will increase exam performance. What is the null hypothesis for this study A. Putting cell phones in airplane mode will increase exam performance B. Putting cell phones in airplane mode will decrease exam performance C. Putting cell phones in airplane mode has no effect on performance D. None of these are the null hypothesis for this study

C. Putting cell phones in airplane mode has no effect on performance

A researcher believes that having students put their cell phones into airplane mode before studying for an exams will increase exam performance. What is the IV for this study? A. Students B. Airplane mode and not airplane mode C. Exam performance D. Cell phones E. Cell phone availability

IV = cell phone availability (whether or not the cell was on ) Levels - airplane mode and not airplane mode

One- and Two-Tailed Tests

If a distribution only has one tail, we can reject that model if the data we have is in the most extreme 5% of that one tail

ALWAYS ANSWER: Could have come from Must have come from when looking at the result of the model

COULD HAVE even though it might line up perfect, it is still an approximation and not actual truth. it is enough that we do not reject the model, but it is never MUST

What does it mean when we reject the null hypothesis? It means that our experiment was corect. It means that our research hypothesis is correct. It means means that the result was unlikely to be due to chance alone. It means mean that our research is important.

It means means that the result was unlikely to be due to chance alone.

What does it mean when we fail to reject the null hypothesis? It means that we cannot rule out the null hypothesis as one possible origin story for our data it means mean that our research hypothesis must be wrong. it means that the results were probably due to the null hypothesis It mean that the results must have been due to the null hypothesis

It means that we cannot rule out the null hypothesis as one possible origin story for our data

Research Hypothesis: This drug lowers heart attacks. If the experimental data showed an increase in heart attacks among those who took the drug, what should we do? A. Reject the null B. Fail to reject the null C. Reject the research hypothesis D. Fail to reject the research hypothesis

Null = the drug has no effect on heart attacks Reject the null because the result is incredibly unlikely if the drug has no effect on heart attacks. WE ARE NOT TESTING THE RESEARCH HYPOTHESIS, WE ARE SIMPLY TRYING TO SEE WHETHER OR NOT THE NULL CAN BE REJECTED since the result still happened (even though it is at the tail of the distribution, we can still reject the null)

What if the data we collected in the real world is very unlikely to occur based on the model we are evaluating?

Option 1: the model is not the correct explanation for the data SO we REJECT THE MODEL

A researcher believes that feeding field mice large quantities of caffeine will cause them to dig deeper burrows. To study this, he tracks two communities of field mice: one community that has access to "standard" food sources and one community where all the nearby food has been supplemented with caffeine. After 30 days, he measures how deep underground each communities' burrows go. What is the research hypothesis for this study?' Null

That caffeine affects burrow depth Null - That caffeine does not have an effect on burrow depth

The data from a small sample is more likely to: be far less variable than the underlying population is accruately represent the underlying population underestimate the mean of the population deviate away from the expected result

deviate away from the expected result (smaller the more likely)

The Research Hypothesis

is an Origin Story The research hypothesis says that the data you collected that shows some difference or change or relationship came about

A model is a process that generates some data. A model is also an origin story:

it is one possible explanation for where some real-world data came from

"Very Unlikely" when referring to a model

it means that if the outcome is more extreme than 0.05, then we reject the model (if the result is in the outer tails of the histogram (2.5% to the right or 2.5% to the left)

A model is a _____ that generates _______ process; data approximation; answer shortcut; outcome simulation; probabiltiy

process; data

If we go out into the world and collect some data and that data does not line up with what our model says are typical results we should: accept the data accept the model reject the data reject the model

reject the model (the least likely upper 2.5% of the results) or lower 2.5%

Can sea otters distinguish between happy and sad faces? A friend of mine has a pet sea otter* and he claims that he's taught his otter to understand the difference between happy and sad facial expressions. He says he keeps four different colored balls in his swimming pool for Skittles to play with: blue, red, orange, and yellow He says he has trained Skittles to retrieve the orange ball when he makes a happy face. ...and to retrieve the yellow ball when he makes a sad face. Generate a research hypothesis and its corresponding null hypothesis

research: Sea otters can distinguish between sad and happy faces null: there is no correlation between whether or not sea otters can detect sad or happy faces, correct ball retrievals are just due to randomly guessing correctly

When we simulate a model thousands of times, the outcome is: The distribution of outcomes that would allow us to accept the model The distribution of null results The average result from the model the distribution of results that are likely to occur if this model is correct

the distribution of results that are likely to occur if this model is correct

fail to reject the model

the model looks like the data (everything is right) we are saying that the origin story is not rules out and is possible, so we are not rejecting it

Rejecting the model

we don't think the model that was created is a good origin story for the data that was collected

Goal: Reject the Null Model

1: create the Null Distribution We can simulate the null model thousands of times to generate the distribution of the results that we would expect to get if the null hypothesis were true 2: Are our actual results very unlikely in that distribution? If the actual experimental results that we got when we collected data in the real world are very rare in the distribution of results that we would expect to get if the null were the correct origin story, we can reject the null model as a good explanation of our results

The null hypothesis says: That your experiment did not work Any measured difference between the conditions in your sample was a function of chance alone That your experiment was poorly designed That there is a better explanation for your data than the research hypothesis

Any measured difference between the conditions in your sample was a function of chance alone

The null model or null hypothesis

Because the world is a noisy place, that is why there is a change in the data that you collected the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

Frank's paintings are extremely valuable, making forgery a concern. At a recent auction, a new piece "by Frank" is for sale. Frank is very secretive and refuses to confirm the authenticity of the new piece. This piece has Frank's standard 1000 grid layout with red, blue, and green squares. However, some critics are suspicious because the ratio of colors doesn't seem quite right. 400 of the boxes are red, and the other colors each occupy 300 boxes each . Frank never deviates from his method of choosing colors randomly, with equal probability. What is the probability that Frank would create a painting with at least 400 red squares? How many coins do you use? Probability of heads? How many times do you run it?

Coins = 1,000 POH = 0.3 because (blue, green, red and red is 1/3) Run = 10,000 About 333 will be red

Suppose that my friends* kidnapped me for a weekend birthday getaway. They blindfold me, put me on a plane, and we fly for a couple of hours, but refuse to say where we are going. (I hate FL) In my head .... Research hypothesis: Null hypothesis: you get off the plane and are surrounded by mountains (you aren't in FL) so that means that: If the data we collect is very different from what the model predicts, we can reject the null. OR you get off the plane and are surrounded by beach You fail to reject the null (because there is a strong possibility that you are in FL but we still dont know that for 100% sure)

R: We are going somewhere fun and exciting N: We are not going somewhere fun and exciting (FL)

Rejecting the null vs. fail to reject the null

REJECT: The result was unlikely because of chance alone. If our experimental results are very unlikely under the null model, we will reject the null model as an explanation of our data. (is in the bottom 2.5%) - can help research hypo FAIL TO REJECT: The result was likely due to chance. If our experimental results are not that unlikely under the null model, we fail to reject the null model (is not in the bottom 2.5%) - does not help research hypo

If we want to know how often events occur out in the real world, why can't we just observe them lots of times and then calculate probabilities? Mark all that apply. You would not get accurate results if you tried that Sometimes that approach is too expensive The real world is too messy Some things do not happen very often

Sometimes that approach is too expensive Some things do not happen very often

Suppose that there several M&M factories around the world. Most of which you don't know anything about. One is in NY and you have learned that the mix of colors in a bag of M&Ms from that factory is known to be about 24% blue, 13% brown, 16% green, 20% orange, 13% red, and 14% yellow. You open a 1 lb bag of M&Ms which has 500 M&Ms in it, and you count 87 red M&Ms inside. Does it seem reasonable that the bag was from the NY factory? (the distribution is shown on the other side to solve this problem)

The data would be unusual based on the model, so it is likely from somewhere else and not the NY factory (87 is in the lower tail, so it is very unlikely)

What is the advantage of running thousands of simulations? After thousands of simulations, you can pick the one outcome that is correct. The distribution lets us calculate probabilities of outcomes we care about. Thousands of results sounds more impressive than just one result, so it's easier to get published. If we run many simulations at least one of them must eventually be correct. If you only run one simulation you won't have a mode.

The distribution lets us calculate probabilities of outcomes we care about.

When a psychologist says an outcome is very rare, she typically means that: The observed outcome and the outcomes more extreme than that outcome were less than 5% likely The exact outcome is only 5% likely The outcome has never been seen in an experiment That the outcome was close to the middle of the distribution

The observed outcome and the outcomes more extreme than that outcome were less than 5% likely

In a certain town there are two farms. On the large farm, about 45 chicks are hatched each day. On the smaller farm, there are only about 15 chicks hatched each day. As you may suspect, about 50% of all chicks born are roosters, but on any give day, the percentage of roosters born may be higher or lower. Across one year, both farms count the number of days on which 60% or more of the chicks hatched are roosters. Which farm will have more days where 60% or more of the hatchings are roosters? The small farm There's no way to know The large farm They will be about the same

The small farm This is because the smaller the population size, the more likely it is for something to happen. If the farm as 1,000 chicks there is less of a high probability that there are more roosters than a farm that has 50 chicks.

Using a model for porbabilities

creating a model of an event can help us simulate it over and over again, thus giving us good approximations

If we set the cutoff for rejecting the model at the least likely 5% of the results in each tail, thats too much because we would be cutting off 10%. So instead we are going to:

Use a cutoff of 2.5% in each tail so the total is 5%

Run an experiment and collect data We set up an experiment with 30 trials, on each trial my friend either smiles or frowns, Skittles looks at his face, dives into the pool, and brings back one of the balls. We track the number of correctly colored balls (orange for happy, yellow for sad) that Skittles retrieves. In thirty trials where my friend made happy or sad faces, his otter retrieved the appropriately colored ball 14 times. Does this data provide evidence that his otter can distinguish between the two faces?

Use coin flip Coins - 30 POH - (1/4) 0.25 trials - 10,000 The histogram that we created when we simulated the null model is the distribution of results we would expect to get if the null hypothesis were the correct origin story Since he retrieved it correctly 14 times, and that is located at the very end of the distribution, that means that it is "very rare" So this means that the results were very unlikely to happen if the null hypothesis was correct, so we reject the null model.

How do we know which hypothesis is correct?

We dont. But we can try and rule out the null hypothesis as an origin story

If we have a normal distribution, what tool can we use to calculate the percentage of the results that are above or below a specific value? A. Central Tendency B. Standard Deviation C. Variability D. Z Scores E. Inferential Statistics

Z Scores

What is a model

a model is a formal description of a process that generates data

Calculating the exact probability of an outcome: is never possible can provide a very accurate answer in some, but not all cases is the only way to determine how likely an outcome will be Does not provide an accurate answer

can provide a very accurate answer in some, but not all cases

A local fast food restaurant sells five different sizes of French fries: kids, small, medium, large, ginormous. They say that people order across the five sizes more or less equally. On a day when the restaurant sells 217 orders of french fries, what is the most likely number of large fries they would sell? coins POH Runs Range

coins - 217 coins POH- 1/5 (K,S,M,L,G = 5 and L is one of them) so 0.20 Runs = 10,000 ( to know the answer look at the highest point ( or mode) of the graph)