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NYU - CAS 10 - Class Notes - Week 4

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• This is a directional hypothesis

• Looking at one hypothesis: Wanting to see if they have higher IQs

• One tailed test

• The alpha I was using to reject the directional hypothesis was on one side of the distribution

• The directional hypothesis results in a one tailed test • Alpha region = rejection region

• If you ask the question: Does living near power stations change your IQ results in a non directional hypothesis & two tailed test

• A one tailed test had a bigger rejection region, easier to prove wrong

• The way to reduce type 2 error: A one tailed test makes it harder to make a type 2 error

• The rejection region is larger

• The bigger the rejection region, the harder it is to make a type 2 error which is failing to reject Don't forget about the age old question of Why is it important to unsettle the historical narrative about columbus’s “discovery” of the americas?

• The way to reduce type 1 error: Reduce alpha

• If you are testing a drug, and have 10 studies where only the tenth says the drug works and only publish that study to the project ???? you are making a type 1 error

• If I change alpha that doesn‘t change beta.

1

• Question: Is 103.48 due to chance or due to living near power station?

Don't forget about the age old question of What are the three stages of sleep?

• Null Hypothesis Testing:

• We don’t prove anything, we gain evidence for – we

strengthen an argument

• We will disprove they are the same as everyone else if they live near a power station (not prove they are different)

2

We also discuss several other topics like What are the scientific method used in making research?

3

• WE set up two hypothesis:

• Two statements about what we think is “really“ going on If you want to learn more check out Where was new france located?

• The two statements have to be mutually exclusive and exhaustive

• Exhaustive: Covered all possibilities within your study

• Mutually exclusive: If one is true, the other one can’t

be true

• The Null Hypothesis: A hypothesis of generally no different – they are just like everybody else

• Need a null hypothesis distribution

• A sampling distribution of the mean

4

• P level: The probability of our result, assuming the null hypothesis to be true.

• Significants means that our P level was less than alpha

• If the P level is less than alpha: What you’re saying is that the probability of your results is so small that we don’t think it was due to chance

• Why? Because we are using the distribution that is due to chance Don't forget about the age old question of What are the 4 questions of film criticism?

• We reject the null hypothesis

• In our example: We are failing to reject the null hypothesis • The grey dotted curve: Is a distribution where the distribution is smarter because they are living near power station

• If we do not reject the null: Any variance we are seeing is due to chance

5

• Alpha: is a probability of 0.05 o 0.01 If you want to learn more check out What is a hydroxyl?

• The amount of risk we are willing to take of being wrong • Probability cut off

6

• In the context of hypothesis texting: Our Z-Score is called a test statistic

• Actual Situation = reality / truth

• Under actual situation is my two hypothesis

• On the left: My decision as a researcher

• Type 1 error: Saying there is a difference when in fact there Is not • How does this happen?

• Chance: The individuals in our sample is too extreme • The probability of this result is alpha

• Alpha is called the level of significance

• Alpha is set by the researcher before they do the study • Type 2 Error: Failing to reject the null when it is really false • The probability of this result is beta

• This could be caused by a weird sample (chance)

• Power: The probability of rejecting the null when it is false • P= 1 – beta

• IF you make alpha very small, beta will get larger

• If you decrease the probability of making type 1 errors, you increase the probability of making type 2 errors

• Z score = test statistic

• You set Type 1 error to 0.5 or 1.0 before you start the analyzation • 0.5 is stricter

7

Top Hat:

Q: The probability of your result being due to chance, provided that the null hypothesis is true is called

A: Alpha

B: P Level

C: Z-score

D: z critical value

P level: The probability of whatever sample I got under the null hypothesis distribution.

Alpha: The probability of making a type 1 error; the level of significance

Type 1 error: Rejecting the null hypothesis when it was actually true To determine significance: Compare p level to alpha

Q: A Type 1 error is:

A: rejecting the null hypothesis when it is false [ This is power] B: Rejecting the null hypothesis when it is true

C: Failing to reject the null hypothesis when it is false

D: Failing to reject the null hypothesis when it is true

• Type 1 and type 2 hours happen by chance – > you get a weird sample

• Type 1 errors are worse than type 2 error, in general. • Power is the compliment of beta (type 2 errors) -> they add up to 1

8

• Big Question: Does tutoring make a difference

• Hypothesis is about tutored students

• 2 Hypothesis: [they are both mutually exclusive and exhaustive] • H sub 0 is the null hypothesis

• H sub 1 is the alternative hypothesis

• In this example: We reject the null hypothesis

• The p level is smaller than alpha

• P level (0.0082) = z score (2.40)

• If not told, always assumed the alpha is 0.5 and we are doing a two tailed test

• Is the mean of tutored students different from the mean of the students who take the AP test who aren’t tutored? : Yes it is

• In SPSS the p-level is referred to as Sig.

9

• DV = dependent variable

• We don’t do sample tests very often because they are lousy designs

• They are only as good as the sample

• There is no control

10

• Null (ineffective) experiment = An experiment where the null hypothesis is true

• Alpha is the percentage of the null experiments that we declare significant

• Only 5% of the ineffective experiments are declared significant • NOT 5% of the experiment itself

11

• A type 1 error is only from a null experiment

• Alpha is like a spam filter -> it keeps the bad emails from getting into your inbox

12

Top hat:

We can reduce the probability of making a Type 1 error by: Decreasing alpha

Q: In order to test significance you need to compare.

A: The p level with alpha

B: The p level with the z critical value

C: The calculated z with the z critical value

D: The calculated z with the p level

13

• A total number of significant results are made of ineffective experiments and effective experiments

14

• Population Mu stands for those who use drugs

• We reject the null hypothesis…The campaign worked! 15

Step 1: Null Hypothesis

Saying: The population mean of the kids that learn this new method are the same as everyone else.

Step 2: Alternative Hypothesis

Step 3: Set alpha

Step 4: Make mean into a z-score.

Step 5: Compare z score with alpha.

- We rejected the null hypothesis

- We have significance!

16

• This is a directional hypothesis

• Looking at one hypothesis: Wanting to see if they have higher IQs

• One tailed test

• The alpha I was using to reject the directional hypothesis was on one side of the distribution

• The directional hypothesis results in a one tailed test • Alpha region = rejection region

• If you ask the question: Does living near power stations change your IQ results in a non directional hypothesis & two tailed test

• A one tailed test had a bigger rejection region, easier to prove wrong

• The way to reduce type 2 error: A one tailed test makes it harder to make a type 2 error

• The rejection region is larger

• The bigger the rejection region, the harder it is to make a type 2 error which is failing to reject

• The way to reduce type 1 error: Reduce alpha

• If you are testing a drug, and have 10 studies where only the tenth says the drug works and only publish that study to the project ???? you are making a type 1 error

• If I change alpha that doesn‘t change beta.

1

• Question: Is 103.48 due to chance or due to living near power station?

• Null Hypothesis Testing:

• We don’t prove anything, we gain evidence for – we

strengthen an argument

• We will disprove they are the same as everyone else if they live near a power station (not prove they are different)

2

3

• WE set up two hypothesis:

• Two statements about what we think is “really“ going on

• The two statements have to be mutually exclusive and exhaustive

• Exhaustive: Covered all possibilities within your study

• Mutually exclusive: If one is true, the other one can’t

be true

• The Null Hypothesis: A hypothesis of generally no different – they are just like everybody else

• Need a null hypothesis distribution

• A sampling distribution of the mean

4

• P level: The probability of our result, assuming the null hypothesis to be true.

• Significants means that our P level was less than alpha

• If the P level is less than alpha: What you’re saying is that the probability of your results is so small that we don’t think it was due to chance

• Why? Because we are using the distribution that is due to chance

• We reject the null hypothesis

• In our example: We are failing to reject the null hypothesis • The grey dotted curve: Is a distribution where the distribution is smarter because they are living near power station

• If we do not reject the null: Any variance we are seeing is due to chance

5

• Alpha: is a probability of 0.05 o 0.01

• The amount of risk we are willing to take of being wrong • Probability cut off

6

• In the context of hypothesis texting: Our Z-Score is called a test statistic

• Actual Situation = reality / truth

• Under actual situation is my two hypothesis

• On the left: My decision as a researcher

• Type 1 error: Saying there is a difference when in fact there Is not • How does this happen?

• Chance: The individuals in our sample is too extreme • The probability of this result is alpha

• Alpha is called the level of significance

• Alpha is set by the researcher before they do the study • Type 2 Error: Failing to reject the null when it is really false • The probability of this result is beta

• This could be caused by a weird sample (chance)

• Power: The probability of rejecting the null when it is false • P= 1 – beta

• IF you make alpha very small, beta will get larger

• If you decrease the probability of making type 1 errors, you increase the probability of making type 2 errors

• Z score = test statistic

• You set Type 1 error to 0.5 or 1.0 before you start the analyzation • 0.5 is stricter

7

Top Hat:

Q: The probability of your result being due to chance, provided that the null hypothesis is true is called

A: Alpha

B: P Level

C: Z-score

D: z critical value

P level: The probability of whatever sample I got under the null hypothesis distribution.

Alpha: The probability of making a type 1 error; the level of significance

Type 1 error: Rejecting the null hypothesis when it was actually true To determine significance: Compare p level to alpha

Q: A Type 1 error is:

A: rejecting the null hypothesis when it is false [ This is power] B: Rejecting the null hypothesis when it is true

C: Failing to reject the null hypothesis when it is false

D: Failing to reject the null hypothesis when it is true

• Type 1 and type 2 hours happen by chance – > you get a weird sample

• Type 1 errors are worse than type 2 error, in general. • Power is the compliment of beta (type 2 errors) -> they add up to 1

8

• Big Question: Does tutoring make a difference

• Hypothesis is about tutored students

• 2 Hypothesis: [they are both mutually exclusive and exhaustive] • H sub 0 is the null hypothesis

• H sub 1 is the alternative hypothesis

• In this example: We reject the null hypothesis

• The p level is smaller than alpha

• P level (0.0082) = z score (2.40)

• If not told, always assumed the alpha is 0.5 and we are doing a two tailed test

• Is the mean of tutored students different from the mean of the students who take the AP test who aren’t tutored? : Yes it is

• In SPSS the p-level is referred to as Sig.

9

• DV = dependent variable

• We don’t do sample tests very often because they are lousy designs

• They are only as good as the sample

• There is no control

10

• Null (ineffective) experiment = An experiment where the null hypothesis is true

• Alpha is the percentage of the null experiments that we declare significant

• Only 5% of the ineffective experiments are declared significant • NOT 5% of the experiment itself

11

• A type 1 error is only from a null experiment

• Alpha is like a spam filter -> it keeps the bad emails from getting into your inbox

12

Top hat:

We can reduce the probability of making a Type 1 error by: Decreasing alpha

Q: In order to test significance you need to compare.

A: The p level with alpha

B: The p level with the z critical value

C: The calculated z with the z critical value

D: The calculated z with the p level

13

• A total number of significant results are made of ineffective experiments and effective experiments

14

• Population Mu stands for those who use drugs

• We reject the null hypothesis…The campaign worked! 15

Step 1: Null Hypothesis

Saying: The population mean of the kids that learn this new method are the same as everyone else.

Step 2: Alternative Hypothesis

Step 3: Set alpha

Step 4: Make mean into a z-score.

Step 5: Compare z score with alpha.

- We rejected the null hypothesis

- We have significance!

16