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NYU / CAST - Child Advocacy Studies / CAS 10 / What is the null hypothesis?

What is the null hypothesis?

What is the null hypothesis?

Description

School: NYU School of Medicine
Department: CAST - Child Advocacy Studies
Course: Statistics for the Behavioral Sciences
Professor: Elizabeth bauer
Term: Fall 2017
Tags: Statistics
Cost: 25
Name: Statistics for the Behavioral Sciences, Chapter 5
Description: These notes cover the material discussed during lecture on Chapter 5 of Explaining Psychological Statistics 4th ed. Cohen, Barry (2013)
Uploaded: 10/01/2017
32 Pages 46 Views 9 Unlocks
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• This is a directional hypothesis  


What is the null 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  


What are the types of errors?



• 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?  


What is bayes's theorem?



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

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