06-Statistical Inference at Fachhochschulstudiengänge Hagenberg | Flashcards & Summaries

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1. Motivation behind Statistical Inference

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to make (or back up) assumptions about a population from a sample of it. because not every single one can be measured.

2 different approaches: estimation and hypothesis testing

Sample has to be random to prevent bias


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2. What is the difference between a population parameter and a sample statistic?

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  • a population parameter is the true value in the whole population.
    E.g.: Population "Class of 21" sex true value: 20 girls, 10 boys
  • a sample statistic is any statistical parameter calculated from a sample of the population
    E.g.: 10 people randomly chosen from class: 7 girls, 3 boys > calculated 70% girls.


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3. What is statistical estimation?

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an estimate of a population parameter based on sample statistic 


point estimate: a single value that approximates a parameter

interval estimate: a range of values that approximates a parameter

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11. What is the correct interpretation of a confidence level (e.g. confidence of 95%)


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Out of all intervals computed from samples at the 95% level, 95% of them should contain the parameter's true value


in 95% of the cases, the true value lies within the 95% confidence interval of the sample's estimate.

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12. Describe the concept of statistical hypothesis testing

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is used to investigate a relationship between 2 variables.

We take the null-hypothesis H0, (saying that the variables are independent) and calculate the statistically significance of it. If we find enough evidence to reject the H0 we conclude that there is a relationship (with xx% confidence -> "the result would be in 100-xx % cases just coincidence")

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13. What is a null hypothesis? What is an alternate hypothesis?

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H1 represents our scientific interest / statement to be tested. Eg. We want to see if bigger houses are more expensive. So H1 would be "there's a correlation between the size and the price of a house". 

H0 represents the default position: what we have to assume as long as we don't find any evidence against it. Then we conclude the null hypothesis H0 "House size and prize are independent" this.

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14. What is a "p-value" What is "significance" in the context of hypothesis testing?

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p-value: probability to coincidencely get a test result which is at least as extreme as the result, if the null hypothesis is true.

it is NOT the probability of hypothesis is true

it is NOT showing an effect size or importance


significance: (1 - confidence) is that level, we set to decide if a result contradicts the null hypothesis or not.

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17. What are the steps of hypothesis testing (systematic approach)?

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1. Identify the null and alternate hypotheses 

2. Identify the relevant test statistic and its distribution 

3. Compute the value of the test statistic from the data 

4. Construct the rejection region 

5. Compare the value to the rejection region and make a decision. 

6. Formulate the decision in the context of the problem.

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18. Common pitfalls when assessing statistical significance?

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a smaller sample is more easily influenced by noise

statistically significance doesn't imply medical significance

p-value is NOT probability of 0-hypothesis beeing true

p-value does NOT show effect size or importance

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5. Describe the terms subject and variable in the context of Statistical Inference

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Subject: a human, animal, or things (i.e. community, culture, societal aspects, medical, etc.)

Variable: a characteristic that varies between subjects (e.g. age, income, height)

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10. What information does a confidence statement convey?

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2 Types: 

  1. a random variable falls in a fixed interval
    • How confident are we, that a estimate lies within a interval around the true value?
  2. a random interval covers a fixed value
    • How confident are we that the true value lies in the interval? This is NOT the probability that it lies in the interval, since both values are fixed now.





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4. What is the foundation of quantitative statistical inference?

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A representative (not-biased) sample of adequate size (to reduce error), randomly drawn from a well-defined population.

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Q:

1. Motivation behind Statistical Inference

A:

to make (or back up) assumptions about a population from a sample of it. because not every single one can be measured.

2 different approaches: estimation and hypothesis testing

Sample has to be random to prevent bias


Q:

2. What is the difference between a population parameter and a sample statistic?

A:
  • a population parameter is the true value in the whole population.
    E.g.: Population "Class of 21" sex true value: 20 girls, 10 boys
  • a sample statistic is any statistical parameter calculated from a sample of the population
    E.g.: 10 people randomly chosen from class: 7 girls, 3 boys > calculated 70% girls.


Q:

3. What is statistical estimation?

A:

an estimate of a population parameter based on sample statistic 


point estimate: a single value that approximates a parameter

interval estimate: a range of values that approximates a parameter

Q:

11. What is the correct interpretation of a confidence level (e.g. confidence of 95%)


A:

Out of all intervals computed from samples at the 95% level, 95% of them should contain the parameter's true value


in 95% of the cases, the true value lies within the 95% confidence interval of the sample's estimate.

Q:

12. Describe the concept of statistical hypothesis testing

A:

is used to investigate a relationship between 2 variables.

We take the null-hypothesis H0, (saying that the variables are independent) and calculate the statistically significance of it. If we find enough evidence to reject the H0 we conclude that there is a relationship (with xx% confidence -> "the result would be in 100-xx % cases just coincidence")

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Q:

13. What is a null hypothesis? What is an alternate hypothesis?

A:

H1 represents our scientific interest / statement to be tested. Eg. We want to see if bigger houses are more expensive. So H1 would be "there's a correlation between the size and the price of a house". 

H0 represents the default position: what we have to assume as long as we don't find any evidence against it. Then we conclude the null hypothesis H0 "House size and prize are independent" this.

Q:

14. What is a "p-value" What is "significance" in the context of hypothesis testing?

A:

p-value: probability to coincidencely get a test result which is at least as extreme as the result, if the null hypothesis is true.

it is NOT the probability of hypothesis is true

it is NOT showing an effect size or importance


significance: (1 - confidence) is that level, we set to decide if a result contradicts the null hypothesis or not.

Q:

17. What are the steps of hypothesis testing (systematic approach)?

A:

1. Identify the null and alternate hypotheses 

2. Identify the relevant test statistic and its distribution 

3. Compute the value of the test statistic from the data 

4. Construct the rejection region 

5. Compare the value to the rejection region and make a decision. 

6. Formulate the decision in the context of the problem.

Q:

18. Common pitfalls when assessing statistical significance?

A:

a smaller sample is more easily influenced by noise

statistically significance doesn't imply medical significance

p-value is NOT probability of 0-hypothesis beeing true

p-value does NOT show effect size or importance

Q:

5. Describe the terms subject and variable in the context of Statistical Inference

A:

Subject: a human, animal, or things (i.e. community, culture, societal aspects, medical, etc.)

Variable: a characteristic that varies between subjects (e.g. age, income, height)

Q:

10. What information does a confidence statement convey?

A:

2 Types: 

  1. a random variable falls in a fixed interval
    • How confident are we, that a estimate lies within a interval around the true value?
  2. a random interval covers a fixed value
    • How confident are we that the true value lies in the interval? This is NOT the probability that it lies in the interval, since both values are fixed now.





Q:

4. What is the foundation of quantitative statistical inference?

A:

A representative (not-biased) sample of adequate size (to reduce error), randomly drawn from a well-defined population.

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