Class Created Cards

Question 1

What is the difference between one and two-tailed tests in hypothesis testing?

Answer 1

• one-sided tests measure specifically how much the actual data falls above OR below the distribution based on the null hypothesis BUT NOT BOTH
• two-sided tests measure how much the actual data falls above AND below the distribution based on the null hypothesis

Question 2

Is Block 1 the best stats block?

Answer 2

Obviously

Question 3

What does the symbol “r” represent

Answer 3

It represents the correlation coefficient or r = cov(x,y)/(σx*σy) and generaly tells you how close a set of theoretical points are to being fit by a line (for positive slope 1 is a line, 0 is just random points, and for negative slow -1 is a line.)

Question 4

Does population size
impact bias?

Answer 4

No. Bias is only affected by the method of sampling

Question 5

What does the sigma (σ) symbol mean in statistics?

Answer 5

Standard deviation

Question 6

Does rejecting the null hypothesis mean that the null hypothesis is false?

Answer 6

A null hypothesis is saying that we are accepting the alternate hypothesis (the effect of the hypothesis does exist in the population). This does not prove that the null hypothesis is a false statement.

Question 7

What is a good way to think about what the “mean” means?

Answer 7

The mean can be thought of as the fulcrum of a scale, like the balance point of the data. In other words, it’s the most typical value. If you were to select random points from a distribution, the mean would be the closest on average.

Question 8

What is a z-score?

Answer 8

number of standard deviations away from the mean a certain value is

Question 9

What is a good way to think about what the “median” means?

Answer 9

The median is the number that, when organizing data in numerical value, is in the center. Example - 1 4 6 8 9 - median would be 6.

Question 10

Why do we use hypothesis testing?

Answer 10

We use a hypothesis test to account for the uncertainty caused by sampling variation

Question 11

What is a good way to think about what the “mode” means?

Answer 11

The mode is the number in the data that appears the most amount of times.

Question 12

How are greek and roman letters used in statistics?

Answer 12

To represent concepts/words
-greek tends to represent the general population and roman tends to represent the sample population

Question 13

Does sample size impact bias?

Answer 13

No, it doesn’t matter how big or small the sample size is, the results will still be random either way

Question 14

What is the difference between a population and a sample?

Answer 14

A population is the entire group that you are trying to draw a conclusion about while the sample is the group within the population that you collect data from.

Question 15

Are there patterns in randomness? Explain.

Answer 15

Randomness is characterized by the lack of patterns or predictability in the sequence of events. A random process, such as the output of a truly random number generator, will not exhibit any recognizable patterns or regularities in its output.

Question 16

What does p represent in statistics?

Answer 16

p is short for the p-value, which represents the probability of obtaining results at least as extreme as the observed result.

Question 17

What is a population?

Answer 17

A population is a pool which a sample is being drawn from to study and interpret.

Question 18

What does the mu (µ) symbol mean in statistics?

Answer 18

mean

Question 19

What is the symbol in statistics for the mean of a sample distribution?

Answer 19

X̄

Question 20

What are the Four Pillars of Inference?

Answer 20

These are four types of conclusions to take away from data: significance, estimation, generalization, and causation.

Question 21

What happens to the variation of your sampling distribution as you increase the number of trials from which you are collecting the statistic of interest when you are modeling the null hypothesis for some situation using TinkerPlots?

Answer 21

The variation of the sampling distribution decreases with a larger number of trials.

Question 22

A student says, “I wanted to see if the results were due to random chance.” How might a student go about doing this? What is the reasoning behind that approach— why does it work?

Answer 22

A good way to do this would be a Null Hypothesis Test through a Monte Carlo simulation. The first step would be to construct a sampler that corresponds to the probability model suggested in the null hypothesis. Note that the null hypothesis assumes a no-effect model.

Next, you would want to run your sampler at least 500 times and graph the resulting distribution. From this graph, you can get an idea of how likely various results are to be obtained from random chance.

Finally, we compare our observed result to the sample distribution. If the p-value is less than our alpha value than we reject the null hypothesis and say it’s unlikely that this result was generated due to random chance. Thank you for attending my TED talk.

Question 23

What is a p-value?

Answer 23

A p-value is the probability of having a result be at least as extreme as the observed result if the null hypothesis is true.

Question 24

What is a two-tailed hypothesis test?

Answer 24

A hypothesis test where you check if the observed result is significantly higher or lower than the simulated results (both sides)

Question 25

How can you establish statistical significance?

Answer 25

To establish statistical significance, a common approach is hypothesis testing. It involves creating a null hypothesis (no significant difference) and an alternative hypothesis (significant difference), then using a test statistic (such as a t-value or p-value) to determine likelihood of sample data given the null hypothesis. P-value compares the significance level (often 0.05) to determine rejection or non-rejection of the null hypothesis. If p-value is less, it’s considered statistically significant and the null hypothesis is rejected, otherwise it’s not statistically significant and not rejected.

Question 26

What is the term for the standard deviation of a sample distribution?

Answer 26

The standard deviation of a sample distribution is usually called the standard error and written SE.

Question 27

How do you determine an appropriate alpha level?

Answer 27

1 - confidence level. For exmaple, if you want to be 90% certain your analysis is accurate do 1 - .9 = .1 or 10%. This is for one tailed tests, for two tailed tests, divide this number by 2

Question 28

Doespopulationsize impact sampling variability?

Answer 28

The variability will depend on the population size. This is because larger populations are more likely to produce means that are closer to the actual mean of the whole population.

Question 29

What is a sample?

Answer 29

A sample is a set of data that is taken from a population

Question 30

What is the difference between a simulation and a theoretical approach to statistical hypothesis testing?

Answer 30

Simulation and theoretical are two methods of hypothesis testing. Simulation uses simulated data, while theoretical uses mathematical formulas to calculate test statistics and p-values. Simulation is useful when data generating process is complex, while theoretical is suitable when underlying assumptions of the model are met.

Question 31

What is a Hypothesis Test

Answer 31

Testing a hypothesis in comparison to statistical values. One might compare a hypothesis to a null hypothesis, and then make inferences.

Question 32

What are one-sided and two-sided hypothesis tests?

Answer 32

One-sided -A hypothesis test where you check for statistical significance in one direction
Two sided-A hypothesis test where you check for statistical significance in both directions

Question 33

How do you decide if you want to do a one-sided or two-sided hypothesis test?

Answer 33

A one-sided hypothesis test is when you are interested in seeing if the result is either greater than or less than 50% (looking at a difference between groups in a certain direction). A two-sided hypothesis test is when you are interested in seeing if the result is or is not equal to 50% (to check if there is any difference between groups you are comparing).

Question 34

What do you have to adjust for a simulation when you calculate a p-Value? Why?

Answer 34

You have to add one to the denominator and numerator as if you ran one extra trial which obtained your observed result. We do this to ensure we never get a p-value of zero, as there will always be a chance (albeit small) to generate an observed result from random chance.

Question 35

What does variability mean?

Answer 35

The differences between data points in a data set as related to each other or the mean. Examples of ways we quantify variability are range and standard deviation

Question 36

Does sample size impact sampling variability?

Answer 36

Sample size affects sampling variability

Question 37

What’s an “alpha level” and how do you determine one?

Answer 37

An alpha level is a pre-determined value that we compare results to to see if the results are within reason

Question 38

What is a “uniform probability model”?

Answer 38

A probability model which assigns an equal probability to each possible outcome.

Question 39

How do you calculate the ADM (or MAD)?

Answer 39

(Σ|score-mean|)/(total number of scores)

Question 40

How do you calculate the standard deviation?

Answer 40

Find the mean. For each point find the square of its distance to the mean. Sum the values. Divide by the number of data points. This is the variance, the standard deviation is the square root of the variance.

Question 41

What are a few examples of questions we can answer using hypothesis testing?

Answer 41

Is the mean value of a certain measurement (e.g. blood pressure) different between two groups of people (e.g. smokers vs. non-smokers)?

Is the proportion of customers who buy a certain product significantly different between two different marketing campaigns?

Is the average time to complete a task significantly different between two different training methods?

Question 42

How do we measure the spread (variability) of a distribution?

Answer 42

The measure of the spread is the standard deviation

Question 43

What symbols is used in statistics for the sample distribution standard deviation?

Answer 43

SE, standard error.

Question 44

How do we describe the shape of a distribution

Answer 44

The shape of a distribution of data is determined by both the measures of central tendency of the distribitonand the measures of spread of the data. Distribution is symmetric if the data is evenly distributed around the center or is a mirror image on both sides of the center. A bell-shaped: single peak or concentration of data. Right skew: concentrated on the right. Left skew: concentrated on the left.

Question 45

What is the meaning of “statistically significant”

Answer 45

Statistical significance tells us whether a result is due to random chance or some non-random factor

Question 46

What is a parameter of interest in a hypothesis test?

Answer 46

The Parameter of Interest gives you more information about the sample or the population. It is often the mean.

Question 47

In statistical hypothesis testing, what is the symbol for the research question?

Answer 47

In statistical hypothesis testing, the symbol for the research question is typically denoted as H₀ (null hypothesis) and H₁ (alternative hypothesis).

Question 48

How do you calculate the standard error?

Answer 48

Divide the standard deviation by the sample size’s square root.

Question 49

Why do we sample?

Answer 49

We sample because it is difficult to collect data from the entire population.

Question 50

What symbols is used in statistics for the sample distribution standard deviation?

Answer 50

The sigma symbol

Question 51

How do you calculate a p-value?

Answer 51

Numerator: number of points at least as extreme as the observed result + 1
Denominator: total number of simulated results + 1

Question 52

How do you write a null hypothesis?

Answer 52

To write a null hypothesis, restate the research question, add probability, and then state that any variation is due to random chance.

Question 53

In statistics, what symbol is used for the population standard deviation?

Answer 53

σ (lowercase sigma)

Question 54

What does Q1, Q2, and Q3 mean in terms of a distribution (and boxplot).

Answer 54

Q1, Q2, and Q3 are each single points on the boxplot. Q1 is the leftmost side of the boxplot, Q2 is the median of the dataset, and Q3 is the rightmost side of the boxplot. Q1 and Q3 are also the lower and higher edges of the middle 50% range of the distribution.

Question 55

How do you decide on the number of repeats to run when you are modeling the null hypothesis for some situation using TinkerPlots?

Answer 55

The number of repeats should be equal to the sample size of the sample we’re analyzing. The symbol for this number is n

Question 56

What can, and cannnot, be inferred about a population by looking at it’s box plot?

Answer 56

Can: Median, interquartile range, range, min and max

Cannot: Mean, Standard Deviation

Question 57

What are the measures of center?

Answer 57

Mean, median, mode

Question 58

How do you conduct a Monte Carlo Simulation?

Answer 58

Three steps: Set up, Simulate, Evaluate. Run at least 500 trials.

Question 59

How do you calculate a z-score?

Answer 59

Calculate the number of standard deviations the item is away from the mean.

Question 60

How to calculate the interquartile range (IQR)

Answer 60

The IQR is the middle 50% of the data spanning from Q1 to Q3. Once a box plot is divided into 4 sections, the IQR is the middle 2.

Question 61

What is the confidence interval?

Answer 61

range of values that is used to estimate an unknown population parameter.

Question 62

How do you make a stem plot?

Answer 62

To make a stem plot, take the first digit(s) of your numbers and place them sequentially in the left column (don’t repeat values). Then, list out the rest of the digits of each number in the right column.

Question 63

Do you expect to get 5 heads and 5 tails every time you flip a fair coin? Why not?

Answer 63

No. A fair coin has an equal probability of landing heads or tails, but that is a probability not guarantee. If flipped many times you would expect about 50% Heads and Tails

Question 64

What is an interquartile range?

Answer 64

It is the range between the third an first quartile. It is the middle 50%

Question 65

How do we find the range of “typical values”?

Answer 65

The range of typical values of a distribution is defined by the mean of the distribution + or - 2 * standard deviation.

Question 66

What are some things that students get confused about regarding box plots.

Answer 66

The quartiles are not the actual section of data, but is the divider between them. Q1 refers to a line, alike Q2 and Q3. There is technically no “4th quartile” despite having a 4th section. Calling these quartiles is confusing as there are only three.

Question 67

What are stem (stem and leaf) plots?

Question 68

What does p hat (p̂) mean in statistics?

Answer 68

The hat character “^” is usually used to denote that we are talking about a statistic (for a sample) or an estimate/predicted value. The P(x) refers to the proportion of x in the population but the p̂(x) refers to the proportion within a sample. The character π is also sometimes used rather than P.

Question 69

What do students get confused about when describing the skew of a distribution?

Answer 69

When describing the skew of a distribution, students often get confused between left and right skew, since the side with the longer tail defines the skew (rather than the peak).

Question 70

What is “positive skew”? What is “negative skew”?

Answer 70

“positive skew” is when a bell curve has a longer tail on the positive (right) side than the other side.
“negative skew” is when a bell curve has a longer tail on the negative (left) side than the other side.

Question 71

How do we find the range of “typical values”?

Answer 71

To find the range of “typical values,” go two standard deviations to each side of the mean, those two numbers define the range of “typical values.”

Question 72

What is a “false positive”?

Answer 72

A “false positive” is when a result incorrectly assumes something is there/happening

Question 73

What is a “false negative”?

Answer 73

A “false negative” is when a result incorrectly assumes that nothing is there/happing

Question 74

What is an alpha level?

Answer 74

An alpha level is a percentage that one sets at the beginning of a hypothesis test as a measure of the amount of evidence needed to reject the null hypothesis, it’s usually set to 5%.

Question 75

What are three different ways of determining if a point is an outlier?

Answer 75

1. If you display the data, you can identify outliers just by choosing the points that seem too far removed from the rest of the data, especially when considering the variable in question.
2. Any point that is at least 3 SD away from the mean can be considered an outlier.
3. If you use a box plot, then any point at least 1.5 IQRs away from the nearest quartile can be considered an outlier.

Question 76

How do you represent the null and alternative hypothesis using symbols?

Answer 76

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population

Question 77

What is the symbol in statistics for the z-score, aka standard score?

Answer 77

z

Question 78

What are different statistical interpretations of “range”?

Answer 78

The distance between the highest and lowest data points

Question 79

What can, and cannot, be inferred about a population by looking at it’s box plot?

Answer 79

By looking at a box plot, you can infer likely ranges and means

Question 80

What do “quartile 1”, “quartile 2”, and “quartile 3” mean in terms of a distribution?

Answer 80

Quartiles 1 and 3 are the ends of the range of likely values
Quartile 2 is the mean

Question 81

What are some good uses of a boxplot? What statistical need might a boxplot satisfy?

Answer 81

Box plots are good to represent data and to compare to other sets of data

Question 82

What is a “stem plot” (also known as a “stem and leaf plot”)?

Answer 82

A stem and leaf plot is a plot used to represent a set of data. It takes a value and splits it up at the 10s place to show how many of a certian interval there are

for example the values 32 and 34 would be represented by a stem of 3 and leafs of 2 and 4