Pysch Stats: NHST -> T Tests (Harnett 6)

Margin of Error (MoE)

An estimate of the sampling error (the portion of the confidence interval formula to the right of the plus/ minus sign)

What does null hypothesis significance testing do?

It determines whether a difference is statistically significant and whether the observed difference is likely due to chance

• Reject or fail to reject the null hypothesis

P value

The probability of observing a result that extreme just by random chance if there isn’t a real effect

Why is a p value more likely to acheive statistical significance when the sample size is large?

When a sample size is large, the likelihood of statistical signifiance is increased, since random errors are reduced and it’s easier to detect smaller differences

True Positive

When NHST rejects the null hypothesis and the null hypothesis is false

• + is when null is rejected and null is wrong

True Negative

When NHST fails to reject the null hypothesis and the null hypothesis is true

• - is when the null isn’t rejected and null is true

Why does NHST have error?

NHST has error, because it uses a sample, instead of a whole population

• It has error due to sampling error

• Samples don’t always represent the population

Type 1 Error

When you reject the null hypothesis, even though it’s true

• Data is not statisically significant

What is alpha in type 1 errors?

Alpha is the probability of commiting a Type 1 error

• Rejecting a null even though it’s true

Type 2 Error

Failing to reject the null hypothesis when the null is false

• Should have rejected null hypothesis

Beta

The probability of commiting a Type 2 error

• Probability of failing to reject a null hypothesis, when the null is false

What happens when you decrease the likelihood of a Type 1 error?

When you decrease the likeihood of a type 1 error, you increase the likeihood of a type 2 error

• When you decrease the likelihood of a Type I error, you make it harder to reject the null hypothesis. This automatically makes Type II errors more likely

What does it mean when you set the alpha to 0.05?

When you set the alpha to 0.05, you commit the Type 1 error only 5 percent of the time

• Reject the null when it’s true, only 5 percent of the time

NHST Version #1

1. Specify a null hypothesis

2. Calculate a 95% CI based on the sample data (I’m 95 percent confident)

3. Conclusion: Reject the null if the CI doesn’t overlap with the null population mean and fail to reject the null if the CI does overlap with the null population mean

• Less complicated

• Gives an actual estimate (a CI) of the actual effect

NHST Version #2

1. Specify a null hypothesis

2. Calculate a test statistic (like the z test statistic)

3. Calculate the probability of obtaining that test statistic, assuming the null hypothesis (p value)

4. If p is greater than alpha, reject the null and declare significance

• Only evaluates the null hypothesis

In NHST is the alternative hypothesis tested?

No, the alternative hypothesis is not tested through NHST

• Need other methods other than NHST

What is the probability of making a Type 1 error when you reject your null?

If you reject your null, your probability of making a Type 1 error is equal to your p value

• 9 percent chance of rejecting null so more probability of rejecting when shouldn’t

What does it mean about alpha the greater the alpha and the smaller the alpha?

The greater the alpha, the more likely you’ll make a Type 1 error (reject the null when it’s true)

The smaller the alpha, the more likely you’ll make a type 2 error (fail to reject the null, when it’s false)

What is a two tail p test?

A test that calculates the probability that a sample result is significantly higher or lower than the null hypothesis, assessing both directions (tails) of a probability distribution

What is the two tailed p value?

The two tailed p value (non directional test) is twice the one tailed p value, since it adds in the possibility that the answer to your research question is the opposite of what is expected

A psychologist claims that college students sleep an average of 7 hours per night during the semester. Random sample of 64 students report an average of 6.7 hours with a population SD of 1.2 hours.

1. Conduct NHST with CI

2. Conduct NHST with p values

Null hypothesis: College students sleep 7 hours per night during the semester

1. 95 CI= X bar ± 1.96 x (o/ square root of n)

• 6.7 ± 1.96 x (1.2/ square root of 64)

• (6.406, 6.994)

We are 95 percent confident that the true population mean is between 6.406 and 6.994 hours, thus we reject the null hypothesis

1. Z test= (X bar- u)/ SE

2. 6.7- 7/ (1.2/ squre root of 64) = -2

3. Z score of -2= 2%, two tailed so 4%

4. Assuming the null is true, there is a 4 percent chance of observing this data, so reject null

What is degrees of freedom for a t test?

For a t test, degrees of freedom are n-1

What is the formula to estimate the population SD?

We can use Gosset’s formula to estimate the population SD

What does Gosset’s formula, dividing by n-1, rather than just n give us?

It gives us the estimated population SD based on a sample or o hat

What do you need to change if you use Gosset’s formula in your confidence interval estimate?

If you use Gosset’s formula in your confidence interval estimate, you need to compensate for the inaccuracy by increasing the confidence interval range

• Increase the 1.96 number in the 95 percent confidence interval to the number on the t table

• For t table, DF= n-1 and column is tail of CI (ex. for 95 percent CI, tail is 0.05)

NHST Process #1 with Gosset’s Formula

1. Specify a null hypothesis (an expected population mean)

2. Calculate a confidence interval based on your sample data (Using Gosset’s formula)

3. Conclude whether or not to reject the null based on whether or not the CI includes the expected mean

NHST Process #2 with Gosset’s Formula

1. Specify a null hypothesis

2. Calculate a test statistic (WITH GOSSET FORMULA)

3. Calculate the probability of obtaining a test statistic, under the null hypothesis

4. Conclude whether or not to reject the null based on whether or not that probability is small enough

Gosset’s t test statistic

t= X bar - population mean/ SE

• SE= estimated population SD/ square root of n

In NHST, what should you do, if you don’t know the population SD?

You must use Gosset’s formula to estimate the population SD and calculate a t test statistic, instead of a z test statistic

What do you convert a t testic statistic to?

You convert it to a two tailed p value to make it easier to analyze

One- sample t test

Compares a sample mean to an expected population mean

• Needs the expected population mean, sample mean, estimated population SD using the sample