Unit 11: T test, z test and more

Question 1

what does the t test do that the z test doesnt

Answer 1

The one-sample t-test compares a sample to a population to
determine statistical significance, without knowing s (population
SD).
* Also means you cannot calculate standard error of the mean
* So, we need an estimate for σM

Question 1

what do z tests and t tests have in common

Answer 1

Both tests answer:
* is a particular sample likely to have been drawn from a population that has a
specified mean?

Question 2

The Estimated Standard Error of the Mean

Answer 2

Question 3

Answer 3

.59

Question 4

when do we use a t test

Answer 4

When σ is unknown and we need to estimate SEm, then a test statistic
other than the z must be used

Question 5

Degrees of freedom

Answer 5

Degrees freedom (df) is a value indicating the number of independent pieces of information a sample of observations can provide for purpose of statistical inference

The degrees of freedom (DF) in statistics indicate the number of independent values that can vary in an analysis without breaking any constraints.

A change in the df indicates a different t distribution, each with its own critical value.
* As sample size (and therefore degrees of freedom) increases, the t distribution becomes increasingly like z.

Question 6

example of one sample t test

Answer 6

Question 7

what is the formula for standard error

Answer 7

the sample standard deviation/the square root of sample size

Question 8

standard error

Answer 8

The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean. When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population mean

Question 9

Answer 9

0.59

Question 10

when do we use the test statistic t

Answer 10

When σ (sd) is unknown and we need to estimate SEm (standard error), then a test statistic
other than the z must be used

Question 11

Answer 11

Question 12

effect size

Answer 12

An effect size is a specific numerical nonzero value used to represent the extent to which a null hypothesis is false.
As an effect size, Cohen’s d is typically used to represent the magnitude
of differences between two (or more) groups on a given variable, with
larger values representing a greater differentiation between the two
groups on that variable.
When comparing means in a scientific study, the reporting of an effect
size such as Cohen’s d is considered complementary to the reporting of
results from a test of statistical significance

Question 13

Null hypothesis

Answer 13

In scientific research, the null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term “null.”

(in a statistical test) the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

Question 14

alternative hypothesis

Answer 14

the hypothesis that we are trying to prove and which is accepted if we have sufficient evidence to reject the null hypothesis.

Question 15

type 1 error

Answer 15

false positive- you reject the null hypothesis (saying there is a causal relationship) when it’s actually true (there’s no causal relationship)

Question 16

type 2 error

Answer 16

false negative- you dont reject the null hypothesis

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. A type II error produces a false negative, also known as an error of omission. For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.

Question 17

One sample t-test

Answer 17

Difference between the sample mean and the hypothesized mean

Question 18

Independent-samples t-test

Answer 18

Difference between the means of 2 independent groups

independent variable is the grouping variable, which means the scale
is nominal or categorical, specifically dichotomous

dependent has to be continuous/metric

• You have 2 groups, each with its own number of observations, n1 and n2
• Df = (n1 -1) + (n2-1) = n1 + n2 – 2… which is
• Total number of observations – 2

Question 19

Paired t-test

Answer 19

Matched pairs (e.g. siblings, same individuals at 2 time points)
* Difference between the means of the pairs

• Your n stands for the number of pairs
• Df = n – 1

Question 20

what must an independent sample t test have

Answer 20

• Assumptions
• Categorical (binary or dichotomous) independent variable
• Dependent variable Y is continuous or metric
• Random sample
• Independence of observations within and across factors
• One observation should not have any effect or be related to another observation
• Y should be normally distributed within each group (for small samples)
• Homogeneity of variances = Homoscedasticity
• Equal variances across groups

Question 21

what does an apa table need

Answer 21

horizontal, table 1 and title of table under

Question 22

Homoscedasticity

Answer 22

Homoscedasticity, or homogeneity of variances, is an assumption of equal or similar variances in different groups being compared. This is an important assumption of parametric statistical tests because they are sensitive to any dissimilarities. Uneven variances in samples result in biased and skewed test results.

Question 23

Shapiro-Wilk test of normality

Answer 23

the null is that the distribution is
normal

Question 24

cohen’s d cut-off

Answer 24

absolute value

• Small: 0.2
• Medium: 0.5
• Large: 0.8

Question 25

what must be needed for a paired t test

Answer 25

• Dependent variable Y is continuous
• Categorical (dichotomous) IV
• The 2 groups are independent of each other
• Paired t-test
• What you’re testing is matched

Question 26

Nonparametric Tests

Answer 26

In statistics, nonparametric tests are methods of statistical analysis that do not require a distribution to meet the required assumptions to be analyzed (especially if the data is not normally distributed). Due to this reason, they are sometimes referred to as distribution-free tests

Question 27

parametric tests

Answer 27

Parametric tests are based on assumptions about the distribution of the underlying. population from which the sample was taken. The most common parametric. assumption is that data are approximately normally distributed.

Question 28

why parametric over nonparametric tests

Answer 28

parametric has higher power: can find differences easier

Question 29

Wilcoxon Rank Sum Test/Also known as Mann-Whitney U-test

Answer 29

nonparametric version of independent sample t test

The Wilcoxon rank-sum test is commonly used for the comparison of two groups of nonparametric (interval or not normally distributed) data, such as those which are not measured exactly but rather as falling within certain limits (e.g., how many animals died during each hour of an acute study).

if the data deviates heavily from normality, especially in small samples
(think n < 30)
* Assumptions
* Response need to be at least ordinal
* Not too many ties and 0s
* Independent samples

Question 30

Wilcoxon Signed Rank Test

Answer 30

nonparametric version of paired t test

• Compares medians
• 𝐻0: the distribution location is the same for both groups (roughly: no
  differences in the medians)
• 𝐻1 : the distribution location is different across groups (roughly: the
  medians are different)
• Assumptions
• At least ordinal
• Not too many ties or 0s