T-tests

Question 1

What do statistical procedures allow?

Answer 1

–statistical procedures allow us to make probability statements about the likelihood of a given pattern occurring if the observed means were based on samples drawn randomly from the same population.

–If that likelihood is low (typically less than 1 in 20; i.e., 5%) then the observed difference is unlikely to occur if the samples were drawn from the same population.

Question 2

what is one of the main approaches to statistical inference?

What does this involve?

Answer 2

significance testing:

given degree of confidence we can therefore reject the null hypothesis (H_o ; that ‘nothing has happened’ — i.e., that the manipulation of the independent variable has had no effect, or there is **no difference between groups). **

Question 3

When is signifiance- testing/hypothesis -testing conducted

Answer 3

in experiments or studies or questionnaires

There is an alternative/ research hypothesis (difference between groups) and a null hypothesis (where there is no difference between groups)

Question 4

do we always test the null hypothesis, if so why?

Answer 4

we always test the Null Hypothesis (Ho)

Therefore we usually aim to reject the null-hypothesis (Ho), and accept the alternative hypothesis (H1)

statement of what shall occur when observing random process

We need to assume that there is no difference between means until we are certain that some sort of difference exists.

Question 5

what percentage is usually used to reject null hypothesis?

Answer 5

probability the two means coming from the same population is small enough to conclude the two means were unlikely to have been drawn from same population

5% or less

Question 6

what happens after the null hypothesis is rejected?

Answer 6

significantly more likely for the mean to be drawn from the same population

Question 7

what happpens if the likelihoodof the two means being different by chance alone is p>0.05

Answer 7

Therefore, fail to reject Ho and conclude that people are just as likely to consider a child running and a stroller as equally threatening to the driving situation

Question 8

what are two type of errors made in significance testing?

Answer 8

Type I error is when you incorrectly reject Ho (i.e., say that there is a difference between the means when there really isn’t)

A Type II error is when you incorrectly not reject Ho (i.e., say that there is no difference between our means, when in fact there is)

Question 9

How is t-test influenced by the research design?

Answer 9

If the variable is manipulated within-subjects, then you use a **within-subjects t-test. **

If the variable is manipulated between-subjects, then you use a between-subjects t-test.

Question 10

when is the t-test used?

Answer 10

compare the means of 2 groups

compare the means of groups i.e., do the means of our experimental and control conditions differ?

Question 11

when we compare means, we test the

Answer 11

we test the null-hypothesis (Ho), not the experimental hypothesis (H1)

Question 12

t-distribution

Answer 12

sampling distrubition used to test the difference between means when population standard deviation is unknown

Question 13

when is a within-subject t-tet used?

Answer 13

comparing means based on sets of data collected in pairs from same participant

independent variable manipulated within subjects

Question 14

what happens when the value of t is very large?

Answer 14

(either positive or negative) then the probability that a random process could have produced a difference this large will be small

therefore, we will have low inferential uncertainty and be confident results are not due to random error or chance

Question 15

what happens if t corresponds to small probability i.e one less than 5 in 1000?

Answer 15

since this is less than P<5% (1 in 200) chance, we reject the null hypothesis. results not due to chance or random error. students were not responding randomly

Question 16

how to calculate degree of freedom? (df)

Answer 16

N (sample size)

N-1

Question 17

t test

Answer 17

t(N-1) = x̄ - x/ s_{x / root}N

Question 18

when gleaning on data that is different, what other question could be asked?

what can answer this?

Answer 18

whether the means are sufficiently different to infer thatthey reflect a real underlying difference

inferential statistics can tell how likely it is the two sets of repsonses are different if this would have been randomly drawn from same population

Question 19

between subject t-test

Answer 19

compare means from different groups of participants

ise difference score D to compare difference between pairs of scores from same participant

Question 20

hwow can you be confident the two conditions in two gropus reflect real underlying different between groups?

Answer 20

greater dispersion of two sets of responses

more data = more evidence

difference in means relative to amount of error is greater

Question 21

Larger t-values,

Answer 21

small standard deviation

large sample

large difference between means

Question 22

what is the alternative hypothesis H₁

Answer 22

there is a significant difference in research.

two means are drawn from 2 different populations with different means

Question 23

when there is high inferential uncertainty, do we reject or accept null hypothesis?

what about if there is low inferential uncertainty?

Answer 23

not reject null hypothesis (never entitled to accept null hypothesis because statistics cannot prove random process has yielded results)

We reject null hypothesis and accept alternative hypothesis that there is a difference

Question 24

in the t-distribution, where does the rejection regions?

what do we conclude if t-value falls in the rejection region?

Answer 24

the small regions at the tail on both sides where few extreme t-values lie

reject null hypothesis because means are statisically different and accept alternative hypothesis i.e low inferential uncertainty

Question 25

what are critical values?

Answer 25

the values that cuts off rejection region

Question 26

what alpha level correponds to rejection region of 5%? what do we say when t value exceeds critical value and falls in rejection region?

Answer 26

0.05 p\< 0.05 (alpha level)

Question 27

wat happpens if t-value falls outside rejection region?

Answer 27

null hypothesis is not rejected

Question 28

what do we call when the obtained value of t fall in either tail? Test two possibilities (one has to be larger than other) what happens when we hypothesize one mean will be greater than other?

Answer 28

two-tailed test use one-tailed test / directional test by using single rejection region at end of distribution

Question 29

when is one-tailed test used?

Answer 29

researchers know that one mean cannot possibly be larger than other

Question 30

what is alpha level

Answer 30

largest propbability that researcher is prepared to accept in order to reject nul hypothesis

Question 31

what happens when you compare t value (t-obtained), to the critical t-value and t value obtained is \> critical t-value?

Answer 31

If tobt \> tcrit, then reject Ho

Question 32

what is correlation?

Answer 32

the relationship between two variables

Question 33

what is a common way of displaying and observing correlation?

Answer 33

on a scatterplot graph

Question 34

what does negative correlation look like?

Answer 34

Question 35

what does no correlation look like

Answer 35

Question 36

what are examples of correlation questions in experiments and surveys

Answer 36

–what is the *_relationship_* between the amount of physical contact and attraction), but is also typically used in surveys — where you have **multiple values of each variable** (i.e., lots of different levels of contact (not just two) and lots of levels of attraction.

Question 37

difference between positive and negative correlation

Answer 37

positive correlation: one value increases, the other increaes negative correlation: one value increases, the other decreases

Question 38

how do we tell from a scatterplot graph the relationship is stronger? what inference can be made?

Answer 38

the **less scattered the various points are from a straight line** — the more confidently we would be able to estimate or predict one variable on the basis of the other to estimate from someone’s reaction time how much they had drunk, or to estimate from how much someone had drunk what their reaction time would be

Question 39

most frequently, correlations are measured by? an example of this is

Answer 39

–correlation coefficients. and example of this is the Pearson product-moment correlation

Question 40

what does value of r in pearson's r reveal?

Answer 40

–The value of r indicates how strong a correlation is and it can vary between –1.00 and + 1.00.

Question 41

what does r in pearson's r show?

Answer 41

allow us to establish whether high scores on **one variable** are associated with high scores on the other, and low scores on one variable associated with low scores on the other

Question 42

what does r=1 look like?

Answer 42

Question 43

what can you say from r=1?

Answer 43

A correlation of r=1, also means that any one value is totally predictable from Knowledge of the associated value of the other factor

Question 44

what does r= .75 look like? and how often will you get this?

Answer 44

it is unlikely to obtain r=.75

Question 45

what happens if you get r=-0.75? how unlikely?

Answer 45

very unlikely

Question 46

what is a more likely r value one may obtain?

Answer 46

r = 0.45

Question 47

if we obtain r =0.45, how certain are we?

Answer 47

We can still predict one variablefrom the other, but we become less certain

Question 48

if we get r=0, or zero correlation, how likely is our prediciton?

Answer 48

it is impossible to predict one variable from the other

Question 49

when is correlational analysis appropriate?

Answer 49

Correlational analysis is only appropriate for linear relationships

Question 50

when we are using 2 different populations, would displaying results on scatterplot graph be appropriate?

Answer 50

no as this would produce a **very strong correlation,** but it would be more appropriate to simply do a **t-test,** because we are clearly dealing with two different populations.

Question 51

what can outliers do in a scatterplot graph?

Answer 51

Outliers can make a huge difference to your correlation coefficient (r) it is easy to spot outliers in scatterplot graph

Question 52

what is scatterplot graph useful for

Answer 52

in determining the nature of the relationship between variables

Question 53

what is Ho in correlational analysis?

Answer 53

our hypothesis of no correlation.

Question 54

what is the alternative hypothesis in correlational studies?

Answer 54

there is a positive/negative correlation between two variables

Question 55

if r obt is \> than r critical, what do we do?

Answer 55

reject Ho

Question 56

what happens if r value obtained is \< critical value?

Answer 56

retain Ho and conclude that there is **not sufficiently strong evidence t**o indicate that there is a relationship between the variables.

Question 57

how do u calculate degree of freedom in correlational studies?

Answer 57

df=N-2

Question 58

steps of calculating r value

Answer 58

–Determine your Ho and H1 –Plot the data on a scatterplot to see what it looks like –Calculate df (for a correlation, df=N-2) –Calculate r (this can be done by hand or with a stats package) –Compare calculated r with critical values for r (from back of book) for the df and the a you decide to use. –If your **_obtained or calculated r is greater than your critical r_**, then reject Ho, and conclude that there is a significant correlation between your two variables.

Question 59

what happens if r is very low?

Answer 59

s relationship may be **statistically significant** where r is very low

Question 60

how may a researcher's ability to detect correlation be limited? give an example

Answer 60

if one (or both) of the variables whose relationship is being assessed has a low variance, or **restricted range. ** **–extreme case, this is because if there is no variation at all in one variable (e.g., if all values of X are the same — say because all participants in a study consume the same amounts of alcohol) then necessarily r = 0.**

Question 61

what is an example of restricted range?

Answer 61

one or more subgroups demonstrate a ceiling effect, or a floor effect.

Question 62

how does floor effect come about?

Answer 62

when there is small variance in samples eg. taking away good readers and poor readers perform poorly

Question 63

what does ceiling effect look like?

Answer 63

good readers are performing at ceiling level with little variability.

Question 64

what happens if we take the group clustered at the ceiling away?

Answer 64

and correlation drops

Question 65

what is correlational fallacy?

Answer 65

by researchers is to assume that just because **two variables are highly correlated**, this means that one is responsible for **variation in the other.** correlation does not equal correlation

Question 66

why does correlation not equal to causation?

Answer 66

causal relationship between these variables may be **_reversed_** (aggressiveness may cause people to drink more), or the relationship may be the product of a **_third factor_**, like a person’s upbringing. third factor **lead to increase in both variables** rather than the variables having an influence on one another

Question 67

what does hypothesis testing in correlation methodology consist of?

Answer 67

Ho: r = 0, H1: r cannot equal to 0.

Question 68

difference between t-test and correlational test

Answer 68

A t-test is a measure of whether the means of **two samples** may be due to chance. Whereas a correlational test is a measure of whether the li**near relationship between two variables** may be due to chance.