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Research Methods 1 > Chi-Square Test of Association > Flashcards

Chi-Square Test of Association Flashcards

1
Q

What is the probability of an event always between?

A

0 & 1

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2
Q

What does a p-value of 0 mean?

A

There’s no chance that the event will occur.

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3
Q

What does a p-value of 1 mean?

A

The event will always occur

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4
Q

What does P(E) = 0.5 mean?

A

The probability of event (E) is 0.5/ 50%.

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5
Q

Why do we use p-values (from a statistical test)?

A

To decide whether/ not to reject the null hypothesis.

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6
Q

What do p-values represent?

A

The theoretical probability of obtaining our data when the null hypothesis is correct.

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7
Q

What do inferential statistical tests spit out?

A

P-values (& other valuable information)

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8
Q

When do you use the Chi-Square Test of Association?

A

When testing for the presence of a relationship between 2 categorical variables & when you have a between-subjects (unrelated-subjects) design.

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9
Q

What type of test is the Chi-Square Test of Association?

A

An inferential test

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10
Q

When do you use the t-test?

A

When testing for a difference between the means of 2 numerical variables, when you have a between-subjects (unrelated-subjects) design, or a within-subjects (related-subjects) design

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11
Q

What type of test is the t-test?

A

An inferential test

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12
Q

What are 2 examples of experimental hypotheses (HE)?

A

“Medical outcomes differ by treatment centre” & “there’s a relationship between age & playing video games (N=100; 50 adults)”

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13
Q

What is an example of a null hypothesis (H0)?

A

Medical outcomes don’t differ by treatment centre.

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14
Q

How do we test that the results of a study are compatible with the null hypothesis being true?

A

By testing the probability that the results of the study are compatible with the null hypothesis being true

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15
Q

How do we come up with the theory behind a lab report?

A

By developing a novel hypothesis

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16
Q

How do we identify questions when planning a lab report?

A

By designing a study to test your hypothesis

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17
Q

How do we come up with the experimental design behind a lab report?

A

By applying for ethical approval.

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18
Q

How do we incorporate statistics into lab reports?

A

By performing a study, collecting data & analysing the data.

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19
Q

What needs to be presented & evaluated when we write lab reports?

A

Our findings

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20
Q

What do we need to have to perform a study & gather statistical data?

A

An IV & a DV

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21
Q

What is an example of an IV?

A

Type of university

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22
Q

What is an example of a DV?

A

Whether a group survives or dies.

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23
Q

How do we know the level of measurement of data sets?

A

By designing studies to test hypotheses, applying for ethical approval, then performing the studies & collecting & analysing the data.

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24
Q

In a study looking at whether type of hospital, out of 4 different types, affects survival rates, should the proportion of people surviving be similar or different across all 4 locations if the type of hospital makes no difference to the outcome?

A

Similar

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25
Q

In a study looking at whether type of hospital, out of 4 different types, affects survival rates, if all 4 treatment centres are drawn from the same population, are any differences we see due to chance or due to causation?

A

Due to chance

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26
Q

What are 2 examples of categorical data?

A

4 different types of treatment centres & whether patients die or survive.

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27
Q

When can we not compare mean differences between data sets?

A

When we have categorical data

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28
Q

What can we do when we can’t compare mean differences between data sets?

A

Compare portions & decide whether/ not the data collected is compatible with the null hypothesis being true

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29
Q

What is an example of a binary outcome?

A

Whether patients die or survive.

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30
Q

In a study looking at whether type of hospital, out of 4 different types, affects survival rates, what do we do as we can’t compare mean differences between the data sets as each data set contains categorical data?

A

Compare portions & decide whether/ not the data collected is compatible with the null hypothesis being true (i.e., that there’s no systematic difference in survival rates across hospitals).

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31
Q

How can we calculate the probability of observing the pattern of results obtained if the null hypothesis is true?

A

Using inferential statistics

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32
Q

How do we decide whether/ not the data collected from 2 or more portions is compatible with the null hypothesis being true?

A

By using p-values

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33
Q

When do we reject the null hypothesis?

A

If the probability of there being a difference between observed values (results obtained) & what we would expect by chance (if the null hypothesis were true and there is no relationship between sets of data) is low (the p-value is small).

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34
Q

When do we decide that it’s unlikely that we would’ve observed a pattern of results by chance alone?

A

If the probability of there being a difference between observed values (results obtained) & what we would expect by chance (if the null hypothesis were true and there is no relationship between sets of data) is low (the p-value is small).

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35
Q

When can we conclude that there’s a significant relationship between 2 values (e.g. treatment centre & mortality)?

A

If we decide that it’s unlikely that we would’ve observed a pattern of results by chance alone.

36
Q

What do we consider to be a low probability?

A

p <= 0.05

37
Q

When do we fail to reject a null hypothesis?

A

If the probability of there being a difference between observed values (results obtained) & what we would expect by chance (if the null hypothesis were true and there is no relationship between sets of data) is high (the p-value is large).

38
Q

When do we decide that it’s likely that we would’ve observed a pattern of results by chance alone?

A

If the probability of there being a difference between observed values (results obtained) & what we would expect by chance (if the null hypothesis were true and there is no relationship between sets of data) is high (the p-value is large).

39
Q

When can we conclude that there’s no effect of a relationship between 2 values (e.g. treatment centre & mortality)?

A

If we decide that it’s likely that we would’ve observed a pattern of results by chance alone.

40
Q

What do we consider to be a high probability?

A

p > 0.05

41
Q

What is the procedure for testing hypotheses when data are categorical (or nominal)?

A

Carrying out a Chi-Square Test of Association

42
Q

When do we use a Chi-Square Test of Association?

A

When we want to ask questions about the relationship between categorical variables.

43
Q

What are examples of questions about the relationship between categorical variables?

A

“Is there a relationship between life stage & wanting to be a psychologist?”, “does the incidence of mental health disorders differ by country?”, & “is there a relationship between BRCA1/2 test results & clinical decision making?”

44
Q

What are categorical or nominal data?

A

Named (or sometimes numbered) discrete categories (e.g. religion, marital status, disease, & job field)

45
Q

How is nominal (or categorical) data produced?

A

By counting the number of observations in each of multiple categories

46
Q

What are examples of named discrete categories of gender identity?

A

“M”, “F”, “T”, “NB”, & “Ot”

47
Q

What kind of data has no kind of intrinsic/ meaningful order?

A

Categorical/ nominal data

48
Q

What are the basic principles of the Chi-Square Test of Association?

A

It must be used to examine the relationship between 2 variables & establish the probability that group membership by 2 variables occurs by chance, & a standard probability threshold must be applied to test our hypothesis & conclude significance.

49
Q

How are observed (collected) data for the Chi-Square Test of Association organised?

A

In a contingency table

50
Q

How do we know what we would expect by chance?

A

By estimating it from collected data

51
Q

What is the formula for expected frequencies per cell when carrying out the Chi-Square Test of Association?

A

(Row total x column total)/ grand total

52
Q

What does the Chi-Square Test of Association test?

A

Whether there’s a deviation (or difference) between observed & expected values.

53
Q

What do we need a way to measure with observed & expected values?

A

The overall degree to which the observed & expected values differ from each other.

54
Q

What does the Chi-Square Test of Association test?

A

How closely our observations fit the expected model.

55
Q

What is the formula of the Chi-Square Test of Association?

A

χ2 = Σ(O - E)2/ E, where E = expected frequency, O = observed frequency, & Σ = the sum of

56
Q

How do you carry out the formula for the Chi-Square Test of Association?

A

By summing together (Σ) the squared deviations of each observation from their expected values, & dividing each by their expected values.

57
Q

When carrying out the formula for the Chi-Square Test of Association, do you carry out the division first or the addition first?

A

The division

58
Q

Logically, if the null hypothesis were true (p > 0.05), would the observed & expected frequencies of 2 categorical variables be similar or different?

A

Similar

59
Q

Logically, if the null hypothesis were true (p > 0.05), would the calculated value of χ2 be large or small?

A

Small

60
Q

If the observed frequency of adolescents playing video games were 35, and the expected frequency was 27.5, what would the χ2 statistic be?

A

(35 - 27.5)2/ 27.5 = 2.04

61
Q

If the observed frequency of adults playing video games were 20, and the expected frequency was 27.5, what would the χ2 statistic be?

A

(20 - 27.5)2/ 27.5 = 2.04

62
Q

If the observed frequency of adolescents not playing video games were 15, and the expected frequency was 22.5, what would the χ2 statistic be?

A

(15 - 22.5)2/ 22.5 = 2.50

63
Q

If the observed frequency of adults not playing video games were 30, and the expected frequency was 22.5, what would the χ2 statistic be?

A

(30 - 22.5)2/ 22.5 = 2.50

64
Q

If (O - E)2/ E for each of 4 categories was: 2.04, 2.5, 2.04, & 2.5 what would the χ2 statistic be?

A

2.04 + 2.5 + 2.04 + 2.5 = 9.08

65
Q

What are the 3 steps involved in the Chi-Square Test of Association?

A

Extracting/ computing information, calculating the Chi-Square statistic, & converting the Chi-Square statistic to a probability

66
Q

How do we convert a Chi-Square statistic into a probability?

A

By referring to the table of critical values of χ2.

67
Q

To what do we need to refer to determine whether a result is significant (i.e. if we can reject the null hypothesis)?

A

The table of critical values of χ2.

68
Q

If observed frequencies of categorical data are random (& the null hypothesis is true), what will be (or close to) 0?

A

The χ2 value

69
Q

If observed frequencies of categorical data are very different from those expected by the null hypothesis, what will be large?

A

The χ2 value

70
Q

When converting a χ2 statistic into a probability, which column of the critical χ2 values table do we look at?

A

The p-value threshold of 0.050

71
Q

What do we need to calculate when we perform a Chi-Square Test of Association?

A

A degrees of freedom (d.f)

72
Q

How is d.f calculated for a Chi-Square Test of Association?

A

d.f = (C - 1)(R - 1), where C = number of columns in a contingency table, & R = number of rows in the contingency table

73
Q

What is the d.f of a contingency table with 2 rows & 2 columns?

A

(2 - 1)(2 - 1) = 1

74
Q

What is the critical value of Chi-Square at p <= 0.05 & d.f = 1?

A

3.842

75
Q

When performing a Chi-Square Test of Association, when can we reject the null hypothesis?

A

If the χ2 value is larger than its relevant critical value.

76
Q

How would you report the results of a Chi-Square Test of Association if the χ2 value was 9.08, the d.f was 1, N was 100, & the p-value was less than 0.05?

A

χ2 = 9.08, d.f = 1, significance level: p < 0.05

77
Q

Given that the critical value of the following results: χ2 = 9.08, d.f = 1, significance level: p < 0.05, is 3.842, does our calculated χ2 value exceed or fall short of the critical value?

A

It exceeds the critical value

78
Q

If our calculated χ2 value exceeds our critical value, do we reject or fail to reject the null hypothesis?

A

We reject it

79
Q

What are the 4 steps involved in calculating the Chi-Square Test of Association by hand?

A
  1. Compute the Chi-Square statistic (χ2 value)
  2. Establish the critical value of Chi-Square for a probability (p-value) of 0.05 & your degrees of freedom.
  3. If your calculated χ2 value is equal to/ greater than the critical value, you can reject the null hypothesis & conclude that you have found a significant effect.
  4. If your calculated χ2 value is less than the critical value, you fail to reject the null hypothesis
80
Q

How do you calculate the Chi-Square Test of Association using SPSS?

A

By inputting the data in the correct format (SPSS will need to know whether you’re putting in raw data/ contingency table values), then telling SPSS to perform a Chi-Square Test of Association, which will cause SPSS to calculate the exact p-value for you (as well as reporting your expedited values & degrees of freedom)

81
Q

When do you not need to use a Chi-Square critical table of values (& just interpret the reported p-value)?

A

When using SPSS to perform the Chi-Square Test of Association

82
Q

What differs by age category (χ2 = 9.08, d.f = 1, significance level: p < 0.05)?

A

The percentage of people that play computer games.

83
Q

What is 1 conclusion that could be drawn from a Chi-Square Test of Association being performed to examine the relationship between life stage and playing computer games, & the relation between these variables being significant, χ2 (d.f = 1, N = 100) = 9.08, p <= 0.05?

A

That adolescents are more likely to play computer games than adults.

84
Q

When should you use the Chi-Square Test of Association?

A

When you have nominal/ categorical data, when individual frequencies are independent (i.e. when using a between-subjects design) & when expected frequencies are (ideally) not less than 5.

85
Q

When does the Chi-Square Test of Association not lend itself well to directional (e.g. uni-directional hypothesis) interpretation?

A

If a contingency table is larger than 2 x 2 cells.

Research Methods 1 (16 decks)

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