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Inferential tests Flashcards

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1
Q

When should a chi-squared test be used?

A

Categorical design
Looking at the frequency of occurence across two categories

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2
Q

When should a t-test be used?

A

Experimental design
Manipulating variables to look at differences between groups of participants or conditions

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3
Q

When should a correlational test be used?

A

Correlational design
Looking at relationships between two continuous variables

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4
Q

What type of data and hypothesis should be used for a chi-squared test?

A

Nominal (categorical) data
Two-tailed hypothesis - is observed different from expected?

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5
Q

What is the expected frequency in a chi-squared test?

A

Frequency we would predict if belonging to each category were random

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6
Q

What is the observed frequency in a chi-squared test?

A

The frequency that occur in the data set

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7
Q

How is a Chi-squared test calculated? (Equation)

A

The sum of ( (O-E) squared / E )

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8
Q

What is the point of obtaining statistical significance?

A

Means that you can infer something about the entire population from your findings

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9
Q

Why would a chi-squared test not be significant?

A

Small chi-squared value = little difference between observed and expected frequencies

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10
Q

What is a p value and which p value is used in psychology?

A

Probability you have committed a type 1 error (smaller p value = smaller probability that you have committed a type 1 error)
In psychology = 0.05 = 5% chance of type 1 error

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11
Q

How is a chi-squared test reported?

A

x^2 (df, N = XX) = XX.XX, p =.XXX OR p < .001

x^2 means chi square
df = degrees of freedom
N = number of participants
XX.XX = statistic calculated value
p value = significance

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12
Q

What is the difference between a chi-square Goodness of fit and a chi-square Test of association?

A

Goodness of fit:
- One variable
- Frequency table - analyses frequencies across different categories within one variable
Test of association:
- Two variables
- Contingency table - analyses frequencies across different categories for two variables

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13
Q

What is the difference between a frequency table and a contingency table?

A

Frequency table displays different categories of one variable and uses chi square Goodness of fit
Contingency table displays different categories of two variables and uses chi square test of association

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14
Q

What are two important rules of contingency tables?

A

1) Categories should contain frequencies or counts - not percentages
2) Categories should be mutually exclusive - cannot have one participant in multiple categories

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15
Q

What are the assumptions for a chi-squared test?

A

1) The level of measurement of all variables is nominal (or ordinal)
2) Each subject may contribute data to one and only one cell
3) The values in the cells should be frequencies or counts, not percentage
4) The value of the cell expected should be 5 or more in at least 80% of the cells, and no cell should have an expected of less than one
In this case, could combine categories so that expected should be more

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16
Q

What steps are there in the process of psychological research?

A

1) Ask a research question
2) Review existing research
3) Develop a hypothesis
4) Collect data to test hypothesis
5) Analyse the data to draw a conclusion
(If you reject hypothesis, return to step 3)
6) Present and evaluate your findings
Repeat

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17
Q

What are independent and dependent variables?

A

Independent = what you manipulate
Dependent = what you measure

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18
Q

What type of data is the independent variable in an experimental design?

A

Nominal (always)

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19
Q

What type of data is the dependent variable in an experimental design?

A

Continuous - interval or ratio (always)

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20
Q

What is an independent/ between subjects design?

A

Different participants are recruited into each of the conditions

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21
Q

What is a repeated/ within subjects design?

A

One group of participants repeatedly takes part in the study under different conditions

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22
Q

What kind of t-test would be used when there is one condition of the IV?

A

One-sample t-test

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23
Q

What kind of t-test would be used when there are two conditions of the IV and a within subjects design?

A

Repeated (paired sample) t-test

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24
Q

What kind of t-test would be used when there are two conditions of the IV and a between subjects design is used?

A

Independent sample t-test

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25
What does the t value actually calculate?
Between group variance/ within group variance (Difference between the two experimental conditions divided by the variability within the two experimental conditions)
26
When is there likely to be a significant difference? (variance)
When there is more variance between than within groups
27
What are parametric assumptions met through methodological design?
All observations are independent Data collected are at interval or ratio level
28
What parametric assumptions are tested after data have been collected?
Data are roughly normally distributed Homogeneity of variance
29
What does homogeneity of variance mean?
The assumption that there is equal variance across samples The average squared distance of a score from the mean is the same across all groups sampled in a study Data are roughly distributed the same around the mean of a group
30
How is an independent t-test calculated?
t = (m1 - m2/ s1 + s2) x sq root of (n1 + n2) m1 and m2 = average score for group 1 and group 2 s1 and s2 = standard deviation for group 1 and group 2 n1 and n2 = number of observation (participants) in group 1 and group 2 (1s and 2s should be subscript)
31
How is an independent t test calculated if the size of the two groups is unequal?
Should use a different formulae with the 'pooled variance'
32
What is the observed t value from a sample compared to?
Critical t-value
33
What happens when the observed t value is more extreme?
There are more chances to reject your null hypothesis?
34
How can normality and outliers be checked visually?
Using box plots and histograms
35
How are normal distribution and outliers checked statistically?
Shapiro-Wilk test tests whether data differ from a normal distribution
36
When a Shapiro-wilk test is not significant what does this mean?
Data are normally distributed - it does not deviate significantly from a normal distribution
37
How is the homogeneity of variance statistically checked?
The Levene's test tests whether the spread of scores within each group differs
38
What does it mean if a Levene's test is not significant?
The assumption of homogeneity of variance has not been violated and the spread of scores within each condition is the same
39
What is the non-parametric equivalent of an independent t-test?
Mann-Whitney U
40
What is the non-parametric equivalent of a repeated (paired sample) t-test?
Sign test and Wilcoxon signed rank test
41
What is the non-parametric equivalent of a one sample t-test?
Sign test and Wilcoxon signed rank test
42
What should be done if the homogeneity is violated in an independent t-test?
Use Welch correction
43
Is homogeneity of variance relevant for repeated and one sample t-tests?
No - only one sample
44
What does the effect size measure?
The magnitude of the effect - the bigger the effect size the greater the difference is between our two groups How significant something is
45
What numbers are considered small medium and large effect sizes? (Not for correlation)
>/= 0.2 = small effect >/= 0.5 = medium effect >/= 0.8 = large effect
46
What is a measure of effect size?
Cohen's d
47
How are the results of a t-test reported (statistical) ?
t (df) = XX.XX, p=.XXX OR p < .001, d = XX.XX t = t value (the calculated statistic) (use small t and italicise) df = degrees of freedom d = tells you the effect size (report cohen's d wtihout the negative)
48
How to report the results of a t-test (written) ?
An [independent OR repeated measures OR one-sample] t-test was conducted to compare [your DV] in [IV condition 1] and [IV condition 2]. As can be seen on Figure 1, there is a [significant OR not a significant] difference in the scores for [IV condition 1] (M=___, SD=___) and [IV condition 2] (M=___, SD=___, t(df)=____, p = ____, d = ____). The results confirmed/ did not confirm our hypothesis that...
49
How is a repeated measures t-test calculated?
t = md/ sd x sq root of N (d's should be subscript)
50
For repeated measures t-test what should assumptions also be checked for?
Difference between the conditions (JASP does it automatically)
51
What is the one set of data in a one sample t-test compared to?
A reference value (this has to be entered at 'test value' in JASP)
52
How is a one sample t-test calculated?
t = (m - u) / (s / sq root of N) (u should have a tail) m = average score for your sample u = average score of your population of reference s = SD
53
What is a parametric test?
A test that requires data from one of the large catalogue of distributions that statisticians have described. - Based on the normal distribution - require basic assumptions that must be met for the test to be accurate
54
What are the four parametric assumptions?
- Normally distributed sampling population - Homogeneity of variance - Interval or ratio data - All observations are independent
55
What types of data are parametric and non-parametric?
No parametric = nominal and ordinal Parametric = interval and ratio
56
Which parametric assumption is key for independent measures design?
Homogeneity of variance
57
What is a non-parametric test?
A family of statistical procedures that do not rely on the restrictive assumptions of parametric tests. In particular, they do not assume that the sampling distribution is normally distributed.
58
What are tied values?
When ranking scores, if two or more raw scores are the same, the mean of the rank numbers should be calculated so they all have the same rank e.g. raw scores in ranks 2 & 3 are the same, so instead they both have a rank of 2.5 (2+3/2 = 2.5)
59
What is the ideal sample size for evaluating normality?
30+
60
What descriptive statistic should be used for non-parametric tests and why?
Median This is not affected by outliers (Have to have ordinal data)
61
Is parametric or non-parametric more powerful at finding a significant effect?
Parametric (assuming assumptions have been met) - If there is a genuine effect in our data then a parametric test is more likely to detect it than a non-parametric one - This is because parametric tests have a greater sensitivity to the data.
62
What is Mann-Whitney U the non-parametric equivalent of?
Independent T-test
63
How does the Mann-Whitney U test work?
Scores of both groups are ranked together from lowest to highest Calculation is done Basically, if one group is generally in the higher ranks and the other group is generally in the lower ranks, there is likely to be a significant difference
64
What is the equation for Mann-Whitney U?
U = n1 x n2 + (n1(n1 + 1)/2) - T (1s and 2s should be subscript) n1 = number of ppts in group 1 n2 = number of ppts in group 2 T = rank totals - Do this for each group - different rank totals - Then, pick the smallest U value
65
Which U value should be picked after calculating Mann-Whitney U?
The smallest one
66
What is effect size shown as for Mann-Whitney U?
Rank-Biserial Correlation
67
How should the results of a Mann-Whitney U test be reported? (Statistics)
U = XX.XX, p=.XXX OR p<.001, rb = XX.XX (b should be subscript) U = calculated statistic (capital and italics) p = significance rb = effect size (rank-biserial correlation) (report without the negative)
68
How should the results of a Mann-Whitney U test be reported? (Written)
A Mann-Whitney U test was conducted to compare [your DV] in [IV condition 1] and [IV condition 2]. This test was used as we had an experimental between groups design, and these parametric assumptions were violated… As can be seen on Figure 1, there is a [significant OR not a significant] difference in the scores for [IV condition 1] (Median=___, SD=___) and [IV condition 2] (Median=___, SD=___, U=____, p = ____, = rb ____). The results confirmed/ did not confirm our hypothesis that...
69
What is the Sign test and Wilcoxon test a non-parametric equivalent of?
Repeated t-test or one sample t-test
70
What is the logic behind the Sign test and the Wilcoxon test?
Scores are ranked If rank scores mainly show increasing values or decreasing values, there is likely a significant effect
71
How is the sign test calculated?
The difference between two conditions of repeated measures is calculated and recorded as either + or - Total + and total - are calculated Smallest value is the sign value N value is total number of + and - (if the difference is 0, this is not counted)
72
How is the Wilcoxon signed rank calculated?
After completing sign test: Sum all the negative ranks Sum all the positive ranks T value is the smallest one
73
What assumptions should additionally be checked on the Wilcoxon test?
Difference between the conditions (Jasp does it automatically)
74
How are the results of a Wilcoxon test reported? (Statistics)
W = XX.XX, p =.XXX OR p< .001, rb = XX.XX (b should be subscript) W = calculated statistic (capital and italicise) p = significance rb = effect size (rank-biserial correlation) (report without the negative)
75
How are the results of a Wilcoxon test reported? (Written)
A Wilcoxon signed rank test was conducted to compare [your DV] in [IV condition 1] and [IV condition 2/ population average]. This test was used as we had an experimental within groups/ one sample design, and these parametric assumptions were violated… As can be seen on Figure 1, there is a [significant OR not a significant] difference in the scores for [IV condition 1] (Median=___, SD=___) and [IV condition 2] (Median=___, SD=___, W=____, p = ____, = rb ____). The results confirmed/ did not confirm our hypothesis that...
76
Why might you get a non-significant result on the sign test, but a significant result on the Wilcoxon test?
Because the Wilcoxon test takes into account the magnitude of the differences and not merely whether there is a positive or negative difference
77
How are the calculations done for a one-sample non-parametric test?
Instead of calculating difference between two sets of scores, the difference is calculated between your sample and the reference (Comparing a specific sample to the rest of the population)
78
How is a one-sample non-parametric test (Wilcoxon) reported? (Written)
(Statistical is the same for repeated and one sample Wilcoxon tests) The DV for our sample was significantly higher/lower/ not significantly different (median = XX.XX) compared to the average population DV (median = XX.XX, full statistic report)
79
How should a non-parametric test result be reported (statistics)
The assumption of parametric tests were violated [justify why - because data are ordinal or because data are not normally distributed**] therefore a [Mann-Whitney U or Wilcoxon signed rank] test was conducted to compare [your DV] in [IV group/condition 1] and [IV group/condition 2]. The results showed is a [significant OR not a significant] difference in the scores for [IV condition 1] (Median=___) and [IV condition 2] (Median=___, W OR U=____, p < .001 or = ____, rb = ____). ** note if thisis the case where normality has been violated, then report the results of the Shapiro E.g: ‘The Shapiro-Wilks revealed that data violated the assumption of normality (p = XXX)
80
What does a correlational design investigate?
The relationship between two continuous variables - Positive, negative or none - No IV and DV - Variables have to be continuous (interval or ratio) or ordinal, not categorical
81
What do different Pearson's r numbers mean?
-1 = perfect negative correlation -0.6 to -0.99 = strong negative correlation -0.3 to -0.59 = moderate negative correlation -0.1 to -0.29 = weak negative correlation 0 to 0.9 = no correlation +0.1 to +0.29 = weak positive correlation +0.3 to +0.59 = moderate positive correlation +0.6 to +0.99 = strong positive correlation +1 = perfect positive correlation
82
What is covariance?
Pearson's correlation looks at this - how much the data points change together
83
What does Pearson's r calculate?
r = covariance between the variables/ variance within the variables
84
What type of data should be used with a Pearson's correlation?
Ratio or interval
85
Does Pearson's look at linear or non-linear relationships?
Linear only
86
What should correlations be checked for?
Outliers
87
What hypotheses can you have for a Pearson's r?
Null hypothesis - no relationship Two tailed hypothesis - there will be a relationship One tailed hypothesis - positive relationship One tailed hypothesis - negative relationship
88
How are the results of a Pearson's test reported? (Statistics)
r (df) = .XX, p =.XXX OR p<.001 r = calculated statistic (lower case and italicise) df = degrees of freedom (N-2) p = significance
89
How are the results of a Pearson's test reported? (Written)
There is a significant positive/negative correlation/ no significant correlation between the two variables (full statistical report), showing that... (explain actual variables)
90
What do effect sizes show for Pearson's r?
r statistic: Small effect = .10 Medium effect = .30 Large effect = .50
91
What is the non-parametric equivalent of Pearson's r and when would this be used?
If one or both variables uses ordinal data: Spearman's rho Ranks scores = non-parametric
92
What is Spearman's rho not as sensitive as Pearson's r to?
Outlying points
93
How are the results reported for spearman's rho? (Statistics)
rs (df) = .XX, p =.XXX OR p <.001 (s should be subscript) rs = calculated statistic (italicised r) df = degrees of freedom (N-2) p = significance
94
How are the results reported for spearman's rho? (Written)
There was a significant positive/ negative correlation/ no significant correlation (full statistic report). This shows that... (describe variable relationship)
95
What should always be done when dealing with correlations?
Always draw and examine a scatterplot and look for the diagonal line of best fit and the slope of this, and look for outliers
96
How should a correlation be reported? (Written)
A [Pearson’s or Spearman correlation] was conducted to test if there is a significant relationship between [variable 1] and [variable 2]. IF RESULTS ARE SIGNIFICANT: There was a significant [positive/negative] correlation (r (df) = .xx, p = .xxx). This shows that… IF RESULTS ARE NOT SIGNIFICANT: The correlation between variable 1] and [variable 2] was not significant (r (df) = .xx, p = .xxx). [no direction to interpret!!!] Note: this is for Pearson, for Spearman, you should report ‘rs’

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