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Flashcards in Statistics Deck (51):

What is descriptive research?

- Aim: to describe characteristics of a sample (what kind, how much etc)

- Used to summarise, organise and simplify sample data

- Often based on measurement of a single variable (univariate statistics)

- Relies on measures of central tendency, frequencies, spread, distributionel shape, etc


What is inferential research?

- Null hypothesis testing

- Aim: to infer characteristics of the population

- Often interested in multiple variables (bivariate, multivariate) - Relies on a wide range of different tests (e.g. correlation, regression, t-tests, ANOVA, chi square etc.)

- Allows us to make probability statements about how confident we can be that our sample findings reflect the ”true” of things


Level of measurement: What are the two main types of variables?

- Categorical

      - binary (2 levels)

      - nominal (3+ levels)

      - ordinal (ordered, no equal intervals)

- Continuous (Interval, ratio)

      - Interval (ordered, equal intervals, no absolute zero)

      - Ratio (ordered, equal intervals, absolute zero)


How can you keep error to a minimum?

- By making sure we use careful sampling strategies and use measures that are valid and reliable

- Validity+reliability=credibility


What are the critical values of z-scores?

- 95% of z-scores lie between -1.96 and 1.96

- 99% of z-scores lie between -2.58 and 2.58

- 99.9% of z-scores lie between -3.29 and 3.29


What does the z-score represent?

- The distance a particular observation is away from the mean, measured in standard deviations

- The standard normal distribution has a mean of 0 and a standard deviation of 1


What are the two ways you can carry out inferential hypothesis-based research?

- Correlational research (observing what naturally happens without interfering)

- Experimental research (manipulationg one variable and observing the effect on another variable – can be used to infer cause/effect)


What are the two types of experimental designs?

- Independent/between subject (different participants in different groups)

- Dependent/repeated measures (same participants exposed to all conditions)


What is systematic variance?

- Variation due to genuine effect

- Variance that can be explained by our model

- Signal/effect - What we want to measure


What is unsystematic variance?

- Noise/error

- Small differences in outcome due to unkown factors


What is the most important formula of all? :-)

- outcome=(model)+error

- the way that effect and error is measured varies for each type of statistical test

- But for a test to be ”significant”, effect should be considerably greater that error (chance)


What is the null hypothesis?

- What we actually tests in statistics

- Assumes that there is no effect, then try to reject this

- H0: no effect in the population


What is the alternative hypothesis?

- What we’re really interested in, when trying to reject the null hypothesis

- Can be:

      - Non-directional: H1: There is an effect in the population

      - Directional: H1: There is this effect in the population


What are significance tests for?

- For determining whether to reject or fail to reject the null hypothesis

- For determining by how many percents confidence we reject the null hypothesis (typically 95%, 99% or 99.9%)


What are the z-distribution, t-distribution, F-distribution etc?

- Test statistics

- A statistic for which we know how frequently different values occur

- Theoretical sampling distributions that assume the null hypothesis

- Test statistic=variance explained by the model (effect)/variance not explained by the model (error)


What is the confidence level for p<.05 p and>

- P<.05>

- P<.01>

- P<.001>


If p is high (p>.05)…

- … the null applies! :-)


If p is low (p<.05>

- … the null must go! :-)


What is the relationship between critical values, significance and confidence?

- As critical value increase (gets further away from null), confidence increases

- As confidence increases, p (probability of making a type 1 error) decreases

- Confidence+p=1.0 or 100%


What are critical cut-offs dependent on?

- Type of test - 1 vs 2 tailed significance

- P level

- Degrees of freedom (calculated different for different tests)


What is a type I error?

- False positive

- Saying there is an effect when there isn’t

- ”You’re pregnant” to a man :-)


What is a type II error?

- False negative

- Saying there isn’t an effect when there is

- ”You’re not pregant” to a pregnant woman :-)


What is NHSTP?

- Null Hypothesis testing procedures

- Black and white thinking -> limitations

- We should take a middle ground, combining NHSTP and effect sizes


What is the point of confidence intervals?

- Can be useful in helping us to estimate the range within which the true population mean (or some other parameter) would fall in most samples

- Typically 95% (p<.05>


What is an effect size?

- A standardized measure of the size of an effect

- Comparable across studies

- Not as reliant on the sample size


What are the effect sizes we’ve learned?

- Pearson's r

- Cohen's d

- R2

- Odds ratio

- Cramer’s V


When and how should we test for normality?

- For all parametric tests

- Using the K-S/Shapiro-Wilks test


When and how should we test for homogeneity of variance?

- Independent t-test

- Independent ANOVA

- Using Levene’s test


When and how should we test for sphericity?

- Dependent ANOVA

- Using Mauchly’s test


What do you usually assume, when assuming normality?

- That the sampling distribution of the parameter (e.g. means, or mean differences for a dependent t-test), or the residuals for regression, are normal in shape

- Not that the distribution of the sample data must be normal


What does the K-S and Shapiro Wilks tests tell you?

- Significant test at p<.05 of normality>

- Non-significant test at p>.05= normality is OK

- We want a non-significant test!


What do you do, if there’s a difference between K-S and Shapiro-Wilks?

- Use shapiro-wilks :-)


What is the central limit theorem?

- As sample size increases, the random sampling distribution tends towards a normal distribution regardless of the shape of the sample data

- The tendency increases as sample size increases

- Can usually be argued with a sample size of >30

       - For independent tests: at least 30 in each group

       - For dependent tests: at least 30 overall!

- Can also be argued if K-S/Shapiro Wilks tests show problems with normality


What if there’s a problem with normality? :-(

- If large sample size, argue to meet normality assumptions on the basis of the central limit theorem

- If not: Use a transformation (consider bootstrapping)

- Or: use a non-parametric test


What is the homogeneity of variance?

- The assumption that the variance in the outcome variable is approximately equal at all levels (groupings) of the independent variable

- If variance is approximately equal for all groups, there is homogeneity of variance

- If variance is not equal across groups, there is heterogeneity of variance, and the assumption is vioalted


When is the homogeniety of variance relevant?

- Independent designs

- For independent t (independent t-tests)

- For F tests (independent ANOVA)


How can we assess homogeneity of variance?

- Using Levene’s test

- Non-significant Levene’s test at p>.05=homogeneity of variance 

- We want a non-significant Levene's test!


What if we violate the assumption of homogeneity?

- For independent t-tests: if Levene’s test is significant, meaning there is heterogeneity of variance, we should report the t-statistic and degrees of freedom from the equal variances NOT assumed row in SPSS output

- For Independent ANOVA: If Levene’s test is significant, meaning there is heterogeneity of variance, report corrected F and df values such as Welch’s F


What is the assumption of Sphericity?

- Similar to the assumption of homogeneity, but for repeated measures designs

- The variances of the differences between groups are expected to be equal


How do you test for sphericity?

- Calculating the differences between each pair of conditions - Calculating the variance of these differences

- Determining if the variances are approximately equal

- (If variance 1=variance 2=variance 3…., the assumption of sphericity is met)


How can we assess sphericity?

- Using Mauchly’s test

- Non-significant Mauchly’s test p>.05=sphericity 

- We want a non-significant Mauchly's test!


What if there’s a violation of sphericity?

- If Mauchly’s test for sphericity is significant at p<.05>you should report your findings from a corrected row in the SPSS output 

(e.g. Greenhouse-Geisser or Huynh-Feldt correction)


Why do assumptions matter?

- Many of the most common statistical tests (parametric tests) are only reliable if these assumptions are satisfied or corrections are made

- If we use uncorrected parametric tests with problematic data, there is a greater risk of drawing inccorect conclusions (type I error, especially)


What has more power? Non-parametric or parametric tests?

Parametric tests!


What are the key factors in determining which test to use?

- Aim of research

- Level of measurement of IV and DV (categorical vs continuous)

- Research design (for group tests - independent vs repeated measures)

- Normality (e.g. K-S tests)

- Sample size (to argue CLM for independent tests: 30 in each group, to argue CLM for dependent tests: at least 30 overall)

- Homogeneity of variance and Sphericity

- Post hoc tests (if ANOVA)


What is correlation?

- Determining how two continuous variables are related

- E.g. what relationship, if any, exists between number of hours spent studying for an exam and exam performance?

- Correlation DOES NOT equal causation :-)


What is the most widely used correlation coefficient?

- Pearson' r

- Ranges from -1 (perfect negative relationship) to +1 (perfect positive relationship


What is Cohen's rule of thumb for Pearson's r?

r>.1 (small effect)

r>.3 (medium effect)

r>.5 (large effect)


What is Cohen's rule of thumb for Cohen's d?

d>0.2 (small effect)

d>0.5 (medium effect)

d>0.8 (large effect)


What is Cohen's rule of thumb for Odds Ratio?

OR 1.49 (small effect)

OR > 3.49 (medium effect)

OR > 9.0 (large effect)


How do you generally report results using APA format?

1: State the type of analysis you conducted

2: state the overall finding in normal words (including mean or Mdn, SD)

3: report the DF and test statistic (F, t etc)

4: report the significance level (p)

5: report effect size (including direction) (fx r, d, OR)