Statistics

Question 1

The Scientific Method

Answer 1

A logical, systematic approach to the solution of a scientific problem

1. Develop theory; observations, literature review, prior research
2. Construct a hypothesis
3. Design a study
4. Analyse data
5. Draw conclusions

Question 2

What is a parameter?

Answer 2

A numerical summary of a population. Such as mean, median, range… of a population

Question 3

What are the types of data?

Answer 3

• Quantitative; numeric i.e. age, height, weight

- Qualitative; descriptive i.e. favourite colour, suburb, type of car

Question 4

What does discrete data include?

Answer 4

Only limited set of values

• Nominal: values where order is arbitrary (i.e. gender, ethnicity, etc), unordered, categorical also known as binary, dichotomous, indicator variable (qualitative)
• Ordinal: scale where ranking matters but are not consistently correlated (i.e. NYHA), ordered categorical (e.g. level of education, high-school, under/post degree) (qualitative OR quantitative)

Question 5

What does continuous data include?

Answer 5

Unlimited values

• Interval: have legit mathematical values (i.e. temperature), numeric scale with consistent differences between points (i.e. standardist IQ) (quantitative)
• Ratio: equal intervals and meaningful zero point (i.e. height, wt, time, length), numeric scale with consistent differences between points and absolute zero (weight in kilos) (quantitative)

Question 6

When does experimental manipulation occur?

Answer 6

Between subjects -> independent groups

- Within subjects/repeated measures: related groups

Question 7

What is measurement error?

Answer 7

An error that occurs when there is a difference between the information desired by the researcher and the information provided by the measurement process

Question 8

What are extraneous and confounding variables?

Answer 8

Extraneous: another variable that is not the IV or DV
Confounding: An extraneous variable that can potentially explain the relationship between the IV and DV
- Example: age reading ability, year of school in children
- IV: age, DV: reading ability, Confound: year of school

Question 9

What is the measurement type of the variables?

Answer 9

Categorical data: discrete categories or groups

• Frequency tables and bar chart / pie chart
• Numeric data: a score on a scale
• Numeric summary statistics (mean/median/mode, standard deviation) and a histogram

Question 10

Consider the following aspects when summarising data:

Answer 10

• Typicality (mean, median and mode)
• Variability (range, IQR, std dev, variance)
• Shape (skew, kurtosis)

Question 11

What features does a normal distribution have?

Answer 11

1. Variability
2. Unimodality
3. Central tendency
4. Symmetrical
5. Mesokurtic

Question 12

What is a z-score?

Answer 12

Z-scores are standardised scores, measuring the difference between a score and the mean, expressed in std dev units
z = score - mean / std dev

Question 13

What is the central limit theorem?

Answer 13

• Distribution of sample means will be approximately normal

- Mean of the sample means will be the same as the population mean

Question 14

What is standard error?

Answer 14

• Standard deviation of sample means = Standard Error

- Standard Error = std dev / square root N

Question 15

What is null hypothesis significance testing?

Answer 15

• Analysing data from a sample, to see whether it can make a contribution to a field of knowledge
• Conservative approach: begin by assuming the null hypothesis is true, then
  test whether we have evidence against that
• Summarise data and compute a test statistic

Question 16

What is the hypothesis testing procedure?

Answer 16

1. Decide on alpha
2. Calculate test statistics
3. Compare obtained with critical statistic
   obtained >= critical -> reject H0
   obtained < critical -> don’t reject H0

Question 17

What are T-tests?

Answer 17

Inspecting mean scores on a numeric variable

T-test = signal-to-nose ratio

Question 18

What are one-sample t-tests?

Answer 18

Average score on variable in the population from which the sample is drawn signficantly different to a known number?
- Is the population’s mean score different to another population?
t = sample mean - test value / SE (sd / root N)

Question 19

What are assumptions?

Answer 19

Conditions that need to be met for the test to be valid

Question 20

What are assumptions of a one-sample t-test?

Answer 20

1. Variable is on a numeric scale (interval or ratio)
2. Variable is normally distributed in the population
3. Observations are independent

Question 21

What are t-statistics?

Answer 21

Is the ratio of signal (difference between means) to noise (variance around the mean)

• The bigger the t-statistics = 1: signal to equivalent to noise
• Null hypothesis significance testing: how likely is it that we obtained this t-statistic if the null hypothesis is true

Question 22

What are independent samples t-test?

Answer 22

• Comparing 2 group means
• Is there a difference between means of 2 (independent) groups?
  t = sample mean of group 1 - sample mean of group 2
  / square root of std dev 1/n1 + stddev2 / n2

Question 23

What are the assumptions of independent-samples t-test?

Answer 23

1. DV is on a numeric scale
2. DV is normally distributed in the population within groups
3. Variance of DV is equal between groups
4. Observations are independent (within and between groups)

Question 24

What are paired t-tests?

Answer 24

Is there a difference in average scores between 2 related groups?
- Same person over 2 time points or 2 conditions
- Related people
- 2 observation (Scores) are non-independent (related)
one numeric DV, one categorical IV

Question 25

What are the assumptions of paired samples t-test?

Answer 25

1. Outcome variable is on a numberic scale 2. Difference scores are normally distributed in the population 3. Observations are related across groups, independent across pairs

Question 26

What is Shaprio-Wilk's test of normality?

Answer 26

- A statistical test of whether the population from which the sample is drawn is normally distributed - Applies to numeric (quantitative) variables only - Use to see if the assumption of normality is met in CONJUNCTION with a graph and/or numeric descriptive statistics

Question 27

What are confidence intervals?

Answer 27

- Display the variability around the point estimate (mean) - Point estimates have a greater precision, interval estimates have greater accuracy - Range of values that estimate an unknown population parameter (95% confidence interval)

Question 28

Example of conclusion for Results section

Answer 28

Results showed that there was a statistically significant increase in the proportion of time that infants spent gazing at the singer of the familiar song, compared to the singer of the unfamiliar song, under the test condition (Mt = 0.59, SDt = 0.18) compared to the baseline condition (Mb = 0.52, SDb = 0.18), t(31) = -2.04, p = .022, which suggests that the infants preferred the familiar song melody.

Question 29

How are effect sizes indicated?

Answer 29

- How big is the difference in means between 2 groups? - How big is the mean difference score? - Many different kinds of effect sizes - Standardised vs unstandardised

Question 30

What is Cohen's D?

Answer 30

One effect size measure of group differences (expressed in SD units) d = mean group 1 - mean group 2 / pooled standard deviation (root sd2^2 + sd2^2) / 2 d >= 0.2 = small effect d >= 0.5 = medium effect d >= 0.8 = large effect

Question 31

What is a correlation?

Answer 31

- Linear (straight line) relationship between 2 numeric variables

Question 32

What is a positive correlation?

Answer 32

An increase in one variable is assoicated with an increase in other variable e.g. number of hours studying and exam perofrmance

Question 33

What is a negative correlation?

Answer 33

An increase in one variable is assoicated with a decrease in the other variable i.e. inverse e.g. greater the number of children, less sleep parents get

Question 34

What is pearson's correlation coefficient?

Answer 34

- Ranges from -1.00 to +1.00 closer to 0, weaker; closer to +/- 1, stronger ― 0 to .10 = very weak-to-no relationship ― .10 to .30 = weak relationship ― .30 to .50 = moderate relationship ― .50 to 1 = strong relationship

Question 35

What are the assumptions of a correlation?

Answer 35

1. Both variables are numeric (and approximately normally distributed) 2. Any relationship is linear (i.e. it’s not non-linear) 3. No substantial outliers or gaps in data 4. Independence of observations

Question 36

Correlations and Scatterplots

Answer 36

1. Is it monotonic? 2. Is it linear? 3. Is it positive or negative? 4. Effect of X on Y? 5. Strength of correlation? 6. Any outliers? 7. Any gaps?

Question 37

How we formulate conclusions

Answer 37

1. Identify the hypothesis (hypotheses) 2. General descriptive statistics (understanding the sample and data collected) 3. Identify variables involved in the hypothesis (what they are and what type they are) 4. Identify the appropriate statistical test for the hypothesis 5. Check the assumptions for the test 6. Run the test and make conclusions

Question 38

How can we validly interpet p-values?

Answer 38

* When the assumptions of the hypothesis test are met * When the hypothesis we test has a valid theoretical basis * When we conduct exactly one hypothesis test on a sample * There is an implicit assumption that only one test is performed * If we have >1 DV this basis fails

Question 39

What is an efficency vs type 1 error?

Answer 39

We need to ‘do something’ about 𝛼 because we have tried to be efficient in our research and test several hypotheses in one study, rather than conducting several independent studies. • This is very efficient but increases the probability of type I error • We counteract this risk by making it tougher to reject H0 • But it goes against the probability basis of hypothesis tests