Research Method + Stats Flashcards
What is a pseudoscience?
a claim/belief that is presented as scientific but doesn’t use the scientific method, lacks empirical evidence and cannot be reliably tested
it is more like advice
What is psychology the science of?
the scientific study of the human mind and behaviour
how we think, feel and act
what challenges does psychology have as a science?
much of what we are interested in is unobservable
there is a question of whether we can really study human behaviour without being subjective
give a brief history of psychology as a science
- Freud - claimed to be scientific but relied heavily on introspection
- Behaviourists - only study things that are directly observable, only focussed on the S –> R
- Cognitive - makes predictions then subjects them to empirical testing, no need for direct observation
- Neuroscience - look inside the human mind and directly observe what’s happening
What is induction?
evidence gathered from multiple observations
however this cannot guarantee that it will happen again in the future
What is falsifiability?
Who came up with the concept?
the need to have the possibility to disprove a theory
if we find supporting evidence, then the theory is upheld as undefeated
Karl Popper
What is a scientific conjuncture?
a scientific question that must be falsifiable
What is Bayesianism?
The idea that beliefs come in degrees
Can express the likelihood of future events based on past knowledge
Provides a measure of a state of knowledge
What are the characteristics of a good scientist?
- Uncertain
- Sceptical
- Open-minded
- Cautious
- Ethical
What are some limitations of science?
You can’t answer questions about:
- Value
- Morality
- The supernatural
What is the hypothetico-deductive method?
- Identify behaviour of interest and generate theory
- Theory is generally derived from inductive reasoning
- Generate a hypothesis from theory - needs to be objective and falsifiable
- Subject hypothesis to empirical testing to gather evidence
- Hypothesis isn’t supported = refine or abandon
- Hypothesis is supported = uphold theory as undefeated with an estimate of confidence
What was the replication crisis?
Who was a key person here?
Methodological crisis where we couldn’t replicate the results of studies
Bem showed that people were being influenced by the prospect of being published in a journal - they were finding significant results when there weren’t any to be found (false positive)
What is a random error?
- Random error – obscures the results (normally averages out)
Longitudinal design: problems and solution
o Problem – its not possible to counterbalance order
o Solution – control group
Cross-sectional design: problems and solutions
o Problem – its not possible to randomly assign ppts
o Solution – matching
What are the types of developmental design?
- Between subjects: “cross-sectional”
- Within subjects: “longitudinal”
What is pre-test post-test control group design?
- split ppts into 2 groups and manipulate the IV in one group only
- The inclusion of a CG allows us to account for any order effects that might be present
- We can then statistically control for the difference in the treatment group accounted for by the order effects
- This is a mixed design – got within and between subjects components
What is Within subjects design without counterbalancing?
- Counterbalancing order that ppts are exposed to levels of IV is not always possible
- E.g., examining the effectiveness of mnemonic training on memory performance
- The order in which ppts are exposed to levels of IV is fixed
o Likely to be differences between time 1 and time 2 other than the variable of interest - Have to be cautious about inferring causality
What is matched pairs?
- Even better than matching the groups on the basis of potentially moderating variables
- Compare individuals from the same background but who are in different levels
- However, this frequently isn’t possible. Also, always the possibility of other variables influencing that haven’t been considered
What is matching?
- Identify potentially moderating variables and match the groups on this basis
- E.g., similar age, similar weight, similar experience etc.
What is Between subjects design without random allocation (quasi-experimental)?
- The assignment of ppts to the experimental conditions is pre-determined
- E.g., comparing pre-existing alcohol consumption groups: alcoholics vs non-alcoholics
- This poses a serious problem as there are likely to be differences between the groups other that the variable of interest
- Have to be cautious about inferring causality
Your choice of subject design depends on?
Concerns –
o Between subjects – eliminates order effects
o Within subjects – eliminates individual differences
Number of ppts available -
o Within subjects designs require fewer ppts
What is a factorial mixed design?
- One IV used between measures
- The other IV uses within measures
- E.g., night shift and then with and without alcohol, day shift and then with and without alcohol
What is a Fully repeated measures factorial design (within subjects)?
- Ppts would complete all levels in the IVs
- Ppts would complete 4 different conditions if two IVs were used
What is a Fully independent factorial design (between subjects)?
- For first IV you assign ppts to one or the other condition
- For the second IV you assign ppts to one or the other condition
- Effectively end up with 4 different groups
What is a factorial design?
- Experimental designs with 2 or more IVs
What is counterbalancing?
- Split the group of ppts in half
- Level 1 then level 2, and level 2 then level 1
- Order effects will still influence the ppts performance, but the effects of that influence will be evenly spread across each level of the IV
What is random allocation?
- Ensure each ppt is equally likely to be assigned to any IV levels
- Distributes the occurrence of potential moderating variables equally among experimental conditions
- Prevents experimenter (un)intentionally biasing their results
- Enables the use of powerful stats tests that can help determine causal relationships between variables
- Could achieve by tossing a coin, pulling straws, pulling names from a hat etc.
What is a within subject design (repeated measures)?
- Ppts exposed to both levels of the IV
- Potentially moderating characteristics are kept equal across levels
- Requires fewer ppts
- Problem of order effects – effects that occur as a result of taking a test more than once (could do better on test because they’ve done it before and know what’s coming or could do worse because they’ve done the test before and are tired of it)
- Can use counterbalancing
What is a between subjects design (independent groups)?
- Ppts are assigned to one level of the IV
- All subjects are inherently different and these differences have the ability to affect the outcome (individual differences)
- Can’t eliminate the effects of these other variables
- But we can minimise the effects by spreading their influences across the different levels of the IV
- Can use random allocation
What is the subjects design?
– the assignment of participants to experimental conditions
What is the dependent variable?
- The variable that is measured
- We compare differences in the DV under the different levels of the IV
What is an independent variable?
- The variable we manipulate
- Each have at least two levels e.g., conditions
What is the experimental method?
- A research design which allows us to make causal inferences about one or more variable of interest
- The researcher manipulates one or more variables and measures the effect on other variables
- All other variables are to be kept constant
What is ratio data?
Give an example
Ratio –
- Highest level of data
- Equal intervals and a true zero point
- E.g., height, distance, time
What is interval data?
Give an example
Interval –
- Intervals between successive values are equal
- But no “true” zero point (no absence of something)
- E.g., temperature, shoe size
What is ordinal data?
Give an example
Ordinal –
- Data can be ranked along a continuum
- Intervals between ranks are not equal
- E.g., race positions, attractiveness
What is nominal data?
Give an example
- Lowest level of measurements
- Category membership
- Numbers assigned serve as labels but do not indicate numerical membership
- E.g., gender, political party, religion
What are the scales of measurement?
- Nominal (category membership)
- Ordinal (ranked/ordered)
- Interval (equal increments but not real 0 point)
- Ratio (equal increments and real 0 point)
True or False
If you operationalize a construct it becomes a variable?
TRUE
What type of definition defines a variable?
An operational definition
What type of definition defines a construct?
A theoretical definition
What is a variable?
- anything that can assume multiple values (can vary)
- An event/condition the researchers observes/measures
- Variables must be operational – explicitly stated
What is a construct?
- A construct is the building block of a theory
- Theoretical concepts formulated to serve as causal/ descriptive explanations
- Don’t directly indicate a means by which they can be measured
Hypotheses make specific predictions and must be:
- Falsifiable
- Testable
- Precisely stated (clearly defined and unambiguous)
- Rational (needs to be consistent with known knowledge)
- Parsimonious (the explanation needs to be the simplest possible)
Theories are a collection of proposals that:
- Define
- Explain
- Organise
- Interrelate
What is a hypothesis?
– a clear but tentative explanation for an observed phenomenon
- it is testable
What is a theory?
– a broad encompassing framework.
Puts a collection of propositions/hypotheses together to explain a set of observed phenomena
What is a fact?
statements that are under no dispute.
Direct observations of phenomena that occur consistently over time
What is methodological triangulation?
The convergence of findings of methodologically varying studies which can lend acceptance to a theory pattern.
What is methodological pluralism?
The use of multiple methods
What are the quantitative research approaches?
Descriptive – describe a behaviour
Relational – predict a behaviour based on its relationship with another behaviour
Experimental – allows us to determine the cause of a behaviour
What are some criticisms of qualitative research?
- can’t apply notions of reliability or validity,
- can’t generalise to other members of the population
What is qualitative research?
- descriptive, often text-based,
- not experimental (inductive approach) but still empirical,
- focuses on underlying meaning of behaviours,
- typically small samples,
- asks more open-ended questions and so allows for unexpected answers.
What are some criticisms of quantitative research?
- humans are complex so this would be oversimplifying things,
- fails to recognise the subjective nature of research with humans,
- doesn’t look in depth at differences between individuals (focuses on averages and views population as homogenous)
What is quantitative research?
- collection of numerical data,
- subscribes to hypothetico-deductive approach,
- takes place in controlled settings,
- focuses on describing, predicting and identifying causes of behaviours,
- typically uses large samples,
- focus on structured methods
What are the goals of Psychology?
- describe behaviour
- predict behaviour
- explain behaviour
- control behaviour
What is the role of teaching in Open Science?
Teaching open science – need to teach its principles and promoting the methodological practices.
Advantages – promotes best practice, increases critical evaluation research
What are the types of replication research?
Direct replication – reproduce the elements that produced the original findings (are similar findings produced in subsequent attempts?)
Conceptual replications – change at least one aspect of the original procedure e.g., changing the sample (assess whether similar findings are produced under different conditions?)
What role does replication research have in Open Science?
Replication research – process of repeating research to verify findings
Enables confidence in results and helps build theories
What is exploratory research?
Exploratory research – focuses on generating hypotheses/research questions
What is confirmatory research?
Confirmatory research – focuses on confirming hypotheses/research question
What role does preregistration have in Open science?
Preregistration – researchers encouraged to submit plans for specific research questions and analyses they will conduct prior to data collection (transparency), reduces risk of false positives.
Promotes confirmatory research
What role does reproducible analyses have in Open Science?
- need to provide materials to enable others to generate the exact same results as those reported.
- need adequate documentation to be kept in order to do this
- Good principles: clear annotations of what documents are, store original data files separately, record all steps of data processing, use open-source software
What role does APA have in Open Science?
- APA requires researches to make data available with editors for 5 years after publication - verification, analytic reproducibility
What is the benefit of research needing public access?
- Research needs public access - allows for accumulation of knowledge, increased citation of work, more media coverage, supports meta research practice
What is Open Science?
A set of practices used to overcome limitations of previous scientific research.
Concerned with reproducibility and replicability
Research practices and data needs to be transparent and accessible
What is exploratory research?
Exploratory research – focuses on generating hypotheses/research questions
What are the sources of confounding variables?
- Selection – bias resulting from the selection/assignment of ppts to the different levels of the IV
- Results in ppts who are assigned to different levels of the IV differ systematically in some way that could influence the measurement of the DV- Particular problem for quasi-experimental designs
- History – uncontrolled events that take place between testing conditions
- Maturation – intrinsic changes in the characteristics of ppts between different test occasions
- Instrumentation – changes in the sensitivity/ reliability of measurement instruments during the course of the study
Confounds can result in us measuring:
- An effect of the IV on the DV when it is not present
- No effect of the IV on the DV when it is present
How can we eliminate confounding variables?
o Random allocation/counterbalancing spreads the influence of extraneous variables (so that they do not become confounding variables
What type of validity does confounding variables threaten?
Internal validity
What is a confounding variable?
- Extraneous variables that disproportionately affect one level of the IV more than other levels
- Add constant/systematic error at the level of the IV
How can we eliminate extraneous variables?
o Use random allocation or counterbalancing
o Results in an even addition of error variance across levels of the IV
What is an extraneous variable?
- Undesirable variables that add error to our experiments – add error to the measurement of the DV
What is a constant error?
- Constant errors – bias the results (more problematic)
What are the sources of confounding variables?
- Selection – bias resulting from the selection/assignment of ppts to the different levels of the IV
o Results in ppts who are assigned to different levels of the IV differ systematically in some way that could influence the measurement of the DV
o Particular problem for quasi-experimental designs - History – uncontrolled events that take place between testing conditions
- Maturation – intrinsic changes in the characteristics of ppts between different test occasions
- Instrumentation – changes in the sensitivity/ reliability of measurement instruments during the course of the study
What are the sources of confounding variables?
- Selection – bias resulting from the selection/assignment of ppts to the different levels of the IV
o Results in ppts who are assigned to different levels of the IV differ systematically in some way that could influence the measurement of the DV
o Particular problem for quasi-experimental designs - History – uncontrolled events that take place between testing conditions
- Maturation – intrinsic changes in the characteristics of ppts between different test occasions
- Instrumentation – changes in the sensitivity/ reliability of measurement instruments during the course of the study
What are the sources of confounding variables?
- Selection – bias resulting from the selection/assignment of ppts to the different levels of the IV
o Results in ppts who are assigned to different levels of the IV differ systematically in some way that could influence the measurement of the DV
o Particular problem for quasi-experimental designs - History – uncontrolled events that take place between testing conditions
- Maturation – intrinsic changes in the characteristics of ppts between different test occasions
- Instrumentation – changes in the sensitivity/ reliability of measurement instruments during the course of the study
What is external validity?
The ability to generalise our results
Why do we gather data from samples?
To infer population parameters
What is snowball sampling?
- Recruit small number of ppts and then use those initial contacts to recruit further ppts
- Biases the sample, but useful if you want to recruit very specific populations
What is an opportunity/convenience sample?
- People who are easily available
- But can lead to a biased sample
What is a cluster sample?
- Researcher samples an entire group/cluster from the population of interest
- Need to be cautious about generalising results – cluster unlikely to be representative of the entire population
What is a stratified sample?
- Proportional: specified groups appear in numbers proportional to their size in the populations
- Disproportional: specified groups which are not equally represented in the population, are selected in equal proportions
What is a systematic sample?
- Draw from the population at fixed intervals
- Problematic in populations with periodic function
What is a random sample?
- gold standard
- Each member of the population has an equal chance of being selected
- Usually quasi-random e.g., because we don’t have access to everyone in a population
Why do we sample?
- Time – difficult to collect data from everyone quickly
- Money – expensive to collect data from everyone
- Access – not possible to reach all members of a population
- Sufficiency – pattern of results doesn’t change much even if we have data from everyone
What is a sample?
– a subset of individuals from the larger population
- For any population, there are many possible samples
- Vary in size
- Defined by sample statistics e.g., measurements which describe the sample
- Sample statistics are used the infer population parameters
What is a population?
– the entire collections of things that we are interested in
- Defined by population parameters e.g., measurements which describe the population
- Vary in size
What is multifactorial causation?
– phenomenon is determined by many interacting factors
Why is it hard to determine true causation?
human behaviour is very complex and it is usually impossible to control for all other factors – because its usually impossible to identify them all
What is true causation?
Need to satisfy necessary and sufficient criteria in order to make true claims about causality:
- Sufficient – y is adequate to cause x
- Necessary – y must be present to cause x
True causation can only be established when necessity and sufficiency criteria are satisfied
What can construct validity be assessed in terms of?
- Convergent validity – correlates with tests of the same and related constructs
- Discriminant validity – doesn’t correlate with tests of difference or unrelated constructs
What is construct validity?
– is the construct we are trying to measure valid?
o E.g., does the construct itself exist?
o The validity of a construct is supported by cumulative research evidence that is collected over time – together, supporting the existence of the construct itself
What is criterion validity?
– does the measure give results which are in agreement with other measures of the same thing?
o Concurrent: comparison of new test with established test
o Predictive: does the test predict outcome on another variable
What is face validity?
– does it looked like a good test?
What is content validity?
does our test measure the construct fully?
What is internal consistency?
- determines whether all items are measuring the same construct
o E.g., split-half reliability: questionnaire items split into two groups and the halves are administered to ppts on separate occasions
o Beware of order effects – e.g., if they have answered similar questions before
What is parallel form of reliability?
– if we administer different versions of our measures to the same ppts, would we obtain the same results
o Different versions can be useful to help eliminate memory effects as the questions are different
o Beware of order effects – might still improve because they’ve had experience of a similar test
o Fatigue effects – might be fatigued the second time around if same ppts are used
What is inter-rater reliability?
– measures fluctuations between observers
What is test-retest reliability?
– measure fluctuations from one time to another
o Important for constructs which we expect to be stable (e.g., personality type)
o Beware of order effects
What is validity?
= accuracy (truthfulness)
- The extent to which it is measuring the construct we are interested in
What is reliability?
= consistency (precision)
- The extent to which our measure would provide the same results under the same conditions
What is reactivity?
- Awareness that they are being observed may alter behaviour
- Can threaten internal validity if ppts are more influenced by reactivity at one level of the IV than the other
- Resulting artefacts can be: subject based (demand characteristics), experimenter related (experimenter bias)
- Counter reactivity by using blind procedures (either single or double)
What is population validity?
is our sample representative?
What is bimodal data?
Data that has two modes
What is the danger of non-normal data?
- Danger – mean is distorted by the tails which are the more extreme values
What is non-normal data?
- Has a tail either to the right or left – skewed data
- Positively skewed = long tail to the right, peaks at the left
- Negatively skewed = long tail to left, peaks at the right
- E.g., reaction time – tends to be positively skewed
What is normally distributed data?
- Many naturally occurring variables are Normal
- E.g., height, IQ (not naturally occurring but has been defined as this)
- If we don’t have much data then the normality can be difficult to see in a histogram
- As sample size increases, the normality will emerge
What is distribution of data?
the manner in which data for a particular variable is spread over its range is commonly referred to a its distribution
What is a data summary plot?
- Plot bar showing mean (categorical data) or line graph (numerical data)
- Plot error bars showing +/- 1s.d.
What is a scatter plot?
shows the relationship between variables
What is a box plot?
Seems to be plotted vertically instead of horizontal?
What is a histogram?
- Good way to inspect data o Can see if there’s any odd-looking scores o Can see the mode o Can see how spread out the scores are o Can see how the data is distributed
How to calculate sample standard deviation?
o Calc mean o Calc deviations o Square deviations o Calc sample variance o Take square root of sample variance – now back in comprehendible units
What is the issue with simple variance?
potential issue is the units used, so if deviations are in hours, when squared the units would become hours squared which isn’t comprehendible
How to calculate simple variance?
o Calc mean
o Calc deviations
o Square deviations
o Calc a slightly adjusted average squared deviation
- You divide by n-1What is a deviation?
o The signed distance of a score from the mean
What is the range?
o Difference between min and max scores
o Range doesn’t always change for distributions with different shapes
What is the mode?
o Easy to calculate from a histogram and easy to understand – the most common value
o Data might have more than 1 mode or no mode at all
What is the median?
o Is insensitive to extreme scores in the data set
o Doesn’t reflect the shape of the scores e.g., doesn’t care how far away the extreme scores are
What is the mean?
o Provides and estimate of the average score in the data set
o Is affected by extreme data points
What are measures of central tendency?
They provide an indication of a “typical” score in the data set
Why is it important to summarise data?
- Data can be very complex and therefore it is useful to summarise it
- Allows for interpretation
What is a sample statistic?
– a quantity that describes some characteristic of a sample with respect to a specific variable
- E.g., sample mean, sample range etc.
- We can always calculate these from a sample
- Sample statistics provide an estimate of population parameters
What is a population parameter?
- a quantity that describes some characteristic of a population with respect to a specific variable
- E.g., population mean, population range etc.
- Not usually possible to calculate
- Might be given to you if available
Factors in deciding sample size?
o Design
o Response rate
o Heterogeneity of population
What is important to consider when looking at sample size?
- Size matters
- Sampling error can result if your ample is not large enough
- Trade off between size and time/cost
What is ecological validity?
does the behaviour measured reflect naturally occurring behaviour?
What is a SND table and how do you use it?
- Table that provides values of areas underneath the SND in different ranges
- Find z-score (first column) then decide if you want the area above or below this score
- If z-score is negative, use the positive value in the table but be careful when choosing above or below because the scores will be flipped
o E.g., z-score = -2 and you want the area below. On table you will use z-score 2 but use the area above - If you have a range that is bounded e.g., 70
How do you obtain a z-score?
- Obtained by subtracting the population mean from x and then dividing by the population SD – (x-µ)/σ
What is a z-score?
- Z measures how far away your sample is from the population mean in multiples of the SD
- If you were to find z-scores for all points on a normal distribution, you would find that it would form a normal distribution with mean 0 and SD 1 – N (0, 1)
- The area underneath a normal distribution above/below some variable value of x EQUALS the area underneath N (0, 1) above/below z
What is conditional probability?
- Probability of an event given that something else is known/assumed e.g., A|B
What is probability?
– a measure of how likely it is that an uncertain event will occur
What is the normal distribution?
- Bell-shaped
- Symmetric about the centre
- Tails never reach 0 – go towards infinity
- The area under the centre is always equal to 1
- Very close to 0 by the time it gets to 3 SD from the mean – can use this to draw a rough idea of a normal distribution
What is the danger of bimodal data?
- Danger – mean is not representative
- Tends to suggest an issue with your experiment – more than one underlying population
How do you find a z-score for a SDM?
z-score = (x-µ)/(σ/√N)
What is central limit theorem?
- Given a population with a mean and SD, the sampling distribution of the mean approaches a normal distribution with a mean and SD sigma/ square root N as N increases
- This is true regardless of the underlying distribution – so even if your population is not normal, the distribution of means sampled from it will be
What is SDM a distribution of?
SDM is a distribution of sample means for samples of size N drawn at random from the parent population
What is a parent population a distribution of?
Parent population is a distribution of individual scores x (e.g., from an individual person or thing)
What are the properties of the sampling distribution of the mean (SDM)?
- Mean which is the same as the parent population
- SD is different to that of the parent population – find by calculating σ (of p pop)/√N (sample size)
- SD is called the standard error of the mean (s.e.m.) or standard error (s.e.)
- S.e.m. must be smaller than SD of the parent population because you are diving by something that is bigger than one
What does the sampling distribution tell us?
- Tells us important info about how a statistic changes from sample to sample
- What is the mean value of the statistic over all samples?
- How variable is the statistic over all samples?
- What shape is the distribution of the statistic over all samples?
How do we generate a sampling distribution?
- Take a sample (size N) from a population
- Calculate a sample statistic (e.g., mean, SD etc.)
- Add the new statistic to a frequency plot (a histogram) of the sample statistic
- Repeated the above 3 steps multiple times
What does the magnitude of a sampling error depend on?
The sample size
- Bigger sample = big sampling error less likely
- Smaller sample = big sampling error more likely
Why do sampling errors occur?
- It occurs because in our sample we don’t have all the members of the population
What is a sampling error?
Sampling error – the error associated with examining statistics calculated from a sample rather than the population
True or False, if centred on sample mean, there is a 5% chance that the population mean falls outside of this range and vice versa (for a 95% confidence interval)?
TRUE
True or False, if centred on sample mean, there is a 95% chance that the population mean is also in the range and vice versa (if looking for a 95% confidence interval)?
TRUE
What does a 95% confidence interval mean?
A 95% confidence level means that if we repeated our sampling many times and worked out a new CI each time centred on our new sample mean we would expect the population mean to be in the interval on 95% of those repeats
For a sample drawn at random from a normal population N (µ, σ) with known s.d. σ ,the 95% CI for the population mean is centred on the sample mean m and goes from?
m – (1.96 x σ√N) to m + (1.96 x σ√N)
What is a confidence interval?
– describes an interval (e.g., a range) of values for our population parameter, together with a specified level of confidence that the parameter is in that range
What is an interval estimate?
– a range of possible values of a population parameter e.g., confidence interval
What is a point estimate?
– a single value estimate of a population parameter e.g., sample mean
What is the p-value?
p-value = the conditional probability associated with your sample statistic
What is the value of α in stats?
α = 0.05
What do values of p < α suggest?
suggest inconsistent with H0: reject the null
What do values of p > α suggest?
suggest not inconsistent with H0: fail to reject null
True or false, If we fail to reject the null (H0) then we can claim to have evidence for the null hypothesis?
False
True or false, If we were able to reject the null (H0) in favour of the research hypothesis (H1) then we can claim to have evidence for the research hypothesis?
True
What are the steps for null hypothesis testing?
- Formulate research hypothesis o Null hypothesis (H0) o Research hypothesis (H1) - Collect data - Evaluate inconsistency with H0 and data o How inconsistent are the data with H0? - Reject or fail to reject H0? - Interpret in context
What do values of p > α suggest?
suggest not inconsistent with H0: fail to reject null
How do you conduct a z-test?
- Use NHST framework
- Calculate inconsistency with mean by calculating the z-score, use the table to find the associated p-value and compare this to 0.05 to decide whether to reject or fail to reject the null hypothesis
When is a z-test used?
- To check if a sample mean that has been obtained is different from some population mean
What is a 1 tailed hypothesis that is right hand tailed?
- Something is better than the population
- H1: sample mean > population mean
- Looking for p-value above score
What is a 1 tailed hypothesis that is left hand tailed?
- Something is worse than the population
- H1: sample mean < population mean
- Looking for p-value below score
What is a two tailed hypothesis?
- Something is different than the population
- H1: sample mean =/= to population mean
- Looking for p value above and below score – have sample mean and then also find another value the same distance away from the population mean but on the other side. E.g., population mean = 67.5, sample mean = 70.7, the difference is 3.2 so the other value you should consider is 64.3 (z-score will be the same for the two)
- Conditional probability = 2 x p-value
When can you formulate a 1 tailed hypothesis?
- There is previous research
- You can predict the effect
What is a type I error? Why does it occur?
- Rejecting the null hypothesis when it was correct – occur due to sampling error
What is a type II error? Why does it occur?
- Failing to reject the null hypothesis when it was incorrect
- Arise due to a number of reasons such as a biased sample, an error in the experimental task, sample size was too small etc.
Why do we use α = 0.05?
- It is small so it is difficult to reject the null hypothesis but not so small that it is impossible to do so
- It is a compromise between type I and type II errors
How is a student’s t distribution similar to SND?
- Bell-shaped, symmetric, uni-modal
How is a student’s t distribution different to SND?
- Has a lower peak, higher tails, have more variance
When is a student’s t distribution used?
- When population s.d. is unknown
Does student’s t distribution include a variety of t tests?
yes
How do you find the t statistic?
T(m) = (m-µ) / (s/√N)
How do you find the estimated standard error?
(s/√N) – estimated standard error
When using t distribution table, what value should you use for v?
When using t table – t (v = N-1) – subtract 1 off of sample size
How do you find confidence intervals when population s.d. is unknown?
- For 95% of repeat sample mean m would be within:
o Some number c e.s.e.’s of µ
o (µ- (c x s/√N) to µ+ (c x s/√N)) - To find c:
o Find t value for 0.025% in one tail (or 0.05% for 2 tails)
How do you conduct a 1 sample t test?
- Same as a z test except:
- Work out e.s.e.
- Find t statistic
- Find if t stat is inconsistent with critical value for corresponding t(n) and significance level
- Reject or fail to reject H0
- Interpret in context
When do you use a 1 sample t test?
- Use to test whether sample mean you have is different from some given or hypothetical population mean
