Inferential Statistics: Mann Whitney, Wilcoxon, Si
- Mann Whitney:(ORDINAL/INTERVAL, INDEPENDENT MEASURES) a test to see if there is a significant difference between 2 sets of data which produces a calculated value of U. If the calculated/observed value is equal to or less than the critical value, then the difference between the two sets of scores is significant. - Wilcoxon: (ORDINAL/INTERVAL, REPEATED MEASURES)a test to see if there is a significant difference between 2 sets of data which produces a calculated value of T. N = number of participants who did not have the same score. If the calculated/observed value is equal to or less than the critical value, then the difference between the two sets of scores is significant. - Binomial Sign: (NOMINAL, REPEATED MEASURES) a test to see if there is a significant difference between two sets of data that produces a calculated value of S. N= number of participants who did not have the same score. If the calculated/observed value is less than or equal to the critical value, then the difference between the two sets of data is significant. - Chi-square:(NOMINAL, INDEPENDENT MEASURES) a test of association which produces a calculated/observed value of X squared. DF (degrees of freedom) calculated using number of rows in a table minus 1 x number of columns minus 1. If calculated value is equal to or higher than the critical value, then the association is significant.
Inferential Statistics: Criteria for using paramet
· Criteria for using a parametric test: To use appropriate parametric tests of difference or correlation the data has to meet the criteria for using a parametric test. These are that: the data must be interval or ratio, the data must have a curve of normal distribution and the variances should be similar.
· Criteria for using a specific non-parametric inferential test (Mann Whitney U test, Wilcoxon signed ranks test, Chi-square, Binomial sign test and Spearman’s rho)
Inferential Statistics: Using Statistical Tables o
· Using statistical tables of critical values
- To find out if results are significant statistical tests are used to analyse the data according to formulae. Once the formula is used the final result is the calculated value which is then compared to a critical value to see if it is significant.
- The factors which impact the critical values are the significance level set, the sample size and sometimes if the research is investigating a 1 or 2 tailed hypothesis.
Inferential Statistics: Probability and Significan
- This is the likelihood of something happening, researchers would want to have an idea of what they will accept as the probability of the independent variable influencing the dependent variable.
· Significance levels
- This is the level at which researchers will reject the null hypothesis and accept the alternate. In psychology the accepted percentage of probability of the IV having affected the DV is 95% and the percentage of it being due to chance is 5%.
Type One vs. Type Two Errors
· Type 1 errors (FALSE POSITIVE)
- When the alternate hypothesis is accepted and the null hypothesis is rejected when it should have been accepted.
· Type 2 errors (FALSE NEGATIVE)
- When the alternate hypothesis is rejected and the null hypothesis is accepted when it should have been rejected.
Mathematical Symbol Meanings
- = (equal to)
- < (less than)
- << (a lot less than)
- >> (a lot greater than)
- > (greater than)
- ∝ (proportional to)
- ~ (approximately)
Methodological Issues: Reliability
Reliability: Reliability is the consistency of research or findings or whether test can be used more than once and produce consistent results Internal: Refers to the consistency of results of a test across items within that test e.g. do participants score similarly on two different memory tests in the same study. External: Refers to the extent to which a test score varies from one time to another e.g. do participants who score well in the first study score well in a later study. Inter-rater: This is established so that different observers consistently rate or observe the same behaviour in the same way Test-retest: Used to test external validity as if the procedure is standardised it will be replicable. The same results on a retest as on an original test show external reliability. Split-half: Used to test internal reliability. If the first half of a test receives the same level of scores as the second half of the test it would prove the test to be reliable.
Methodological Issues: Generalisability
- There are a number of factors that limit the generalisability of findings from a sample: gender bias, age bias and culture bias. If there is bias in the study, then the ability to generalise the results to the target population is limited so the results lack generalisability. Results are affected by generalisability not samples.
Methodological Issues: Representativeness
- A sample should be representative of the target population that it is drawn from. If a sample is representative, it allows the findings to be generalised. It is extremely difficult to select a representative sample meaning that researchers have to be careful about applying the study to a broader population. Samples are affected by representativeness not results.
Raw Data and Recording
· Design of raw data recording tables
- Raw data is the data psychologists collect from each participant. To record the data researchers, use raw data recording tables the type of data suggests the best type of recording table e.g. for nominal data usually tally charts are used to show how often a behaviour is shown. Each table should have clear labels and participants are usually identified by letters or numbers to keep the data confidential.
· Use of raw data recording tables
- The tables are used to get an overview of the data and to identify any anomalies so that the appropriate measure of central tendency can be used.
Inferential Statistics: Normal vs. Skewed Distribu
· Normal distribution curves: Data from a representative sample of the target population will tend to fall into the curve of normal distribution. This is where all measures of central tendency occur at the highest point in the curve and 50% of the data lies on the left of the highest point and 50% of the data lies on the right of the highest point.
· Skewed distribution curves.:The distribution curve representing data from a skewed or unusual data set then the result would be a skewed distribution curve. The mean would be different from the mode and there would be more or fewer low scores or high scores. A negative skew is a skew to the left. Meaning that there are fewer people at the lower end and more at the higher end of the scores. The mean and median are not the same, the mean is less than the mode (the most frequent score was high). A positive skew is a skew to the right. Meaning that there are fewer people at the higher end and more at the lower end of the scores. The mean is higher than the mode (the most frequent score was low).
Qualitative vs. Quantatitve
· Quantitative data
- This is numerical data an advantage of this is that using numbers to measure variables is that it allows for easy comparisons to be made between participants as well as summarising it using averages or percentages. It is easier to establish the reliability of results when quantitative data are collected as they are replicable. However, it can lack ecological validity as everyday responses aren’t usually numerical.
· Qualitative data
- This is non numerical data and usually consists of descriptions in words of what was observed or what a participant is feeling. This data tells us more about the experiences of subjects in the study and can be used in reports of interviews, responses to open questions and participants reports of what happened in the study. The advantage of it is that it gives rich detailed data and is more valid but it is harder to make comparisons between participants or to summarise the data.
Levels of data (NOIR)
- Nominal level data: Simple categories of behaviour and how often they occur: One problem with this type of behaviour is that it doesn’t tell us how many times one participant shows the behaviours or if behaviours are repeated by individual participants. - Ordinal level data: Records the behaviour for each participant individually and shows which participant did which behaviour and indicates the position of a participant in a group allowing psychologists to rank participants based on their performance. A problem with this type of data is that the gap between the rating points is not fixed or equal so it is usually non-numerical e.g. levels of happiness - Interval level data:has equal intervals so gives order as well as showing how much difference there is between the highest scoring participant and lowest scoring participant (e.g. seconds to measure how quickly a task was done etc.) This type of data is detailed and gives the most differences about the participant’s behaviour of the other three types but the problem with this type of data is that the measurements do not have a true zero. If the measurements have a true zero, then they are considered ratio data e.g. height and weight.
Standard&Decimal Form, Significant Figures and Mak
Standard form: a mathematical shorthand used when dealing with very big or very small numbers e.g. 200000 = 2 x 10 to the power of 5.
Decimal Form:the normal way of presenting behaviour e.g 3.5, 3.05 and 3.005 are all in decimal form but with a different number of decimal places.
Significant figures: When a number has a lot of decimal places it is shortened to a significant figure, in psychology 3 is usually the max. number of significant figures e.g. 3.141519 becomes 3.142 to 4 significant figures and 3.14 to 3 significant figures) Make estimations from data collected: Psychologists are more interested in statistical analysis than estimating from data but it could be that looking at a set of data psychologists might want to estimate a mean if they didn’t have individual scores.
Primary vs. Secondary
· Primary data
- This is the data gathered directly from the participants e.g. observations, test results and answers on a questionnaire. An advantage of this is that it specifically informs the research making it more valid.
· Secondary data
- This is when psychologists can’t actually carry out the research themselves and have to use pre collected data e.g. hospital information on admissions, advantages are that data is usually collected over a period of term so trends can be analysed. However, there is no certainty that the data was collected in a valid or reliable way.
Descriptive Statistics: Why Psychologists use it
· Psychologists use statistics to summarise the data, this is where psychologists can calculate information such as the averages to summarise the data so that they can make comparisons between the groups’ scores to see if they support the researcher’s prediction.
- Ratios=A way of expressing proportions.
- Frequency tables (tally chart)=A simple way of presenting data.
- Line graph = Useful for showing behaviour over time.
- Pie charts=Help to show each behaviour as a proportion of total.
- Bar charts=Useful and meaningful way of presenting data from an experiment to see if the data appear to support the alternative hypothesis or not.
- Histograms=Can only be used if the data are continuous.
Presenting Correlational Data
· Scatter diagrams
- Drawn to represent a correlation that depict the direction of the correlation (positive/negative) and the strength of the correlation (strong/weak).
- Positive correlation = right to left on the scatter diagram, negative correlation = left to right on the scatter diagram. The closer the scores are to falling in a straight line the stronger the correlation is and the more spread out the scores the weaker of the correlation. Also shows the anomalies showing if the relationship has exceptions to the general trend.
- Proportionality means that a correlation has a linear property e.g. as one variable increases by a certain amount the other variable increases by the same proportion. Inverse proportionality is when one variable doubles, the other variables halves.
Descriptive Statistics: Measures of Dispersion (RV
· Measures of dispersion: These show how widely dispersed or spread out the scores are.
- The range = lowest score subtracted from the highest score and then add one.
- Variance = how much a set of numbers is spread out, a variance of 0 indicates that all values are identical, a small variance indicates that the scores a very close to the mean and a high variance indicates that the data are spread out and away from each other. To calculate the variance, you work out the mean, subtract the mean from each participant’s score and then square the results and then work out the mean of the squares.
- Standard deviation = the square root of the variance. It can tell us much more about detailed information about how spread out the data is around the mean, median and mode.
Descriptive Statistics: Measures of Central Tenden
· Measures of central tendency:These show the middle point or most frequent number. They tell us about the average participant in any data set but they can be influenced by anomalous data.
- The mean = adding up all scores and dividing by the number of scores. By comparing mean scores researchers can see that the results give evidence for their initial predictions. When measuring things like time, weight or height then the mean average is the best and most accurate measure of central tendency. The problem with mean is that anomalies can skew the final figure.
- The median = central point of a set of scores by putting all the scores in size order and finding the central point. This is used when measuring in whole numbers.
- The mode = the most frequently occurring number in the set. This is only useful when scores are repeated and not where all items are different in the set. It can also measure qualitative data unlike the mode or median.
Methodological Issues: Validity
-Validity:This is how accurate a piece of research or test is at measuring what it aims to measure. -Internal:When the IV is what is having an effect on the DV rather than any extraneous variables. -Face:This is how good the research looks to be testing what it is meant to be testing. -Construct:This is where a study measures all aspects of the behaviour it sets out to measure. The results of the test should be able to be correlated with other tests of the same construct. -Concurrent:This is where a test or piece of research gives the same results as a previous study then the study would have high concurrent validity. -Criterion:This refers to how much one measure predicts the value of another measure (can include concurrent validity). The test/research can predict certain behaviours e.g. IQ testing success in education. -External:The extent that the results of the research can be generalised to other settings beyond the study. -Population:How accurately the test or study measures behaviour in the general population (effected by gender bias, age bias and culture bias) -Ecological:How lifelike a piece of research is, it considers the method used and if the task given to the participant is like that which would be met in real life. Low ecological validity can limit the usefulness of the research.
Methodological Issues: Social Desirability vs. Dem
· Social Desirability
- This is shown by participants who want to present to image of being a good member of society e.g. behaving in the way society wants. This would not reflect true behaviour so would lower validity.
· Demand Characteristics
- When participants behave in a way that they think the researcher would want them to act, this can often happen if the participant guesses the aim of the research because it is obvious or they are taking part in a repeated measures design. If demand characteristics are displayed, it can reduce the validity as behaviour shown may be artificial.
Methodological Issues: Researcher/Observer Bias
· Researcher/observer bias
- This is where the researcher/observer show bias when collecting and when analysing their data. If an observer wants to see a particular behaviour, they may pay closer attention to it. In some situations, it would be easier in some situations to gain objective data e.g. if the researcher wasn’t aware what the participant had been exposed to.
- Inter-rater reliability avoids this bias as it ensures that all observers are noting things consistently but it doesn’t eliminate the bias being present in all observers.
- Once the data is gathered this bias may be imposed on the interpretation of the data (less likely with quantitative data).
Methodological Issues: Researcher/Observer Effects
· Researcher/observer effects
- This is where the participants can be influenced by the researcher’s presence either because of the awareness of being watched or the characteristics of the researcher watching you. This may reduce the validity of the research as the results may not accurately reflect your true behaviour.
Methodological Issues: Ethics (RESPECT)
- Respect (informed consent, right to withdraw, confidentiality)
- Considers the necessity for gaining consent from participants, allowing participants to withdraw from situations they find distressing and maintaining confidentiality.
Informed consent = Consent should be gained from all participants and informed as far as possible as to the nature of the research. If children are taking part consent must be gained by a parent or in loco parentis by teachers but even then the right of the child not to take part must be considered.
Right to withdraw = Participants must have the right to withdraw from the study. At the end of the research a participant must be allowed to withdraw their data if they want to.
Confidentiality = the right to data being kept entirely confidential and not identifiable by any means.
Methodological Issues: Ethics (COMPETENCE)
- The need for psychologists to work with their capabilities not giving advice to participants if not qualified to do so and to check their research with their peers.
Methodological Issues: Ethics (RESPONSIBILITY)
- Responsibility (protection of participant, debrief)
- The need to protect participants and to ensure that participants are fully debriefed.
Protection of participants = The participants should be protected from all physical and psychological harm.
Debrief = The participant should leave the research the same as when they arrived so any deception should be removed and they should be told the aim of the study. They are again given the right to withdraw, assured of confidentiality and can ask any questions.
Methodological Issues: Ethics (INTEGRITY)
- Integrity (deception)
- There should be high standards regarding honesty, accuracy, clarity and fairness when carrying out research and avoid deception wherever possible.
Deception = Deception should be kept to a minimum and participants should be made aware of the nature of the study as soon as possible.