Experimental design, types of data, sampling, displaying data: histograms

Within and between subjects designs

-          When we deisgn an experiment, we must decide whether to use a within subjects design, or a between subjects design.

      Between subjects: Participants only take part in one condition of the study and the results are compared between the two groups.

      Wuthin subjects: Particoants take part in both conditions over consecutive days and the results are compared between each other.

-          More participants needs with BS design to get enough power for meaningful stats

-          Differences in performance may be due to group difference and not related to the IV (randomisation, baseline differences)

-          There may be a problem in interpreting your results if the 2 groups are treated ‘differently’. The first group may react differently.

Order effects: practice learning effects, boredom and fatigue.

Counter-balancing: Assign half of group to condition A and half to condition B.This was practice/fatigue effects will be 'cancelled out' and can be assessed statistically if recorded.

-          ‘sample’ – individuals participating in your study

-          ‘Population’ – the wider groups about which you wish to learn

-          Important for external validity

-          If sample is not ‘representative’ from the population – cannot generalise.

Example:

-          Attitudes of Irish people to have sex before marriage

-          A sample of women from a Catholic church would not be representative of the population.

Example:

-          University student sample – are they representative of the population of the UK? No, age, economic status etc differ from the population.

Methods to select a study population (sample) that approximates a specific larger population that you aim to make inferences about.

Probability sampling: using methods to ensure that sample is representative of the population we want to infer about.

Random: Sample is not structured to approx population.

Statified random sampling: select sample that matches important population charaterisitics.

Quota sampling - A sampling method of gathering representative data from a group.

Non-probability sampling: more widely used. Based on convenience. External validity may be reduced.

Opportunity sampling: The 'take whoever comes along' approach. Certain topics will attract certain people. Volunteers more likely to be: female, higher educated, high SES, higher intelligence, more curious.

Studies yield results or data

-          Data are usually number/category counts – quantitative

-          Some words, interpretation – Qualitative

-          Appropriate analysis techniques (e.g stats) depend on study design and data characteristics

Quantitative data (measurement data): data obtained by assigning numbers to events or objects in a systematic way (measurement)

Categorical data:

-          Unordered (nomial) versus ordered (ordinal)

-          E.g. counts or numbers of observations in each of a number of categories

Degree

Male

Female

Psychology

31

74

Maths

268

71

Law

24

27

Quant data – levels of measurement

Categorical (discrete values)

     Nominal

-          The use of number as names for the category that an object or event belongs to.

-          E.g., in a studt, we may decide to label females as 1, and males as 2

-          These number have nothing to do with the object itself; boys are not twice the value of girls, footballers number 2 is not half as good as number 4.

-          Numbers are used only to distinguish between objects where all we know if that they are different

Ordinal

-          The size of the number does represent something about the quantity of whatever is being measured.

-          However, neither the size of the difference between numbers, nor the ratio of the number, is informative.

-          Number used only to place objects in order.

-          E.g, the ranking of degree results: a first is ‘better’ than a third, but it is impossible to quantify ‘how much better’ the first class degree is.

CONTINUOUS DATA

Interval

-          The differences between the numbers are equal, and that indicates that there are equal differences in whatever is being measured.

-          Ratios between differences are meaningful

-          Ratios between values are not as zero point is arbitrary.

-          E.g., degrees centigrade. We know that the difference between 0 and 10 degrees is the same as the difference between 10 and 20 degrees. Lowest value can be less than 0 – range depends on measurement type and zero point can be arbitrary.

-          Kelvin scale would be ratio data as 0K is true zero point (0K = -273.15C)

-          Equal intervals between objects represent equal differences; the differences are meaningful.

CONTINUOUS DATA

Ratio

-          If something is measured at 100cm, it is ten time as long as something that is 10cm.

-          There is also a true zero point, where there is complete absence of whatever is being measured.

-          Measurements of length, time, height, and weight etc, are true ratio scales.

-          A ratio scales is one with a true zero point, where ratios between numbers are meaningful.

-          Counts of values with categories in a variable

-          Can be shown as table or in a bar chart

-          Example: test scores of a sample of 10 students

-          Absolute counts of values can be turned into probability by dividing total (n)

-          Percentage =probability * 100

Special bar chart for continuous variables to see the shape of data distribution

-          Number of peaks

-          Mode (most frequent measurement in a variable, next lecture)

-          Spread of the data (variance)

-          Symmetry:

-               Is the main peak roughly in the middle?

-               Do the positive and negative tails look similar?

-               Related to skew

-          Number of categories (bins) determines the number of bars in the histogram

-          Stats program sets defaults but you can override

-          More fine grain and thus usually more deviation from symmetry becomes apparent as we use more bins.

-          Where categories are continuous (e.g., increasing continuous values), bars should be joined

-          Bar height represents frequency or %

-          Bar width represents width of a category, so equal categories have equal widths.

-          Comparing two distributions with different numbers means you should use %, not n, to make scales directly comparable.

-          Use the correct type of graph for the type of data

-              E.g., bar charts for categorical data and histograms for continuous variables.

-          Label the graph clearly and include units of measurement – title, axes

-          Make the plot neat and clear – use same colours for same categories across graphs, include a key, don’t have too many categories.

-          Include sources for external data

-          Have a (numbered) caption that explains the graph concisely.