D.0 – arithmetic and numerical computation — OCR A-Level Psychology
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D.0 – arithmetic and numerical computation explained
D.0 – arithmetic and numerical computation covers 3 specification points, including Converting data in standard form from a… and Calculating the percentages of cases that fall….
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Open a point below for its explanation and revision guidance.
Recognise and use expressions in decimal and standard form (to include: converting data in standard form from a results table into decimal form in order to construct a pie chart)
Standard form writes a value as a number between one and ten multiplied by a power of ten, which is how journals print very small probabilities without a queue of zeros. Converting back to decimal is a shift of the decimal point: a positive power shifts it right and makes the value larger, a negative power shifts it left and makes it smaller, and the size of the power is the number of places moved. Psychology needs this whenever a printed results table reports frequencies or proportions in powered notation and ordinary numbers are wanted before a chart can be drawn. The sector angle for each slice is that category's share of the grand total multiplied by three hundred and sixty degrees, so every category has to be converted first and the finished angles should sum to a full turn.
Use ratios, fractions and percentages (to include: calculating the percentages of cases that fall into different categories in an observation study)
An observation produces tallies, which can be expressed as fractions, ratios, or percentages of the total coded behaviours. To calculate a percentage, divide the count for one category by the total and multiply by 100. For example, if 18 out of 60 cases fall into a category, the fraction is 18/60 (simplifying to 3/10), the ratio of that category to others is 18:42 (or 3:7), and the percentage is 30%. The same arithmetic converts inter-observer agreement into a percentage, and converts a before-and-after difference into percentage change, where the divisor is always the original value. Piliavin et al. report subway data in this form, with the cane victim helped on 62 of 65 trials (95%) and the drunk victim on 19 of 38 (50%). Fractions, ratios, and percentages express the same relationship, allowing comparison of unequal groups.
Estimate results (to include: commenting on the spread of scores for a set of data, which would require estimating the range)
Estimating is the habit of knowing roughly what a figure should be before and after you compute it, and the worked case here is spread. The range is the largest score minus the smallest, a single number rather than a pair, and it can be read off a table in seconds, which is what makes it a quick check on a standard deviation or on a graph that looks wrong. Rounding each score to the nearest ten and taking the difference gives an estimate that should land close to the exact value, and when it does not the arithmetic is at fault. Interpretation is where the marks sit: a spread that is wide next to the mean warns that the mean represents nobody in particular and hints at an anomalous score, while a narrow one shows participants behaved alike and makes a small difference between conditions more convincing.
Your focus
- Explain the purpose of using standard form in psychological research to represent very small probability values.
- Calculate decimal values from data presented in standard form within a results table.
- Apply converted decimal frequencies to calculate sector angles and construct an accurate pie chart.
Show all 9 objectives
- Calculate the percentages of cases that fall into different categories in an observation study.
- Convert raw data into fractions and simplify them.
- Express relationships between behavioural categories using part-to-part ratios.
- Calculate an estimated range for a set of data by rounding extreme scores before subtracting the lowest from the highest value.
- Evaluate the use of the range as a measure of dispersion compared to the standard deviation.
- Analyse the spread of scores in a dataset to interpret the consistency of participant behaviour and the representativeness of the mean.
D.0 – arithmetic and numerical computation exam tips
Marking Points
- Credit is for the working as much as the value, so name the power, say which way the point moves, and give the decimal, writing 3.5 multiplied by ten to the power of minus three as 0.0035.
- A pie chart mark needs the angle calculation set out, which is the frequency for the category divided by the total and then multiplied by three hundred and sixty, with a check that the angles sum to a full circle.
- Markers reward the conversion being applied to every row of the table before anything is drawn, and the converted figures being quoted to a stated and sensible precision.
- Explaining why standard form is used at all, that it keeps very small probability values readable and comparable at a glance, earns the explanation mark.
- The percentage mark depends on the right denominator, which is the total number of observations or trials in that condition, not the number of participants and not the total across both conditions.
- Percentage change is credited when the difference is divided by the original value and then multiplied by 100, with the direction of travel, increase or decrease, stated.
- Showing the fraction before converting it, for example 18 out of 60 becoming 30 percent, protects the method mark even when the arithmetic slips.
- Ratios must be expressed correctly, comparing part to part (e.g., 18 occurrences to 42 non-occurrences is 18:42, simplifying to 3:7) rather than part to whole, unless specified.
- Saying why percentages or ratios were needed, namely that they allow two groups of unequal size to be compared when the raw counts would mislead, earns the explanation mark.
- The range is credited as one value with its units, found as highest minus lowest, and quoted alongside the mean rather than in place of it.
- An estimate earns credit when it is justified, for example by rounding the extreme scores to the nearest ten before subtracting, and then checked against the exact figure.
- Comment marks are for interpretation, so say that a wide spread means the scores varied greatly and the mean may not represent the group, and that a narrow spread means a consistent set of results.
- The standard evaluative point is rewarded: the range uses only two scores and is distorted by a single extreme value, whereas the standard deviation uses every score.
Examiner Tips
- 💡This is normally a low tariff calculation inside a longer research methods question, so write the converted values into a labelled table first, because the later marks depend on those figures being right.
- 💡If the question states an accuracy, follow it exactly, since an unrounded string of decimals can lose the accuracy mark even when the conversion itself is correct.
- 💡You may be asked to justify a pie chart over a bar chart, so have the reason ready: a pie chart shows each category as a share of one whole set of observations.
- 💡Observation questions often print a completed tally chart and ask for one category as a percentage, so find and write down the total row before you divide anything.
- 💡If asked to explain why percentages were reported, tie the answer to comparing conditions of different size rather than saying that percentages are easier to read.
- 💡Write the calculation on the answer line even when only a final figure is requested, because visible working can still be credited when a value is copied across wrongly.
- 💡Estimation items usually appear as a short comment on a printed table, so scan the top and bottom of the column first and state the spread before discussing anything else.
- 💡When asked to comment on the spread, do not stop at the number; say what it implies for how well the mean represents the sample.
- 💡If invited to suggest a better measure of dispersion, name the standard deviation and give the reason, because the name alone rarely earns the second mark.
Common Mistakes
- Shifting the point the wrong way, so a negative power produces a value larger than one. A negative index always makes the number smaller than the digits alone suggest.
- Counting digits rather than places, which turns 2.5 multiplied by ten to the power of minus two into 0.0025 when it is 0.025.
- Using the percentage as the angle, so a category holding a quarter of the observations is drawn as a sector of twenty five degrees instead of ninety.
- Adding percentages that were calculated on different totals and treating the sum as meaningful, which happens whenever the conditions ran for different numbers of trials.
- Confusing a percentage point difference with a percentage change, so a rise from 20 percent to 30 percent is called a rise of 10 percent when it is ten percentage points and a rise of 50 percent.
- Expressing a ratio as a fraction of the total (e.g., writing 18:60 instead of 18:42 for a part-to-part ratio) or failing to simplify fractions and ratios to their lowest terms.
- Writing the range as an interval, for example from 12 to 30, when the range is one number, here 18.
- Forgetting that the two extreme scores alone set the range, so one participant scoring near zero can make two very different data sets look equally variable.
- Presenting an eyeballed estimate as the calculated answer with no working, which loses the method mark even when the number happens to be close.