Side by Side
Simple random sampling draws units one at a time from a complete list so that every combination is possible. Systematic sampling picks a random start and then every kth unit down the list. Both give each listed unit the same chance of selection; systematic is quicker to carry out in the field, but it can fail silently if the list has a pattern. For the general idea of chance-based selection, see random sampling and the wider menu of sampling methods; if you also need groups, read cluster vs stratified sampling.
At a Glance
| Factor | Simple Random Sampling | Systematic Sampling |
|---|---|---|
| How units are chosen | Random numbers pick units independently | Random start, then every kth unit |
| Possible samples | Every combination of n units | Only k different samples |
| Chance of selection | n / N for every unit | n / N for every unit (with a random start) |
| Needs a frame | Yes, a complete numbered list | Yes, an ordered list, or a walking route in the field |
| Effort | Generate and check n random numbers | Generate one random number |
| Main risk | None from order; frame errors still apply | Periodic patterns in the list; hard to estimate variance exactly |
| Helpful side effect | None | If the list is sorted by a useful variable, it spreads the sample across it (implicit stratification) |
| Best for | Short lists, data already in a spreadsheet | Long paper lists, exit queues, shelves of files, household listing in the field |
Both methods rely on a good sampling frame. Neither fixes a list that misses people. For the wider family, see sampling methods and random sampling.
Worked Example
Worked Example: Selecting Every kth Household
A fictional community health program has a household list of N = 1,200 and needs n = 60 completed interviews.
Compute the interval: k = N / n = 1,200 / 60 = 20.
Pick the random start: choose a whole number between 1 and 20 using a random number generator or a random-digit table. Say it returns 7. Record the method and the seed or the table row.
Select: household numbers 7, 27, 47, 67, 87, and so on, adding 20 each time.
Check the end: the 60th household is 7 + 59 x 20 = 1,187, which is within the list, so you get exactly 60.
Every household has a 60 / 1,200 = 1 in 20 chance of selection, because each of the 20 possible starts is equally likely. Households 7 and 8 can never both be selected, which is the price of using only 20 possible samples.
Add an allowance for non-response after this step, not before: if you expect 85% to respond, you need 60 / 0.85 = 70.6, so 71 selected households, and the interval becomes 1,200 / 71 = 16.9. See the Cochran formula page for how the size n is found and rounded.
When N Divided by n Is Not a Whole Number
Suppose the list has N = 1,250 and you still want n = 60, so N / n = 20.83.
Option A: round the interval down to 20. Pick a start between 1 and 20. Starts 1 to 10 give 63 households (the last is the start + 62 x 20, at most 1,250); starts 11 to 20 give 62. The sample size varies by one or two. This is fine when you can accept "about 60".
Option B: keep the fractional interval 20.83. Choose a random decimal start between 0 and 20.83, say 7.4. Add 20.83 each time and round each result up to the next whole household number:
| Draw | Calculation | Household selected |
|---|---|---|
| 1 | 7.40 | 8 |
| 2 | 7.40 + 20.83 = 28.23 | 29 |
| 3 | 28.23 + 20.83 = 49.07 | 50 |
| 4 | 49.07 + 20.83 = 69.90 | 70 |
| 60 | 7.40 + 59 x 20.83 = 1,236.57 | 1,237 |
This gives exactly 60 selected units and still treats every household equally.
Pitfalls and Choice
When Systematic Sampling Goes Wrong
- Periodic lists: Suppose each listed village block has exactly 20 households, always numbered with the head's household first. An interval of 20 with a start of 1 selects only head households. Whenever the interval matches a repeating cycle in the list, the sample is biased. Look at how the list was built before choosing k.
- Ordered by the outcome: A list sorted by income or distance from the clinic spreads the sample across that order, which is often helpful. But a random start still matters, and you cannot treat the result as a simple random sample without noting the effect.
- Variance estimation: With one random start, there is no unbiased variance estimate from the sample alone. Analysts commonly treat the sample as simple random (usually conservative when list order is useful) or use a paired-selection or multiple-start approach. State which one you used.
- Field "every kth" without a frame: Counting every 5th house along a street can work as a listing step, but the starting point and direction must be random and recorded, or it becomes a convenience sample.
Which Should You Use?
| If this is true | Choose |
|---|---|
| The list is in a spreadsheet and has under a few thousand rows | Simple random sampling |
| You must run a sample from a long paper list or queue | Systematic, with a random start |
| You do not know how the list was ordered | Simple random sampling |
| The list is sorted by a variable you care about | Systematic, with the order documented |
| The design has clusters | Select clusters with a method suited to their sizes, then apply either method within clusters; see cluster sampling |
For a reproducible draw from a numbered list, use the sample selection feature of the .
Frequently Asked Questions
Is Systematic Sampling Probability Sampling?
Yes, when the start is random and the list is complete. Each unit has a known chance of selection. Without a random start, or with a list that omits units, it is not.
Can I Start at 1 Every Time?
No. Starting at the same position gives the first unit probability 1 and some units zero. Use a random start each time.
Does Systematic Sampling Need a Different Sample Size?
For most M&E surveys, size it as if it were simple random, then adjust for any clustering or weighting you add. The sample size method does not change; only the way you pick the units.