Anova with Random or Nested Factors

ANOVA models can contain fixed and/or random factors. For fixed (effect) factors, we are interested in studying the specific levels in that factor. For a random (effect) factor, data are collected for a random sample of possible levels, with the hope that these levels are representative of all levels in that factor. This approach can be appropriate where there are a large number of possible levels.

Models that contain both fixed and random factors are called mixed models. We will also consider nested models where one factor is lower in the hierarchy compared to another factor.

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6 thoughts on “Anova with Random or Nested Factors”

  1. Hello Charles,

    I need help with a complex (it seems to me..) design:

    1) Cell cultures were prepared from donors of two age group (Young/Aged).
    2) Each culture was exposed to 4 different treatments (each treatment in a different batch).
    3) A certain cellular response was measured in several X cells in each batch.

    My scientific question is: do age modifies the effects of the treatment in the cell response?

    I understand I got 2 fixed crossed factors (Age and Treatment) and a random factor (Culture) crossed for Treatment but nested for Age. And measurements are replicated for each Age/Treatment/Culture cell.

    Would be possible to analyze it with excel?

    Thanks in advance

    Reply

  2. Hello Charles,

    I need help with a complex design:
    1) Cell cultures were prepared from donors of two age group (Young/Aged).
    2) Each culture was exposed to 4 different treatments (each treatment in a different batch).
    3) A certain cellular response was measured in several X cells in each batch.

    My scientific question is: do age modifies the effects of the treatment in the cell response?

    I understand I got 2 fixed crossed factors (Age and Treatment) and a random factor (Culture) crossed for Treatment but nested for Age. And measurements are replicated for each Age/Treatment/Culture cell.

    What ANOVA design should I use ?

    Thanks

    PS: Charles, thanks for your excellent web.

    Reply

  3. Charles, your site is so helpful.

    Could you help me figure out the right model to apply?
    Agricultural experiment, studying whether any among 7 treatments (1 is a control) has significant effect.
    Design:
    A field of trees is selected, divided into replicas.
    In each replica, 6-tree groups (called Blocks) are designated where the 6-trees are of normal health and are next to each other.
    Treatments are randomly assigned to the Blocks, each Treatment applied to 1 Block in each Replica.
    Each tree is measured using several types of health measures.

    I thought the right model might be One-Way ANOVA with subsampling:
    SStotal = SStreatment + SSreplica + SSblock
    variation = devsq()
    SSblock = sum(across all Blocks) of variation(within Block)
    SSreplica = sum(across all Treatments) of variation(Block means) * trees-per-block
    SStreatment = sum(across all Treatments) of variation(Treatment means) * trees-per-block * replicas
    Ftreatment = MStreatment / MSreplica
    Freplica = MSreplica / MSblock

    But I’m left with a few questions:
    – is the Replica a Random or Fixed factor? Random because it’s not meant to represent any specific effect. Fixed because every replica is located in the same field (may not represent a random sample of a broad range of fields).
    – do I need to have an interaction term in my model? My thinking was that I don’t anticipate interaction effects and I can’t think of a reason to care about them.
    – what else would you point out or advise?

    Reply

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