/* Simple program for Analysis of Variance (ANOVA) */

#include <stdio.h>
#include <stdlib.h>

#define MAX_ROWS 10
#define MAX_COLS 10

main()
  {
    float value;
    float observations[MAX_ROWS][MAX_COLS];
    float row_means[MAX_ROWS];
    float col_means[MAX_ROWS];
    float row_effects[MAX_ROWS];
    float col_effects[MAX_ROWS];
    float sum, grand_mean;
    float sst, ssa, ssb, sse;
    int i, j, rows, cols, numobservations;

    /* Find out size of input data */
    scanf("%d %d", &rows, &cols);
    if( rows > MAX_ROWS )
      {
	printf("Too many rows of data!!\n");
	exit(0);
      }
    if( cols > MAX_COLS )
      {
	printf("Too many columns of data!!\n");
	exit(0);
      }

    /* Read in data values and echo them to user */
    printf("Starting ANOVA of the following data...\n");
    sum = 0;
    numobservations = 0;
    for( i = 0; i < rows; i++ )
      {
	for( j = 0; j < cols; j++ )
	  {
	    scanf("%f", &value);
	    printf("%8.3f  ", value);
	    observations[i][j] = value;
	    sum += value;
	    numobservations++;
	  }
	printf("\n");
      }
    /* Compute the grand mean */
    grand_mean = sum / numobservations;
    printf(" Grand Mean:  %8.3f\n", grand_mean);

    /* Compute row means and row effects */
    for( i = 0; i < rows; i++ )
      {
	sum = 0;
	for( j = 0; j < cols; j++ )
	  {
	    sum += observations[i][j];
	  }
	row_means[i] = sum / cols;
	printf(" Row %d mean:  %8.3f\n", i, row_means[i]);
	row_effects[i] = row_means[i] - grand_mean;
	printf(" Row %d effect:  %8.3f\n", i, row_effects[i]);
      }

    /* Compute column means and column effects */
    for( j = 0; j < cols; j++ )
      {
	sum = 0;
	for( i = 0; i < rows; i++ )
	  {
	    sum += observations[i][j];
	  }
	col_means[j] = sum / rows;
	printf(" Column %d mean:  %8.3f\n", j, col_means[j]);
	col_effects[j] = col_means[j] - grand_mean;
	printf(" Column %d effect:  %8.3f\n", j, col_effects[j]);
      }

    /* Compute SST */
    sst = 0;
    for( i = 0; i < rows; i++ )
      {
	for( j = 0; j < cols; j++ )
	  {
	    sst += (grand_mean - observations[i][j]) * (grand_mean - observations[i][j]);
	  }
      }
    printf(" SST:  %8.3f\n", sst);

    /* Compute SSA for rows */
    ssa = 0.0;
    for( i = 0; i < rows; i++ )
      {
	ssa += row_effects[i] * row_effects[i];
      }
    ssa *= cols;
    printf(" SSA:  %8.3f\n", ssa);

    /* Compute SSB for columns */
    ssb = 0.0;
    for( j = 0; j < cols; j++ )
      {
	ssb += col_effects[j] * col_effects[j];
      }
    ssb *= rows;
    printf(" SSB:  %8.3f\n", ssb);

    /* Compute SSE */
    sse = sst - ssa - ssb;
    printf(" SSE:  %8.3f\n", sse);

    /* Compute SSA/SST and SSB/SST */
    printf("Factor A (rows) has SSA/SST = %8.3f%%\n", ssa * 100.0 / sst);
    printf("Factor B (columns) has SSB/SST = %8.3f%%\n", ssb * 100.0 / sst);
    printf("Error has SSE/SST = %8.3f%%\n", sse * 100.0 / sst);
  }