int main(){
apop_db_open("data-census.db");
gsl_vector *n = apop_query_to_vector("select in_per_capita from income "
"where state= (select state from geography where name ='North Dakota')");
gsl_vector *s = apop_query_to_vector("select in_per_capita from income "
"where state= (select state from geography where name ='South Dakota')");
double n_count = n->size,
n_mean = apop_vector_mean(n),
n_var = apop_vector_var(n),
s_count = s->size,
s_mean = apop_vector_mean(s),
s_var = apop_vector_var(s);
double stat = fabs(n_mean - s_mean)/ sqrt(n_var/ (n_count-1) + s_var/(s_count-1));
double confidence = 1 - (2 * gsl_cdf_tdist_Q(stat, n_count + s_count -2));
printf("Reject the null with %g%% confidence\n", confidence*100);
}
//apop_vector_mean is a macro, so we can't point a pointer to it.
double mu(gsl_vector *in){ return apop_vector_mean(in);}
apop_data* multiple_imputation_variance_base(multiple_imputation_variance_t in){
/*The first half of this is filling in the values. In an attempt at versatility, I allow users to
give any named column, be it numeric or text, for every piece of input info. That means a whole lot
of checking around to determine what goes where---and a macro. */
Apop_assert_c(in.base_data,NULL, 1, "It doesn't make sense to impute over a NULL data set.");
Apop_assert_c(in.fill_ins, NULL, 1, "Didn't receive a fill-in table. Returning NULL.");
data_to_data stat = in.stat? in.stat : colmeans;
//At the end of this macro, you've got rowcol and rowtype, valuecol and valuetype, &c.
#define apop_setup_one_colthing(c) \
int c##col = apop_name_find(in.fill_ins->names, in.c##_name, 'c'); \
int c##type = 'd'; \
if (c##col==-2){ \
c##col = apop_name_find(in.fill_ins->names, in.c##_name, 't'); \
c##type = 't'; \
Apop_assert(c##col!=-2, "I couldn't find the c##_name %s in the column/text names of your fill_in table.", in.c##_name); \
}
apop_setup_one_colthing(row)
apop_setup_one_colthing(col)
apop_setup_one_colthing(value)
apop_setup_one_colthing(imputation)
Apop_assert(!(rowtype=='t' && !in.base_data->names->rowct),
"the rowname you gave refers to text, so I will be searching for a row name in the base data."
" But the base_data set has no row names.");
Apop_assert(!(coltype=='t' && !in.base_data->names->colct),
"the colname you gave refers to text, so I will be searching for a column name in the base data."
" But the base_data set has no column names.");
//get a list of unique imputation markers.
gsl_vector *imps = NULL;
apop_data *impt = NULL;
if (imputationtype == 'd'){
Apop_col_v(in.fill_ins, imputationcol, ic);
imps = apop_vector_unique_elements(ic);
} else impt = apop_text_unique_elements(in.fill_ins, imputationcol);
int len = imps ? imps->size : impt->textsize[0];
int thisimp=-2; char *thisimpt=NULL;
apop_data *estimates[len];
for (int impctr=0; impctr< len; impctr++){
if (imps) thisimp = gsl_vector_get(imps, impctr);
else thisimpt = impt->text[impctr][0];
Get_vmsizes(in.fill_ins); //masxize
int fillsize = maxsize ? maxsize : in.fill_ins->textsize[0];
for (int i=0; i< fillsize; i++){
if (!(thisimpt && apop_strcmp(in.fill_ins->text[i][imputationcol], thisimpt))
&& !(imps && thisimp==apop_data_get(in.fill_ins, i, imputationcol)))
continue;
int thisrow = (rowtype=='d') ?
apop_data_get(in.fill_ins, i, rowcol)
:apop_name_find(in.base_data->names, in.fill_ins->text[i][rowcol], 'r');
int thiscol = (coltype=='d') ?
apop_data_get(in.fill_ins, i, colcol)
:apop_name_find(in.base_data->names, in.fill_ins->text[i][colcol], 'c');
if (valuetype=='d') apop_data_set(in.base_data, thisrow, thiscol,
apop_data_get(in.fill_ins, i, valuecol));
else apop_text_add(in.base_data, rowcol, colcol, in.fill_ins->text[i][valuecol]);
}
//OK, base_data is now filled in. Estimate the statistic for it.
estimates[impctr] = stat(in.base_data);
}
//Part II: find the mean of the statistics and the total variance of the cov matrix.
gsl_vector *vals = gsl_vector_alloc(len);
apop_data *out = apop_data_copy(estimates[0]);
//take the simple mean of the main data set.
{ //this limits the scope of the Get_vmsizes macro.
Get_vmsizes(estimates[0]);
for (int j=0; j < msize2; j++)
for (int i=0; i < (vsize ? vsize : msize1); i++){
for (int k=0; k< len; k++)
gsl_vector_set(vals, k, apop_data_get(estimates[k], i, j));
apop_data_set(out, i, j, apop_vector_mean(vals));
}
}
apop_data *out_var = apop_data_get_page(estimates[0], "<Covariance>");
int cov_is_labelled = out_var !=NULL;
if (!cov_is_labelled){
asprintf(&out->more->names->title, "<Covariance>");
out_var = estimates[0]->more;
}
Get_vmsizes(out_var);
for (int i=0; i < msize1; i++)
for (int j=i; j < msize2; j++){
for (int k=0; k< len; k++){
apop_data *this_p = cov_is_labelled ? apop_data_get_page(estimates[k], "<Covariance>")
: estimates[k]->more;
gsl_vector_set(vals, k, apop_data_get(this_p, i, j));
}
double total_var = apop_vector_mean(vals) + apop_var(vals)/(1+1./len);
apop_data_set(out_var, i, j, total_var);
if (j != i)
apop_data_set(out_var, j, i, total_var);
}
return out;
}